Master in Aerospace Engineering

Esther Mas Sanz

Origin and mineralogy of Lunar meteorites. A study for lunar mining and resources exploitation

Master’s Final Degree Project - Report

Director: Dr. Josep M. Trigo-Rodríguez (CSIC-IEEC)

Tutor: Dr. Miquel Sureda Anfres (UPC)

Course: 2019-2020, Spring Semester

Delivery date: 22nd June, 2020 [This page intentionally left blank] Acknowledgements

I want to express my gratitude to the director of my Master Thesis, Dr. Josep M. Trigo- Rodríguez, for his support throughout the project and particularly, during the difficult situation we all have lived under the pandemic of covid-19. Despite the limitations this project has been possible, perhaps not as complete as firstly imagined but still, robust and rewarding. Likewise, I thank Dr.Miquel Sureda for promptly solving all of my doubts and the ESEIAAT administration for rapidly adapting the course to the new circumstances. I also appreciate the effort of my family and beloved ones, for making these hard times easier to bear and for their unconditional support. Finally, my most sincere gratitude for all of those who, during the coronavirus crisis, have taken care of the most vulnerable and those who have ensured that the gears of society kept working. Thank you all. Abstract

In recent years the Moon has become once again the target for many of the most ambitious space projects. Our satellite is expected to provide a permanent base by 2030s and open new possibilities for deep-space exploration and the conquest of Mars. During this decade it is paramount to expand our knowledge on lunar surface mineralogy, chemistry and geology; to prospect it and lay the foundations for the future exploitation of its resources. Lunar achondrites provide interesting information about the main rock-forming minerals of the Moon. These rocks were excavated and delivered to Earth by continuous collisions going on the surface of our satellite. Unfortunately we do not know the exact region of origin of these rocks, so the information provided is only partial. This Master Thesis will study the physico-chemical properties of Lunar meteorites, and will also study the main dynamic pathways followed by Lunar meteorites reaching planet Earth. I declare that, the work in this Master Thesis is completely my own work,

no part of this Master Thesis is taken from other people’s work without giving them credit,

all references have been clearly cited,

I understand that an infringement of this declaration leaves me subject to the foreseen disciplinary actions by Universitat Politècnica de Catalunya - BarcelonaTECH.

Student Name: Signature: Date:

Esther Mas Sanz 22nd June, 2020

Title of the Thesis: Origin and mineralogy of Lunar meteorites. A study for lunar mining and resources exploitation. Lunar Meteorites: Origin and Mineralogy CONTENTS

Contents

List of Figures iii

List of Tablesv

1 Introduction4 1.1 The Moon, our closest neighbour ...... 4 1.1.1 A New Race to the Moon: Lunar Mining ...... 6 1.2 Meteoritics ...... 8 1.2.1 Meteorite classification ...... 9 1.2.2 Differentiated Meteorites: Achondrites ...... 10 1.3 Lunar Meteorites ...... 11 1.3.1 Lunaites Classification ...... 12 1.3.2 Recovery Locations ...... 14 1.4 Lunar Geochemistry ...... 15 1.4.1 Inorganic constituents in Lunar Soil ...... 17 1.5 Lunar Ejecta ...... 20 1.5.1 CREAs ...... 20

I Mineralogy Study 23

2 Chemical and mineralogical characterization of lunar achondrites 23 2.1 SEM+EDX ...... 23 2.1.1 Solver for Mineral Proportions ...... 24

3 Lunar Meteorite Samples 27 3.1 JaH 838 ...... 27 3.1.1 SEM/EDX Microscopy Results ...... 29

i Lunar Meteorites: Origin and Mineralogy CONTENTS

3.2 Dho 1084 ...... 33 3.2.1 SEM/EDX Microscopy Results ...... 34 3.3 NWA 11444 ...... 37 3.3.1 SEM/EDX Microscopy Results ...... 38 3.4 Results Summary ...... 45 3.5 Conclusions ...... 47

II Orbital Dynamics Study 49

4 Introduction 49

4.1 Software and Databases ...... 49 4.2 Previous Works ...... 50

5 Simulations of Lunar Ejecta 51

5.1 Short transfers ...... 54 5.1.1 Variation of launch direction ...... 54 5.1.2 Variation of Ejection Angle ...... 66 5.1.3 Variation of Earth-Moon-Sun configuration ...... 71 5.1.4 Summary of results ...... 76 5.2 Long transfers ...... 77 5.2.1 Case study: Meteorite Impact on the Moon ...... 84 5.2.2 Summary of results ...... 92

6 Conclusions 93

7 Future Work 96

8 Planning 97

Bibliography 98

ii Lunar Meteorites: Origin and Mineralogy LIST OF FIGURES

List of Figures

1.1 Representations of the Moon in prehistory and ancient cultures ...... 4 1.2 Apollo 17 astronaut collecting samples ...... 5 1.3 Water content on the Moon ...... 7 1.4 Classification diagram of meteorites [72] ...... 10 1.5 Lunar meteorites recovery sites statistical analysis. Database for analysis can be found in [36] ...... 14 1.6 Images of the Moon surface ...... 15 1.7 Examples of geochemical bimodality of pristine non-mare rocks...... 17 1.8 Images of metals on the Moon surface ...... 18 1.9 Images of thorium (correlated to KREEP) on the Moon surface ...... 18 1.10 Cumulative percentage impacted with Earth ...... 22

2.1 Energy dispersive X-ray spectrum ...... 24 2.2 Ternary diagram of of the composition of feldspar minerals...... 25

3.1 Location of the JaH 838 meteorite ...... 27 3.2 Mosaic of JaH 838 ...... 29 3.3 Meteorite JaH 838 ROIs ...... 30 3.4 Spectrum 6 JaH 838 ...... 30 3.5 SEM/EDX mapping of JaH 838 ...... 32 3.6 Location of the Dho 1084 meteorite ...... 33 3.7 Mosaic of DHO 1084 ...... 34 3.8 Meteorite DHO 1084 ROI ...... 35 3.9 Spectrum 3 of the mapping of DHO 1084 ...... 36 3.10 Mosaic of NWA 11444 ...... 38 3.11 ROIs of NWA 11444 ...... 39 3.12 Spectrum 3 of the mapping of NWA 11444 (ROI 1) ...... 40

iii Lunar Meteorites: Origin and Mineralogy LIST OF FIGURES

3.13 Spectrum 1 of the mapping of NWA 11444, ROI 2 ...... 41 3.14 Spectrum 1 of the mapping of NWA 11444 (ROI 3) ...... 43 3.15 SEM/EDX mapping of NWA 11444 ...... 44

5.1 Moon Launching Sites ...... 51 5.2 Launching sites and velocities for different directions of launch and ejection angles ...... 52 5.3 Moon coordinates ...... 53 5.4 Velocity vectors in mooncentric and geocentric orbits ...... 53 5.5 Variation of Earth impacts with launch velocity ...... 58 5.6 Trajectories of two particles in geocentric orbits ...... 59 5.7 Evolution of the meteoroid impact population ...... 60 5.8 Evolution of the meteoroid impact population (logarithmic scale) . . . . . 61 5.9 Launch angle of particles according to their launch site...... 62 5.10 Correlation between launch site and Earth collisions with varying launch direction ...... 63 5.11 Correlation between launch site and Earth collisions with varying launch direction at different times...... 64 5.12 Histogram of Earth Impacts as function of ejection angle and ejection velocity 67 5.13 Flat view of the four histograms for Earth Impacts as function of ejection angle and ejection velocity ...... 67 5.14 Comparison between ejection angles ...... 69 5.15 Launch angle of particles according to their launch site ...... 70 5.16 Different Earth-Moon-Sun configurations for lunar ejecta launches . . . . . 72 5.17 Earth impacts for different velocities and initial dates ...... 73 5.18 Minimum time for a lunar ejecta to impact with Earth (histogram) . . . . 75 5.19 Minimum time for a lunar ejecta to impact with Earth ...... 75 5.20 Evolution of launch angles for long time scales...... 78 5.21 Initial orbital elements...... 79 5.22 Final orbital elements...... 79 5.23 Semi-major axis vs. eccentricity evolution in time ...... 80 5.24 Lunar ejecta survivor population after 105 years...... 81

iv Lunar Meteorites: Origin and Mineralogy LIST OF TABLES

5.25 Accumulated impacts % ...... 83 5.27 Detailed map of the Moon surface...... 85 5.28 Impact point and directions of launch for the lunar ejecta...... 86 5.29 Distribution of lunar ejecta after 104 years...... 86 5.30 Orbital elements at collision instant...... 87 5.31 Orbital elements at collision instant...... 88 5.32 Orbital elements evolution of M184...... 89 5.33 Time evolution of the orbital elements for different ejected particles. . . . . 90 5.34 Histogram of Earth collisions...... 91

8.1 Gantt Diagram...... 97 List of Tables

1.1 Denomination of object and phenomena according to diameter range. See [71], [70], [72]...... 9 1.2 Main mineral components found in meteorites [73]. For a detailed list, see Rubin (2005) [58]. Note: The X and the Y in the pyroxene formula refer to two generic cations species that occupy such positions in the pyroxene structure...... 10 1.3 Classifications of a lunar rock ...... 12 1.4 Some dominant minerals on Earth and Moon’s crust ...... 19 1.5 CREAs for lunar meteorites ...... 22

2.1 Table of minerals and correspondent chemical formulation used in MINSQ solver ...... 26

3.1 Chemical Components in wt% for sample spectra and averaged spectrum . 45 3.2 Primary and secondary minerals for sample spectra and averaged spectrum 46

5.1 Geocentric Initial Conditions ...... 54 5.2 Comparison of the simulation settings ...... 55 5.3 Geocentric-stage simulations in Gladman study ...... 56

v Lunar Meteorites: Origin and Mineralogy LIST OF TABLES

5.4 Geocentric-stage simulations...... 57 5.5 Comparison of geocentric-stage simulations ...... 58 5.6 Fate of the lunar ejecta for varying ejection angle and launch speed 2.4 km/s 66 5.7 Comparison between ejection angles...... 70 5.8 Earth impacts for two velocities and different initial dates...... 74 5.9 Initial parameters for second model bodies...... 77 5.10 Fate of the particle with direction of the launch...... 82 5.11 Fate of particles for different launch velocities...... 82 5.12 Properties of target and impactor...... 84 5.13 Coefficient values ...... 88 5.14 Percentage of ejecta in heliocentric orbit and collided with Earth ...... 91

vi Lunar Meteorites: Origin and Mineralogy LIST OF TABLES

Aim

The main objectives of this thesis are:

I The chemical-mineral characterisation of three different lunar meteorite samples and their classification according to the division of the materials forming the lunar surface.

II Studying the orbital dynamics of lunar ejecta, particularly, transfers from the Moon that end up impacting on Earth.

Scope

The scope of this project is divided according the project two sections:

• Mineralogy part

– Inside of the Scope: Analysis of the meteorite data. Interpretation and pro- cessing of the results SEM/EDX results. Identification of primary and secondary (if possible) minerals on the meteorite sample. Classification of meteorite samples into the two possible lunar regions according to the mineralogy obtained. – Out of the Scope: Development of code for calculating mineral proportions (externally obtained).

• Orbit Dynamics part

– Inside of the Scope: Analysis, interpretation and post-processing of orbital dynamics data. This includes creating algorithms to perform the aforementioned tasks, from extracting raw data to the elaboration of graphics, tables and dia- grams. – Out of the Scope: Integration algorithm or similar to calculate the position, velocity and orbital elements of celestial bodies (externally obtained).

1 Lunar Meteorites: Origin and Mineralogy LIST OF TABLES

Requirements

The requirements of this project are:

• Identify the primary minerals on the lunar meteorite samples.

• Provide a suitable classification according to the binary (maria or highland) division of the Moon surface.

• Study the orbits of lunar ejecta, particularly, those that impact Earth.

• Establish comparisons between orbits associated with short transfers and those pro- ducing long transfers of lunar meteorites to Earth.

• Recommend identification method between meteorite and origin location on the Moon surface based on the mineralogy and orbit dynamics study.

Justification

During the 2000s the Moon has gained relevance once more, resulting to be key to further developments on space science and technology. On the decade of 2020s and onward, many promising projects are proposed (and some on-going) by the most powerful nations on Earth (US, China and Russia): placing astronauts back on the lunar surface, plans for a permanent lunar base and exploitation of lunar resources. The latter, when profitable, will be paramount to achieve long-term goals on the Moon and in the conquest of Space. Only our satellite and barely a few near Earth asteroids (NEAs) could provide virtually infinite resources, from water and carbon to metals, rare- Earth minerals or radioactive minerals. Their exploitation is going to change radically the world as we know it today and will boost the Space Age. Back to the Moon, our satellite will become the testing ground for future endeavours but before landing on its surface again, it is necessary to meticulously survey it. Lunar meteorites constitute direct, varied samples of the lunar soil, allowing to study its major chemical components, mineralogy and even geological history. The study of these meteorites not only sheds light on the composition of the Moon but also on its formation and the origin of the Solar System itself. Despite being clear how they originate (lunar fragments reach our planet after being ejected by the impact of an asteroid or a comet

2 Lunar Meteorites: Origin and Mineralogy LIST OF TABLES on the lunar surface), no lunar meteorite has ever been associated with a crater, not even has been witnessed to fall on Earth. For this reason, analysing the orbit dynamics of the lunar meteorites becomes paramount to comprehend the material transfer from the Moon to the Earth.

3 Lunar Meteorites: Origin and Mineralogy

1. Introduction

This work consists of the identification of three lunar meteorite samples and the dy- namical study of lunar ejecta orbits. How does the study of lunar meteorites advance our current knowledge of the Moon? The following sections will give an overview of our unique satellite, its properties and will introduce the reader to the science of meteoritics.

1.1 The Moon, our closest neighbour

The Moon, Earth’s only natural satellite and the second brightest visible astronomical object from our planet, just after the Sun. Since prehistory, mankind was aware of phases and regular patterns of the Moon and used them as a tool to measure time and to describe seasonal changes. The first Lunar Calendar consisted of a series of marks carved into animal bones that recorded lunar cycles, and it dates back to 32,000 BC belonging to the Aurignacian (Upper Paleolithic) Culture [65]. The relatively easy observation of our satellite and the evident effects on our planet, from tide cycles to circadian rhythms on many species (including humans), have made of the Moon an icon not only for astronomy but for mythology, religion, philosophy and art. Lunar deities and the worshipping of the Moon can be found across the world in

(a) Representation of Nepali Moon God, (b) Prehistoric lunar calendar Chandra, in a mandala

Figure 1.1: Representations of the Moon in prehistory and ancient cultures. Images a) and b) extracted from [41] and [65], respectively

completely different cultures [50]: Tot (Ibis god of the moon and wisdom Ancient Egypt),

4 Lunar Meteorites: Origin and Mineralogy 1.1. THE MOON, OUR CLOSEST NEIGHBOUR

Nannan (god of the Moon, Ancient Babylonia), Chandra (lunar deity, Nepal), Xochipili (lunar god, Mesoamerica, Aztec Empire)... However, on 1609 the use of a newly optical instrument developed in Holland just the previous year revolutionised astronomy and subsequently, changed forever our understand- ing of the Moon. Galileo Galilei (and in parallel, Thomas Harriot [50]) observed the Moon for the first time through a telescope and made accurate drawings of its surface, providing evidence for its rocky nature (against the popular belief that it was made out of glass). The use of the telescope initiated a new era of visual exploration of the Moon and many scientists dedicated their lives to the cartographic study of the satellite. It was not until three centuries and a half after this remarkable event that eventually a photography surpassed artistic representations of the Moon. On January of 1959 the Soviet probe Luna 1 managed to do the first fly-by around the Moon and send the images back to Earth. The Moon became the battleground between the Soviet Union and the US during the Cold War in a race to display technological and military superiority. During the decades of the 60s, different robotic missions were sent to pave the path before human exploration, on the American side ([29],[37]): the impact probes Rangers (1961-1965), the Lunar Orbiters (1966-1967) which mapped the surface and enabled to choose a landing site as well as collected micrometeoroid and radiation intensity data, and the soft Surveyors landers that aimed to provide close photographs of the lunar terrain (1966-1968). Culmi- nating with the landing of Apollo 11 putting the first man on the Moon on 20th July of 1969. Up to this date, only a total of 12 astronauts have walked on the Moon, the last crewed mission be- ing the Apollo 17 on December of 1972. The Apollo missions1 have been of special interest as crews used a Lunar Roving Vehicle to travel the surface and investigate in-situ the mechanical properties of the terrain, meteoroid flux, the Figure 1.2: Harrison Schmidt, astronaut of Apollo 17, collecting solar radiation, etc. and brought lunar soil samples. Image extracted from [51] back to Earth a total of amount of 382 kg of rocks and soil from the Moon [29]. The end of the Cold War in addition to a more desensitised public opinion set a new, much more slow pace to the space race that

1Initially, NASA was reluctant to develop Extravehicular activity (EVA) on the lunar surface, exemplified by the constrains imposed to Apollo 11 astronauts. Later, the risk was better quantified and further missions increased gradually the distance of exploration from the lunar module and EVA times. As a consequence, the number of rock samples collected and the overall scientific activities also increased. See [14] for a comparison of EVA times for different missions.

5 Lunar Meteorites: Origin and Mineralogy 1.1. THE MOON, OUR CLOSEST NEIGHBOUR lasted until the late 1990s. The beginning of the 21st century Lunar exploration witnessed a reviving interest and resumed robotic missions with Clementine and Lunar Prospector. Their results suggested that water ice could be trapped in the permanent shadowed regions of the lunar poles, laying the foundations for further observational missions such as the LRO (Lunar Recon- naissance Orbiter) in 2009 [29] and triggering international interest. The space race is no longer a matter of one country but of the international community [37], and countries such as Japan (Kaguya lunar orbiter, 2007), India (Chandrayaan 1 ans 2 lunar orbiters, 2008-2019 respectively) and China’s Chang’e missions have notably contributed to the latest lunar exploration efforts. Furthermore, the space industry does no longer belong uniquely to national space agencies, it shares a common goal with private companies such as SpaceX, Moon Express, Virgin Galactic, Ad Astra Rocket Company (...). It seems that once again a space race has only but started. China recently updated their space program long-term goals to wealth creation for the Chinese nation and alongside Russia is aiming to establish a Lunar Base while the US president (D.J.Trump) referred to NASA’s crewed lunar exploration, the Artemis Program, with the aim to put astronauts back on the surface by 2024. So, once more the Moon is in the spotlight, but... why so?

1.1.1 A New Race to the Moon: Lunar Mining

The Moon is not only a goal in itself but a necessary step for the conquest of space. Its proximity to Earth and its low gravity are ideal to use it as a space camp to test new technology and as launch platform for longer missions. This fact combined with the continuous depletion of Earth resources put special importance on the exploration of extraterrestrial natural resources potential and the feasibility of its exploitation. After many robotic and manned missions, the utilisation of lunar resources has been studied for a long time. In-Situ Resources Utilisation (ISRU) refers to the generation of materials (for construction, life support, as propellants) from the available resources on a celestial body that otherwise, would have needed to be brought from Earth. The development of ISRU technology constitutes a NASA’s core project being managed at Kennedy Space Center, focusing on the extraction and handling of resources and energy in space [56]. According to the current knowledge of the chemical and mineralogical lunar resources which can be realistically used for ISRU, the following resources are considered [3], [56]: • Metals in the lunar regolith, which is rich in a wide amount of minerals such as py- roxene, olivine, ilmenite and has native metals such as Fe and Ni. In addition, the presence of hydrated minerals in the regolith such as H2O, and OH and of rare-Earth

6 Lunar Meteorites: Origin and Mineralogy 1.1. THE MOON, OUR CLOSEST NEIGHBOUR

elements, nowadays widely used for electronic applications. The fact that most met- als are found in the form of oxides (as well as some pure iron particles) makes their extraction costly energy-wise as these components tend to be very chemically stable [56], but their potential use for producing spacecraft parts and repairs in-situ make them more attractive given the mass constraints for space cargo. On the other hand, the extraction of oxygen is specially interesting from a biological point of view: future missions may utilise it to sustain plant growth and for the production of water and other life support processes requiring of oxygen.

• Water ice, probably to be found inside craters of the polar regions which are perma- nently shadowed, could be used as rocket fuel and to support life in a Moon base. On the other hand, some regions of the Moon have been hit by carbonaceous chondritic asteroids, rich in clay minerals. These minerals are composed of sheets of FeO/OH, MgO/OH or AlO/OH connected to SiO4 and in-between this metal bearing sheets it is found H2O absorbed by the sheet or bound to it. If heated at temperatures ∼100-150ºC absorbed water can be released and bound water collected if heated at ∼300ºC[74].

Figure 1.3: Water content on the Moon. The global quantities of water have been determined by a thermal correction model and derived from the Moon Mineralogy Mapper near-infrared reflectance data. The yellow dots mark the Apollo missions landing sites. Extracted from [35].

• Carbon and other organic compounds with significant amounts of C are common in regolith-rich regions of the Moon. Many projectiles that impact with the Moon are CM chondrites (rich in C) that due to the heat of the impact the meteorites de-hydrate and end up as graphitized clasts [58], [76]. Furthermore, it has been theorised of an uncertain amount of hydrocarbons such as ethylene, methane and methanol which

7 Lunar Meteorites: Origin and Mineralogy 1.2. METEORITICS

are the primary molecules for the production of much complex chemical structures such as polymers, resins and plastics [56].

• Solar wind volatiles, such as H, N, C and in particular He-3 isotope, rare to find on Earth and key for future developments in nuclear fusion. Many initiatives on how to tackle the Moon resources challenge are taking place: from 3-D printers that previously construct the necessary infrastructure for lunar mining, to the construction lunar bases to ensure long-term human presence, the utilisation of autonomous robots requiring minimal human intervention and obviously, the mingle of different proposals according to the exploitation stage. One thing is clear, the conquest of the Moon has just begun. Now, our priority is to prospect the Moon: determine the materials that exist, where they can be found and if they are accessible. For this reason, this Master Thesis deals with lunar meteorites, the only objects alongside Apollo collected samples, that the scientific community has available to first-hand analyse the Moon. The following sections will give an overview on meteorites, lunar ejecta and its importance to the determination of lunar soil characteristics and the advance in lunar exploration.

1.2 Meteoritics

In our Solar System we find a large variety of objects, but most of them are classified as minor bodies. Those include comets, asteroids, interplanetary dust, Kuiper Belt and Oort Cloud objects [61]. Some of these objects have an invaluable scientific importance from a cosmological perspective as they have preserved an unaltered composition since the primordial solar nebula or are fragments that once belonged to an ancient planetary body. In other words, they can provide key information about the physico-chemical processes in the formation of our Solar System [70]. Every time an extraterrestrial body reaches our planet, we are receiving a tiny piece of information to better comprehend our neighbouring universe and then, is when meteor science comes into play. Meteoritics deals with meteoroids, meteors and meteorites and also with interplanetary dust and meteoric smoke [47]. According to the International Astronomical Union (IAU) these different terms have the following definitions: • Meteor: light produced by the heating, ablation and ionisation of the atmospheric particles when an extraterrestrial body enters the Earth (or any other planet or satel- lite with a sufficiently dense atmosphere). Commonly known as shooting star.

• Meteoroid: solid objects of few millimetres to a maximum diameter of 1 meter, that

8 Lunar Meteorites: Origin and Mineralogy 1.2. METEORITICS

travel interstellar space. If their radius is less than 10 µm they are classified as inter- planetary dust while if they radius exceeds 10 meters they are considered asteroids (metallic and rocky objects) or comets (mainly ice, rock and dust).

• Meteorite: naturally surviving solid object after a meteor entry. Meter-sized ones might produce scars on the surface of impact, known as craters.

Body in Space Diameter Ranges Phenomena Observable evidence Interplanetary Dust D < 10µm Radar detectable Micrometeorites, IDPs Meteoroids 10µm < D < 1m Meteors, bolides Meteorites (highly unusual to leave a crater) Asteoroids/comets D > 10m Airblasts Impact craters

Table 1.1: Denomination of object and phenomena according to diameter range. See [71], [70], [72].

1.2.1 Meteorite classification

Meteorites are classified according to the degree of processing from their original prede- cessor (see [70] for a more detailed explanation of each classification). Non differentiated meteorites are those that have not suffered from chemical differentiation as they come from bodies of few hundreds of kilometers of diameter that never were melted because the internal energy escaped efficiently to space. These bodies are representative of the first planetesimals, but exhibit much lower porosities as consequence of impacts over the eons [7], [6]. Usually, they are also known by chondrites owing to their inner structure: a set of vitreous spherules of igneous nature referred as chondrules. Their origin is linked to early formation of our Solar System, being the by-product of the protoplanetary disk, much earlier than the appearance of planets themselves. In contrast, those meteorites that come from differentiated planetary bodies have lost the primordial mineral characteristics and present those of the parent body. Their components are the result of numerous metamorphic processes that take place inside planetary bodies of thousands of kilometers in diameter. This differentiated meteorites can be sub-classified into achondrites (or stony meteorites), stony-iron and iron. The main sources for achon- drites are the Moon, Mars and Vesta even though other samples have an unknown origin, probably of more distant objects. In the case of iron and stony-iron meteorites their source origin is the inner mantle of planetary bodies after experiencing a huge impact.

9 Lunar Meteorites: Origin and Mineralogy 1.2. METEORITICS

Figure 1.4: Classification diagram of meteorites [72]

1.2.2 Differentiated Meteorites: Achondrites

The achondrites come from the surfaces of diverse planetary bodies after an asteroid or comet impacts on the surface, excavates a crater and releases rocks with the required energy to overcome the gravitational field, bringing the rocks into heliocentric orbit (where they will be called "meteoroids") [73], [71]. Generally, these objects that reach Earth are the result of collisions between planetary bodies that took place during the last 100 million years ([13], [73], [71]). To comprehend the nature of achondrites, it is important to under- stand the processes ongoing in their parent planetary bodies. Those bodies experiment a segregation of components by chemical affinities (see [73] for a detailed explanation of the differentiation process) and due to the body’s gravity field, heavier components fall to the core while lighter ones remain nearer the surface. Afterwards, melted materials recrystallised to form new minerals that could retain essential features of the primordial components but that completely destroyed the chondrules. Meteorites that come from the inner mantle or the nuclei of the planetary body are stony- iron and iron meteorites, respectively. Those that originated from the surface of the planetary body are the achondrites [73].

Mineral Chemical Composition Pyroxenes XY(Si,Al)2O6 Olivine (Mg,Fe)2SiO4 Plagioclase NaAlSi3 - CaAl2Si2O8 Cromite (Fe,Mg)Cr2O4 2+ 3+ Magnetite Fe Fe2 O4 Ilmenite FeTiO3

Table 1.2: Main mineral components found in meteorites [73]. For a detailed list, see Rubin (2005) [58]. Note: The X and the Y in the pyroxene formula refer to two generic cations species that occupy such positions in the pyroxene structure.

10 Lunar Meteorites: Origin and Mineralogy 1.3. LUNAR METEORITES

Achondrites are an igneous product after the recrystallisation of minerals of the plan- etary crust. They are poor in metals but rich in silicates, pyroxenes and feldspars. Their composition variability is linked to the very same formation of the planetary embryo dur- ing the multiple aggregation stages of other planetesimals and as consequence, to the temperature and time span of the chemical differentiation that occurred. Martian and Lunar achondrites are the most popular as both celestial bodies are in the vicinity of Earth and their surfaces are accessible, specially the Moon, lacking an atmo- sphere. Despite of this, most achondrites are original from unknown bodies, possibly that were disintegrated long ago [73], [71].

1.3 Lunar Meteorites

Lunar meteorites, also known as lunaites, are meteorites from the Moon. As the satel- lite’s radii is big enough to provoke a differentiation process (1738 km), lunar meteorites are of achondritic nature. They reach our planet after the impact of a meteoroid on the lunar surface. The meteoroid exchanges kinetic energy with the fragments (the theory behind that process is outlined in [43], but not needed in the context of this study), thus, the ejected particles accelerate to a velocity greater than the lunar escape velocity (which is approximately 2.38 km/s) and escape the Moon’s gravitational influence [39]. Given that the distance between the Earth and the Moon is relatively small, in astronomical terms (less than 0.003 AU) the transference of lunar material to our planet is quite fast, taking usually less than 100,000 years [13], [73]. The dynamics of these kind of transfers are by no means simple. Many particles will describe trajectories that stabilise within the Hill’s radius of the Earth with small velocities relative to our planet only to later be perturbed by the Moon. After several encounters with the satellite the ejected particle can be gravitationally assisted and gain a speed to escape the Earth-Moon system to eventually stay in an heliocentric orbit . The fate of those objects is diverse eg.: after millions of years they can collide with Earth, with other planets, or remain in an heliocentric orbit. The reader is referred to Section 1.5 for a detailed description of lunar ejecta orbital dynamics. Currently, there are a total of 408 (last update on March 2, 2020) lunar meteorites recognised (see Meteorite Database [39]), even though many are suspected to be paired stones that separated upon the meteoroid’s encounter with the Earth’s atmosphere. These achondrites that arrive to our planet present a wider variability that the Luna and Apollo mission samples, as the latter, even being the largest contributors in terms of weight (a total of 382 kg of rock and soil samples [39]), come from a specific, similar area of the Moon. Hence, lunar meteorites must come from many different locations of the Moon.

11 Lunar Meteorites: Origin and Mineralogy 1.3. LUNAR METEORITES

But, how do we know they actually come from the Moon? Certainly, that is no easy task owing to its poor concentration in iron and many similarities with terrestrial rocks [73]. The definitive link is established using the oxygen isotopic ratios that are identical to terrestrial rocks and reaffirm the close origin of the two planetary bodies forming our binary system [68], [69]. To determine if a rock travelled through space the radioactivity of its nuclides is analysed ([39], [73], [13]. See Section 1.5.1). During the Moon-Earth transfer, the meteoroid is exposed to cosmic-rays that are so energetic they trigger nuclear reactions, changing the isotopes [39] (see Section 1.5.1 for further detail). Radionuclides that are product of cosmic-ray exposure are: 14C, 10Be, 26Al, 36Cl and 41Ca. As radioactivity decays once they arrive to Earth and each of the radionuclides has a particular half-life, it is possible to determine how much time the rock was on the surface of the Moon, how much it spent on space and how long ago it fell on our planet’s surface [39]. Unfortunately, it has not been possible yet determine the source crater of any lunar achondrite.

1.3.1 Lunaites Classification

The classification of lunar meteorites and for that matter, lunar rocks too is quite con- fusing as several disciplines intertwine. A lunar rock can be referred from the perspective of [39]: mineralogy (the minerals that contain), petrology (how the rock formed), texture and rock components (how the mineral grains are disposed) and chemistry (which chemi- cal composition has). The table below shows an example of how the same rock is named according to the aforementioned classifications:

Mineralogy feldspathic Chemistry aluminum-rich Petrology anorthosite Texture and rock components regolith breccia

Table 1.3: Classifications of a lunar rock [39]

Generally, names combine to properly describe rocks that may have the same mineral- ogy but differ in the rock texture, eg. feldspathic regolith breccia vs. feldspathic granulitic breccia. See the Alphanumeric list of lunar meteorites containing the different lunar rock types [36]. In turn, since the very first time the Moon was observed with a telescope, its surface was divided into two categories: the mare (called seas for their flat and dark appearance) and the terra or highlands. The reader is referred to Section 1.4 for a detailed explanation of the two types of lunar terrane and their properties, and can skip this section if already familiarised with lunar rock vocabulary.

12 Lunar Meteorites: Origin and Mineralogy 1.3. LUNAR METEORITES

Breccias

Breccias are rocks made up of bits of other rocks (clasts) in a matrix of finer-grained rock fragments, glass or crystallised melt found in both maria and highlands [39]. They can be classified according to their formation process [39]:

• Impact-melt breccias: igneous rock formed by the cooling of a melt.

• Regolith and fragmental breccias: equivalent to terrestrial sedimentary rocks. Re- golith breccias are these containing different lithologies (then of polymict nature) and containing rocks, mineral and glass fragments in a glassy matrix [57], [63].

• Granulitic breccias: metamorphic rocks that recrystallised by the heat of an impact.)

On the other hand, breccias can be classified strictly by the homogeneity of the rock:

• Monomict breccia: breccia that is entirely made of one kind of rock.

• Dimict or Dilithologic breccias: made of two different lithologies.

• Polymict breccia: general term that includes all non-monomict or -dimict breccias. Their textures vary as much as the conditions for their formation. Polymict breccias include: glassy melt breccias, granulitic breccias, regolith and fragmental breccias.

Basalt

Maria2 rocks rocks are mostly formed by extrusive igneous (volcanic) rocks that are low in silica content, and dark being known as basalts. These rocks formed when the magmas from the Moon’s core erupted into the basins previously formed by impacts of small asteroids (petrology) [39]. Basalts are crystalline, igneous rocks (texture) that contain plagioclase and are rich in iron, containing pyroxene, olivine and ilmenite (mineralogy). Basalts are subclassified according to their chemical composition, for eg.: low-titanium (Ti) mare basalt [39], aluminous mare basalts [76].

Feldspar

Feldspars are silicate minerals abundant on both Earth and Moon’s crust [75], [39]. According to their chemical composition they can be classified as potassium feldspars and plagioclase feldspars. Plagioclases are of the form NaAlSi3O8 (albite) to CaAl2Si2O8 (anorthite)[75]. Lunar highlands are composed of the calcium-rich variety giving the name to the rocks, anorthosites.

2Plural of mare, lunar seas

13 Lunar Meteorites: Origin and Mineralogy 1.3. LUNAR METEORITES

1.3.2 Recovery Locations

No lunar meteorite has ever been witnessed to fall, in other words, has never been observed as meteor [39], [73]. Surprisingly, neither any lunar meteorite has been found in the American continent nor Europe [39], despite many having probably fallen on both continents since the last 100,000 years. It is known that meteorites fall in an homogeneous fashion across the globe [70]. How- ever, they are much easier to find in desert areas such as Antarctica or the Sahara Desert. The aridity and dryness of those deserts keeps the weathering of the meteorite from expo- sure to water minimal. In addition, in the case of Antarctica, the dark fusion crusts of the meteorites stand out in the snow and glaciers thus, making the searching tasks easier. In fact, many lunar meteorites have been recovered in Antarctica by expeditions funded by the US government (ANSMET, Antarctic Search for Meteorites [36]) and by the Japanese government (NIPR [36]). In contrast, meteorites that have fallen in deserts are generally found by locals or experienced collectors.

Figure 1.5: Lunar meteorites recovery sites statistical analysis. Database for analysis can be found in [36]

Northwest Africa and Sahara Desert locations can be confusing and may overlap in territory. Sahara Desert includes areas of Mali, Algeria, Morocco, Libya, Sudan, Mauritania and Niger. Arabian Peninsula has actually 2 findings belonging to the Kingdom of Saudi Arabia and the other 70 in Oman. Al-Kathiri et al.(2005) [31] provides a map of Oman with all meteorite find locations.

It is important to remark that many meteorites falling in deserts also are lost in private collections that sometimes are not even reaching scientific institutions. Additionally, the dark-grey fusion crust that lunar meteorites present and the probable weathering of their surface turns them indistinguishable from Earth rocks. So, many are still awaiting to be collected somewhere in our planet.

14 Lunar Meteorites: Origin and Mineralogy 1.4. LUNAR GEOCHEMISTRY

1.4 Lunar Geochemistry

The Moon is a crucial object of study to the understanding of the evolution of the Solar System and our own planet, Earth. Given its small size (compared to the size of Earth) its internal heat decayed much faster, being able to retain the characteristics of the first hundred Ma of the solar system existence [76]. The Moon is also a window to look back in time and model the history of the near-Earth environment as most of the lunar craters being as old as 3.9 Ga [76], [54]. The first 5-10 meters of lunar crust, the lunar soil or regolith, are constituted by a layer of loose, porous and fine impact-generated debris that is exposed to solar wind, cosmic rays and micrometeorite bombardment [76]. Below the regolith there is either intact rock or a conglomerate of not-so-fine material labelled as megaregolith. Depending on the region of the Moon the depth of regolith varies: marias have only half or a third part the thickness of the regolith found in the highlands [76].

(a) Distinction between the highlands and mare re- (b) Thickness of the lunar crust. GRAIL mission images gions. Clementine mission images [10] [62]

Figure 1.6: Images of the Moon surface. See the correlation between the darker areas (picture a), mare regions) and the low crust thickness, in b). Note that olivine-rich sites correspond mainly to maria

Thanks to the samples acquired by the different Apollo missions, lunar meteorites re- trieved and remote-sensing data collected from satellite missions to the Moon, nowadays there is a more comprehensive understanding of the geochemical composition of our satel- lite. The following lines will give a brief description (summarised from sections 2.9.3 and 2.9.4 of The Moon, P.H.Warren and G.J.Taylor [76], where the reader is referred to an extensive review on lunar geochemistry) of the main minerals and chemical components found in the two distinguished regions of the Moon: the highlands and the maria.

15 Lunar Meteorites: Origin and Mineralogy 1.4. LUNAR GEOCHEMISTRY

Maria

The seas of the Moon, maria, are basalts. This lunar basalt are more MgO+Fe-rich, feldspar-poor basalts, differing from terrestrial basalts. One of the characteristics of mare basalts that differentiates them from those of Earth are the content in volatile species such as alkalis (Na, K, Rb and Cs) and trace metals (Zn, In, Bi and Cd).

Exist different subclassifications of basalts: according to their content in TiO2 (Ti- poor, medium-Ti and Ti-rich [5]), secondary components such as Al2O3 and K (when >11 −1 wt% Al2O3 samples are considered as high-Al, when >2000µg K are high-K [53]) or the presence of abundant minerals (olivine, pigeonite, ilmenite). The mare volcanism not only produced basalts but pyroclastic glasses, usually found as spherules of diameters between 0.03 and 0.3 mm. These pyroclast glasses are also classified following the same criteria as basalts (Ti-, Al- and K) and the colour of its glass.

Highlands

The highlands are ancient regions of the lunar crust mainly form by impactites. Those are characterised by monomict (or known as pristine) and polymict breccias mixed with random bits of the lunar crust. The most characteristic element of their composition is a unique lunar material known as KREEP (K for potassium, REE for Rare Earth Elements and P for phosphorous) and also rocks enriched in uranium and thorium. However, it turns out that KREEP-rich highlands are quite of an exception and are over-represented in the Apollo samples, as proven by the Lunar Prospector maps, being most of highland regolith breccias KREEP-poor. The distinction between pristine rocks and polymict breccias is paramount to compre- hend the igneous processes in the lunar highlands. Non-pristine rocks are those product of impacts of meteorites which in general imply the mixing of siderophile elements3, an abundant presence of silicates, the FeNi metal (which is typically meteoritic in its ka- macite composition) as well as lack of KREEP and isotopic data (when dated extremely old probably not belonging to the Moon).

3Elements that ally with iron and are usually found in the core of planets. Most are transition metals, eg. iridium.

16 Lunar Meteorites: Origin and Mineralogy 1.4. LUNAR GEOCHEMISTRY

Figure 1.7: Examples of geochemical bimodality of pristine non-mare rocks. a) Na/(Na+Ca) molar ratio and b) Eu/Al wt ratio vs. bulk rock mg. Note the two differentiated clusters of FA suite and Mg suite. (Image extracted from [76], see the reference for detailed description of the types of rocks)

On the other hand, determining which rocks are pristine becomes really difficult due to a lack of sampling. Nevertheless, by the 1970s the non-mare pristine rocks were discovered to present a geochemical bimodality: a ferroan anorthositic suite (FA) and a Mg suite. Their distinctness was noticed when comparing the mineral composition data of plagioclase molar Ca/(Ca + Na) vs. mafic silicate mg4 (See Figure 1.7). In turn FA suit rocks do not have uniform compositions and could be further classified into four subgroups according to different mg ratios of mafic silicates and alkali contents of plagioclase. On the other hand, Mg-suite rocks probably formed from mg cumulates5 some of them with ultramafic6 modes.

1.4.1 Inorganic constituents in Lunar Soil

The Moon and the Earth share some of their constituent matter. The average com- position of the terrestrial crust is mainly O (46.6%), Si (27.7%) and Al (8.1%) [52]. The rest of elements are found below the 5% in composition and include: iron, magnesium, calcium, sodium, potassium and others. In comparison, the major elements found in 99% of lunar rocks contain the following elements [64]: O (41-45%), Si, Al, Ca, Fe, Mg and Ti. The remaining 1% has as components [64]: Mn, Na, K and P. As the average element compositions are rich in Si and O in both crusts, it is expected that both the lunar and terrestrial soils are mainly dominated by groups of silicates and silica minerals. Among them will be found olivines, pyroxenes, quartz, feldspars, etc. Nev- ertheless, there are differentiating factors between the Moon and the Earth, particularly due to the atmosphere. On the Moon there is virtually no atmosphere, unlike Earth that exists an oxygen-bearing one. For this reason there is no +3 oxidation state in the Moon,

4mg (≡ MgO/[MgO + FeO]) 5Igneous rocks formed by the accumulation of crystals from a magma 6Igneous rock with low silica content

17 Lunar Meteorites: Origin and Mineralogy 1.4. LUNAR GEOCHEMISTRY all ferrous oxidation states found in minerals are in the form of Fe2+ [64]. This phenomena takes place for other metals with several valences such as Mn and Mg. On the other hand, the presence (or lack of it) of certain elements hints the origin of the rock. For example, the concentration of Cr for lunar samples tends to be much higher than terrestrial ones. On the opposite case, low levels of Na and K tend to characterise lunar rocks compared to terrestrial ones [64]. The Table 1.4 provides a brief summary of some relevant minerals found on both terrestrial and lunar crusts, as well as their X-Ray spectrum. The X-ray spectra shows the relative abundances of the elements that can be estimated directly from the heights of their peaks. These patterns characterise the minerals in terms of their composition and serve as a quick visual identification of a soil sample (see Section 2.1).

(a) (b)

Figure 1.8: Images of metals on the Moon surface. Note that the colour scale of Ti does not correlate with the one of Fe, they are independent. Both metals appear to have higher concentrations on maria than on the highlands. Images of the mission Clementine [10].

Figure 1.9: Images of thorium concentrations (correlated to KREEP) on the Moon. Image taken by the Lunar Prospector and extracted from [34].

18 Lunar Meteorites: Origin and Mineralogy 1.4. LUNAR GEOCHEMISTRY ). 8 O 2 Si 2 (fosterite) to 4 SiO 2 . The image shows the 3 ) and anorthite (CaAl 8 O 3 ), albite (NaAlSi 3 (fayalite) [ 17 ]. The image in the right shows different X-Ray spectrums of 4 SiO 2 Group of minerals foundacteristic in green mafic colour. andFe ultramafic igneous Mineral rocks. compositionsolivine They minerals range have with a from differentdiate Mg char- Mg and atoms. minimum From Mg. top to bottom: maximum, interme- Group of mineralsperature. that form They under aresubdivided conditions according found to of on their igneous crystal highclinopyroxenes system (eg. and pressure in: metamorphic and/or Orthopyroxenes clinoenstatite,roxene (eg. rocks high augite). with [ 17 ]. ferrosilite) tem- different and The number Pyroxenesalso left-side of are different image Mg Mg ions. shows atoms.bottom. an The For orthopy- hand-side both picture images: shows maximum augite on with the top, minimum on the The albite-anorthite range are known asfeldspars. plagioclase and The the image albite-orthoclase shows as alkali an X-Ray spectrum of four different types of feldspar. It is aand metal sedimentary that rocks constitutes [ 17 ].X-Ray the The spectrum primary chemical of formula ilmenite. ore is of FeTiO titanium. It is found in igneous Group of minerals[ 52 ]. found They in are more foundend-groups on than are igneous, half orthoclase metamorphic (KAlSi and of sedimentary the rocks [ 17 ]. minerals The of three the terrestrial crust xene ates e-Ti oxides eldspar able 1.4: Some dominant minerals on Earth and Moon’s crust. The images (extracted from [ 52 ] represent the X-Ray spectrum of the mineral or Olivine Silic Pyro F F Ilmenite mineral subgroup with the x-axis being, for all cases, in [keV]. T

19 Lunar Meteorites: Origin and Mineralogy 1.5. LUNAR EJECTA

1.5 Lunar Ejecta

After analysing the properties of, particularly, lunar meteorites, one question remains unanswered: how did they reach Earth? The atmosphere of the Moon is extremely thin, and unlike the terrestrial one, it is unable to decelerate particles that are either impacting or escaping from the Moon, as small as grains of sand and dust [15]. It is due to the impact of these high-velocity objects (mainly asteroids and comets) that lunar materials are ejected with a velocity above the escape velocity of the Moon (2.38 km/s) [4]. When a projectile of a certain mass impacts the surface of the Moon leaves an impact crater and usually between 3-4 orders of magnitude higher of that of the projectile mass is ejected [43], [4]. Most of the ejected mass falls near the crater and forms continuous ejecta blankets, the rest mainly follows an impact trajectory forming a new crater far away from the initial impact and a small part achieves enough velocity to escape the Moon [4]. Nevertheless, escaping the Moon does not imply that in the future the same ejected particle cannot eventually impact its original parent body. The dynamics of the ejecta are not simple by any means. The ejected particle from the Moon starts its journey inside the Earth-Moon system and it may impact the Earth, the Moon, remain in geocentric orbit (more rarely mooncentric) or escape the system and enter in heliocentric stage, to later impact with other planets or return again to the Earth-Moon system. One thing is clear, there are many possibilities for the fate of an ejected particle and the problem increases in complexity as more bodies are added and the further the timeline is extended: long-range gravitational effects such as secular resonances, collisions with the asteroid belt [20], solar radiation [...] to name just a few, constitute the possible perturbations an ejected particle can experience. The works of Brett Gladman on material transference and particle ejecta between the Earth and the Moon and other terrestrial planets ([21], [19], [18] and [20]) have served as a starting point for this project and as a reference for the current knowledge on the dynamics of lunar ejecta (see Section 5).

1.5.1 CREAs

During the transference from the parent body (in this case the Moon) to the impact body, Earth, meteoroids travel through interplanetary medium where they find highly energetic particles such as solar-wind (SW) particles, solar energetic particles and galactic cosmic rays (GCRs) [13]. The radiometric study of meteorites allows to analyse diverse quantities [21]:

20 Lunar Meteorites: Origin and Mineralogy 1.5. LUNAR EJECTA

• The crystallisation age: the time at which various isotopes were locked into a closed system.

• The 2π depth and age t2π, which measure how far below the surface of the parent body was the meteorite before its launch and the duration of the surface exposure. The isotopes that allow determining the cosmic-rays ages on lunar meteorites (also de 4π stage) are [23]: 3 He, 21Ne, 22Ne, 38Ar, 36Cl, 26Al and 10Be.

• The 4π age t4π that measures the amount of time the meteorite spent in space exposed to radiation fluxes. Ideally, the meteorite can be imagined as a spherical object small enough so that the cosmic rays reach the interior of the material from all solid angles [23].

• Terrestrial age tEART H : time spent in Earth’s orbit since its arrival as meteoroid. To determine the terrestrial ages the isotopes that provide the information are [23]: 14C, 36Cl, 81Kr and 41Ca.

In other words, the way in which energetic particles interact with solid matter leaves hints of the history and origins of the meteorite. For example, solar-wind particles are low energy particles that get implanted into the mineral grains which in turn become saturated of He [21]. In contrast, high energy particles usually from galactic rays are able to produce nuclear reactions with the elements that form the meteoroid producing nuclides (see Table 1 from [13] for the measurements of cosmogenic nuclides in meteorites). Usually, to explain the irradiation history of lunar meteorites a simple one-stage ap- proach is chosen for simplicity, assuming that the Moon leaves no isotope traces and that 4π stage is enough to model it. In that case the parameters that explain the irradiation history are [23]: the size of the meteoroid, the depth of the sample within it, the duration of the irradiation in space and the terrestrial age. A second-stage approach includes the irradiation suffered on the lunar surface which adds two additional parameters [23]: the depth of the sample and the duration of the irradiation. The current knowledge of CRE histories of lunar meteorites is summarised in the following points [23]: • Most lunar meteorites impact Earth in less than 1 Myrs, some of them in less than 0.1 Myr. • Most lunar meteorites contain cosmogenic nuclides belonging to irradiation suffered on the lunar surface. • Many of lunar meteorites are regolith breccias, hence, have been laying on the surface of the Moon and collecting solar wind ions.

21 Lunar Meteorites: Origin and Mineralogy 1.5. LUNAR EJECTA

Meteorite Type Meteorite Name T2π T4π TEarth Feldspathic fragmental/regolith breccia yamato 82192 9 90 NWA 482 0.9 ± 0.2 60-120 Feldspathic impact melt breccia Dhofar 026 <0.003 Dhofar 026 0.01 Dar al Gani 400 <3 <1 ALH 81005 0.0025 9 Dar al Gani 262 0.5 300 Dar al Gani 262 <0.15 Dhofar 025 4-20 500-600 MAC 88104 0.04 210-250 Feldspathic regolith breccia MAC 88104 630 ±200 <0.24 100-600 MAC 88104 >5 0.04-0.05 210-250 MAC 88104 >5 0.04-0.11 100-190 QUE 93069 1000 ±400 0.15 ± 0.02 <15 QUE 93069 >500 0.02-0.05 5-10 Y791197 <0.019 30-90 Calcalong Creek >300 <0.2 <70 Feldspathic/mare regolith breccia Y 79374/981031 <0.02 <20 Y 79374/981031 700 ± 200 <0.12 NWA 032/479 0.042 <80 Mare basalt Y 793169 1.1 ± 0.2 <50 Asuka 881757 0.9 <50 EET 87521 26 <0.1 15-50 Mare polymict breccia EET 87521 <0.01 80 ± 30

Table 1.5: CREAs for lunar meteorites. Data collected from Table 4 of [23]. Only meteorites with a determined 4π-stage value have been included in the table. Time expressed in Myrs.

Figure 1.10: Cumulative percentage impacted with Earth. Data extracted from Table 1.5, time is ex- pressed in [Myr]. The inferior and superior limits are upper and lower values that appear also in the column T4π of Table 1.5.

22 Lunar Meteorites: Origin and Mineralogy

Part I Mineralogy Study

2. Chemical and mineralogical characterization of lunar achondrites

Exist several techniques for the analysis and identification of meteorites, also depend- ing on the information one is seeking. For example, polarised optical microscopes are particularly useful for distinguishing the different minerals on a petrographic thin section. Electron microscopy is used to characterise the elements present in a sample while Raman Spectroscopy unveils the structure of it. For this project only one technique has been used, SEM/EDX, and will be described in detail in this section.

2.1 SEM+EDX

The Scanning Electron Microscopy (SEM) is a very good technique for the analysis of materials. The technique employs a electron beams that provide information of the sample at nanoscale [12]. The bombardment of electrons leads to the emission of secondary electrons, backscattering of high energy primary electrons and X-rays [60]. The Energy Dispersive X-Rays Spectroscopy (EDX or EDS) is an analytical capability were the specific radiation of each element is able to characterise the chemical components of the sample, being a kind of technology usually coupled with SEM [60]. The electron beam interacts with matter in the following way [12]:

• Backscattered electrons are the ones that produce the contrast in the image generated by the differences in atomic number. In this mode, the information depth is about 1 µm [60].

• Secondary electrons give topographic information.

• Cathodoluminescence gives information of the electronic structure and chemical com- position of materials.

• Transmitted electrons describe the inner structure and crystallography.

23 Lunar Meteorites: Origin and Mineralogy 2.1. SEM+EDX

• X-rays are able to identify the type of elements that exist in the sample. The measured intensities are linked to the quantitative information on the element composition and distribution.

Figure 2.1: Energy dispersive X-ray spectrum. a) Typical EDX spectrum. The peaks identify the different elements and their intensity corresponds to the quantification of the element concentration in the sample. b) Scheme of an atom struck by an electron beam. Firstly, the electron beam energises a low energy shell electron or knocks it off from the atom. Secondly, the hole left by the energised electron is filled by a high energy shell electron, releasing energy in the process in the form of an X-ray [12]. Image extracted from [52].

The SEM/EDX analysis used for this project provides two different results that describe the samples: a SEM image and the X-ray spectrum as well as a list with the elements found in the sample and their atomic and weight %. Samples for SEM/EDX need to be compatible with high vacuum or low chamber pressures (1 mbar) [60].

2.1.1 Solver for Mineral Proportions

The resulting data from the SEM/EDX analysis does not directly indicate which min- erals or even chemical components are on the sample. It is necessary to treat the original data (weight percentage of the elements detected in the sample) to obtain the wanted information. With this purpose it is used MINSQ, a least squares spreadsheet method for calculating mineral proportions from whole rock major element analyses. The reader is referred to [22] for an extensive description of the method while the following lines will mention a few key points of its functioning and the particular modifications applies to this project. MINSQ is a least square method adapted to Microsoft Excel TM that allows to estimate the proportions of constituent minerals in rocks, having previously defined a rock litho- geochemical database. The major advantage is its simple use and flexibility to adapt to different lithogeochemical studies. MINSQ is divided into two spreadsheets:

24 Lunar Meteorites: Origin and Mineralogy 2.1. SEM+EDX

• Mineral Composition Calculator: this spreadsheet converts chemical formulae of minerals to chemical compositions in wt%. The user introduces the number of cations of the formula (eg. 3 Si, 1 Al and 1 Na) and are converted to chemical components in wt% (68.74% SiO2, 19.44% Al2O3 and 11.82% Na2O). The cations are preset (Si, Ti, Al, Na...) but the user can modify manually adding or removing them. Each of the cations is linked to a chemical component (eg. Si to SiO2).

• MINSQ: with the result previously obtained by the Mineral Composition Calculator (the wt% of chemical components) and the use of the Solver the estimation of the wt% of mineral composition is made. To do so, the solver uses a database of minerals with its chemical composition in wt% (the database being smaller than the amount of possible chemical components, see [22]). The Solver finds a combination of minerals in wt% that best adjusts the chemical composition of the sample.

Figure 2.2: Ternary diagram of of the composition of feldspar minerals. Image extracted from [55].

Additionally, for this project, another spreadsheet has been used to determine the different Fe valences (Fe2+, Fe0) as each of them constitutes a different cation and leads to a different chemical components. For example, Fe2+ leads to FeO and Fe0 to iron. This particular spreadsheet also uses the Solver to calculate the atomic and weight % of the Fe cations in accordance to the weight and atomic % given by the SEM/EDX analysis. A major drawback of using MINSQ is that both chemical components and minerals must be preallocated, meaning that the Solver is not able to deduce minerals from scratch but from a database designed by the user. The same problem affects the chemical components, it is the user that has to take into account if cations have different valences and they may appear in the composition of the samples. For example, Fe2O3 has not been included in the chemical component list as Fe does not have 3+ oxidation number in the Moon [64]. A different problem is the selection of minerals and if exists independence (or lack of it) in

25 Lunar Meteorites: Origin and Mineralogy 2.1. SEM+EDX their compositions. For example, the method cannot successfully distinguish mixtures of albite and anorthite or oligoclase and anorthite. The method is convenient when the list of minerals is limited and kept simple, in order to distinguish the major changes in the dominant minerals. All of these, must be taken into account when interpreting MINSQ results, regardless if they converge or not, always contrasting the results with available data (eg. already known X-Ray Spectrums).

Mineral Mineral Group Chemical Formulation Source albite feldspar Na(Al2Si3)O8 RRUFF Project anorthite feldspar Ca(Al2Si2)O8 RRUFF Project augite pyroxene Ca0.86Mg0.74Fe0.4Si2O6 WebMineral pigeonite pyroxene (Mg1.35Fe0.55Ca0.1)Si2O6 Mindat clinoenstatite pyroxene Mg2Si2O3 Mindat fayalite olivine Fe2SiO4 RRUFF Project fosterite olivine Mg2SiO4 RRUFF Project labradorite feldspar Ca0.53Na0.44Si2.47Al1.53O8 RRUFF Project troilite iron sulfide FeS RRUFF Project pyrrhotite iron sulfide Fe0.95S WebMineral pentlandite iron-nickel sulfide Fe4.8Ni4.12Co0.08S8 RRUFF Project ilmenite iron-titanium oxide FeTiO3 RRUFF Project chromite iron-chromium oxide FeCr2O4 RRUFF Project zirconolite calcium-zirconium-titanium oxide CaZrTi2O7 WebMineral baddeleyete zirconium oxide ZrO2 Mindat zircon zirconium oxide ZrSiO4 RRUFF Project kamacite iron-nickel alloy Fe0.9Ni0.1 RRUFF Project

Table 2.1: Table of minerals and correspondent chemical formulation used in MINSQ solver. The sources used have been RRUFF Project [11], WebMineral [49] and Mindat [48].This is the database used for the three different meteorite samples and it is based on the information provided on the Meteoritical Bulletin [2]

26 Lunar Meteorites: Origin and Mineralogy

3. Lunar Meteorite Samples

In this section three different meteorite samples are presented. For each of them a brief description of their properties and location of finding is given, afterwards, the SEM/EDX results are exposed.

3.1 JaH 838

JaH 838, officially named Jiddat al Harasis 838, is a lunar meteorite that was found on February 28th of 2003, 28 km south of the Al Ghaftain (Oman) during a desert expedition, meaning nobody witnessed its fall. This lunar meteorite has been classified as mingled regolith breccia as it has presence of mare and KREEPy material and also of HASP and chondritic material. The following information is a summary of the official information published by the Meteoritical Bulletin Database [45], [8].

Location of the Finding

JaH 838 was found on the province of Al Wusta (Oman) at the coordinates 19º 22’ 3”N, 55º 28’ 51” E. The following images show the exact location on the map of both the meteorite and the Al Ghaftain [45]:

(a) View of middle and southern Arabic Peninsula. Includes (b) Detailed view of the finding (Oman) parts of Saudi Arabia, Yemen, Oman, Qatar and United Arab Emirates

Figure 3.1: Location of the JaH 838 meteorite. Images from Google Earth

27 Lunar Meteorites: Origin and Mineralogy 3.1. JAH 838

Physical Characteristics

This lunar meteorite consists of one stone of 34.36 g. It does not present an evident fusion crust but has a typical Omani lunar stones exterior: a frosted and ablated surface. Inside it black-grey with white, brown and grey inclusions. It lacks terrestrial weathering [45].

Petrography

JaH 838 is a fragmental breccia composed principally by [45]:

• Mineral fragments: plagioclase, augite, pigeonite, poor-Ca, pyroxene, olivine, set in a fine-grained matrix

• Lithic clasts: anorthosite, fragmental breccia, gabbro, norite, basalt, pyroxenite and regolith (HASP spherul and chondritic lunar metal). Set in a fine-grained dark gray matrix with Ni-iron, troilite, pyrrhotine, pentlandite, ilmenite, chromite, zirconolite, baddeleyte and zircon.

28 Lunar Meteorites: Origin and Mineralogy 3.1. JAH 838 mm x . Meteorite sample image reconstructed with Photoshop CC 2018 from SEM/EDX SEM/EDX Microscopy Results 3.2: Mosaic of JaH 838, size of the sample 9x7 images. 3.1.1 Figure

29 Lunar Meteorites: Origin and Mineralogy 3.1. JAH 838

We have defined two ROIs for meteorite JaH 838. The first ROI is found in the cell C6, focusing on the white spot that stands out from the rest of the matrix (see figure 3.2) with dimensions 400 × 400 µm × µm. A total of 6 different spectra have been used to perform the analysis, obtaining for each of them the atomic percentage and the weight percentage of the elements detected by the SEM/EDX. The second ROI of the JaH 838 lies at the border between cells C2 and D2 (see figure 3.2) and has a higher resolution, 90×90 µm×µm. In this case, an EDX mapping has been done to observe the distribution of the elements present in the region additionally to their atomic and weight percentages.

(a) Meteorite JaH 838 ROI 1 (b) ROI of JaH 838 for mapping

Figure 3.3: Meteorite JaH 838 ROIs

With these data, the data available from the Meteoritical Bulletin and the MINSQ [22] solver a first determination of the minerals contained in the sample could be made. However, not all spectra converged to a solution, see 2.1.1 for further details on this issue.

Figure 3.4: Spectrum 6 JaH 838. Note the twin-peaks and half size peak of Ca. This configuration is characteristic of anorthite.

30 Lunar Meteorites: Origin and Mineralogy 3.1. JAH 838

• Spectrum 1 and Spectrum 2: These spectra are located in an area where with a bright white granule. There is a high percentage of Fe which seems to point to the presence of anorthite, fayalite and kamacite. However, there is no convergence on the solution.

• Spectrum 3: This spectrum belongs to the matrix of the meteorite, in a darker region. The high peak of Si and presence of Al and Ca, and marginally Mg justifies the mineral composition of albite (85.9%), clinoenstatite (10.3%) and pigeonite (3.8%).

• Spectrum 4: As well as spectrum 3, belongs to the matrix but to a brighter region. The peak of Si is still present but Mg, Al, Ca and Fe also become more prominent. The resulting mineralogy does not show any clear dominant mineral, this is why further analysis (with eg. Raman Spectroscopy) are required. The minerals are albite (4%), augite (32.6%), pigeonite (29.4%), ferrosilite (2.4%), labradorite (28.8%), kamacite (6.8%) and other below 1%.

• Spectrum 5 and Spectrum 6: Both are pointing to the matrix and present almost identical composition. They exhibit a characteristic twin-peak of Al and Si with a lesser (half of that of the peak of Al) peak of Ca. There is also a residual presence of Na, Mg, S and Fe, all of them negligible. The sample is clearly an anorthite (90.2%). The secondary minerals include labradorite (5.1%), augite (2%), clinoenstatite (1.7%) and pyrrhotite (1.1%). The latter is associated with the presence of S.

• Mapping: Even though the mapping also is supported by an X-ray spectrum, this one is the sum of all spectra of the region analysed, so not as useful as the spectrum of a single point, as it will be averaged and interpretation becomes more difficult. Instead, the mapping shows the concentration of each element and where is located in the region. Looking at Figure 3.5 can be seen that the central, more homogeneous part is anorthite (abundance in Si, Al and lesser proportion of Ca). On the other hand, there is presence of troilite or pyrrhotite supported by the high concentrations on the same spot of Fe and S. Finally, it is important to remark a stripe that seems to be only composed by Ca.

The detailed analysis of each spectrum can be found on Section A.3.2.

31 Lunar Meteorites: Origin and Mineralogy 3.1. JAH 838 ) or pyrrhotite (its non stoi- Figure 3.5: SEM/EDX mappingJaH of 838.the Each backscattering imageparticular represents image element of targeted.that the Note for O andis Si, virtually homogeneous the across distribution the sample. The Alare and homogeneous Ca except for mappings partic- ular regions that thereof Fe, is Mg presence andregions S. In of particular, abundant the with S abundance correspond ofindicates Fe the too.( F presence eS This ofchiometric troilite variant). Iron Sodium ) Silicon (i) (f (c) Oxygen Calcium Aluminum (b) (h) (e) Sulfur Carbon Magnesium (g) (a) (d)

32 Lunar Meteorites: Origin and Mineralogy 3.2. DHO 1084

3.2 Dho 1084

Dho 1084, officially known as Dhofar 1084 is a lunar meteorite, also found in Oman, near Zufar. Near this meteorite was found Dho 490 and both were isolated from other lunar stones, however, it has not been determined if they form a pairing [33].

Location of the Finding

The recovery location of this meteorite was 18º 43’ 20”N, 54º 27’ 39” E [44], at the north of Dhofar.

(a) Satellite view the southest region of the Arabic Peninsula (b) Detailed view of the finding in the Dhofar region

Figure 3.6: Location of the Dho 1084 meteorite. Images from Google Earth

Physical Characteristics and Petrography

The stone weights 90 g [59] and its surface is dark grey and crusty. This meteorite has been classified as ”average” FLM (feldespathic lunar meteorite [33]), even though there is no available data of its geochemistry and mineralogy.

33 Lunar Meteorites: Origin and Mineralogy 3.2. DHO 1084 SEM/EDX Microscopy Results 3.7: Mosaic of DHO 1084, size of the sample 13x10 mm. Meteorite sample image reconstructed with Photoshop CC 2018 from SEM/EDX images. 3.2.1 Figure

34 Lunar Meteorites: Origin and Mineralogy 3.2. DHO 1084

For the Dho 1084 meteorite only one ROI has been defined, contained in cell E8. As Figure 3.8 shows, there are many potentially different minerals in this sole region: different brightness points out the presence of different elements as well as varying textures in barely an image of 1200×1200 µm × µm. A total of 9 spectra aim to generate a spectrum of each characteristic region of the sample. This ROI has been chosen for the variability in its mineral composition, to take as a representative sample of the whole meteorite composition. It must be noted that for this case there is no data available from the Meteoritical Bulletin or any other source to contrast the results.

Figure 3.8: Meteorite DHO 1084 ROI

35 Lunar Meteorites: Origin and Mineralogy 3.2. DHO 1084

• Spectrum 1 and Spectrum 2: Spectra characterised by a prominent peak of Si. Among other cations, there is presence of Al, K and Mg. More marginally exist concentrations of 1% and below of Ca, Ti, K and Na. The dominant mineral is albite (80.4%) and the secondary pigeonite (9.9%) and kamacite (1.4%). As the predicted vs. real proportions of Na and K do not suit, it is predicted to be an alkali feldspar with (70%-80%) orthoclase and the rest albite.

• Spectrum 3 and 4: The spectra have in common a large peak of Si and Zr. Minor cations are Ca, K, Al, Mg and Fe. The sample is predicted to be ≈ 80% zircon and as secondary minerals albite (5.2%), augite (4%), pigeonite (3.7%) and labradorite (6.7%). Albite mineral is subject to further analysis to differentiate the amount of albite and of orthoclase.

• Spectrum 5 and 6: Both spectra present a high peak of Ti, medium ones of Fe and Si and below 3% of Mg, Al, Ca, P, Mn and Fe. Results are inconclusive but the sample is suspected to contain ilmenite, an iron-titanium oxide.

• Spectrum 7 and 8: spectra are located in a greyish region that occupies half of the area of study. They are characterised by a large peak of Si, medium ones of Mg, Ca and Fe. There is no dominant mineral in the sample, having all similar percentages: albite (19.2%), augite (23.9%), pigeonite (33.8%) and ferrosilite (16.8%).

• Spectrum 9: This spectrum is located in a darker coloured, scratched part of the matrix. The X-ray has a large peak of Si and two milder ones of Mg and Al. It also has a lower presence of K, Ca, Fe and marginally S. The sample dominant mineral is fairly so, being clinoenstatite (55.1%) followed by labradorite (37.3%). Other secondary minerals include albite (4.7%) and ferrosilite (2.7%).

The detailed analysis of each spectrum can be found on Section A.3.3.

Figure 3.9: Spectrum 3 of the mapping of DHO 1084. Note the prominent peaks of Si and Zr, making evident the presence of zircon.

36 Lunar Meteorites: Origin and Mineralogy 3.3. NWA 11444

3.3 NWA 11444

The NWA 11444 known as Northwest Africa 11444 was collected in an unknown loca- tion in Mauritania and later sold. It is known that several other meteorites were retrieved from the same spot, all of them with a dark, pitted surface colouration due to desert weathering [46].

Physical Characteristics

Gathering a total of 200 fragments, the total mass reaches 1323 g. Some of them have a dark appearance probably owing to the abrasion with the wind during the reentry. In contrast, others have a lighter-coloured exterior surface with different amounts of sand ad- hered to it (presumably for being buried in the terrain before the recovery). All fragments present angular sub-rounded, feldspar-rich clasts up to 1.5 cm in diameter enclosed in a dark matrix loaded with smaller, angular pieces [46].

Petrography

This meteorite is a polymict fragmental breccia that contains minerals and lithic clasts in abundance inside a finer-grain matrix [67]. Fragments are angular and have coarse- grained to aphanitic1 gabbros and basalts as well as a wide range of single-crystal types. The angular crystal fragments can be up to 0.5 mm in diameter and are formed by pla- gioclase, high and low Ca pyroxenes and olivine. Additionally, contains a small amount of Fe, Ni metal grains up to 150 µm [46].

1Referred to igneous rocks when they are so fine-grained that their minerals cannot be appreciated by the naked eye

37 Lunar Meteorites: Origin and Mineralogy 3.3. NWA 11444 mm x . Meteorite sample image reconstructed with Photoshop CC 2018 from SEM/EDX Microscopy Results 3.10: Mosaic of NWA 11444, size of the sample 13x12 SEM/EDX images. 3.3.1 Figure

38 Lunar Meteorites: Origin and Mineralogy 3.3. NWA 11444

In NWA 11444 meteorite a total of 4 ROIs have been defined. Each of the regions chosen has specific interesting features: ROI 1 has two differentiated areas one darker and the other brighter than the matrix; ROI 2 has a crack empty on the edges but filled with a mineral in the central part (seen as a white stripe); ROI 3 has several embedded grains with a particularly large one and ROI4 focuses on the large granule found in ROI 3. As in the other previous meteorites MINSQ has been used to deduce the minerals components of each of the samples (see [22] and Section 2.1.1).

(a) ROI 1, found in cells H5 and I5 (b) ROI 2 found in cell F8

(c) ROI 3 found in cells B10 and C10 (d) ROI 4 for mapping. The region is a magnified granule from ROI 3

Figure 3.11: ROIs of NWA 11444

39 Lunar Meteorites: Origin and Mineralogy 3.3. NWA 11444

Analysis of the spectra of ROI 1

• Spectrum 1 and Spectrum 2: Both spectra belong to the matrix of the meteorite. The X-rays show twin peaks of Si and Al, with one of Ca half of the intensity of the one of Al. There is also the presence of Mg, Na and Fe, although marginally. As in previous cases, the dominant mineral is clearly anorthite (91.4%). Secondary minerals include pigeonite (3.5%), labradorite (4%) and clinoenstatite (1.1%).

• Spectrum 3 and 4: These belong to a brighter region of the matrix inside a granule. The X-Ray is characterised by a large peak of Si and slightly smaller of Mg, that could be almost considered twin peaks. Then, smaller peaks of Fe, Ca and Al. The peak distribution suggest a pyroxene or an olivine. There is no primary mineral and the results need further analysis. Identified minerals include anorthite (21.8%), pigeonite (7.5%), clinoenstatite (7.9%), ferrosilite (1.3%), fayalite (15.4%) and olivine (39.4%).

• Spectrum 5 and 6: The spectra belong in a darker region of the matrix enclosed in a large grain. The X-ray has a prominent peak of only Si. The rest of elements are marginal (Mg, Al, Ca and Fe). The minerals of this sample were unable to identify and requires further analysis.

• Spectrum 7 and 8: These spectra are pointing to granules that are brighter than the colour of the matrix, similar to spectra 3 and 4. Both present a high peak of Mg and Si (twin peaks), and smaller ones of Al, Ca and Fe. As in the case of 3 and 4 the proportion of elements suggests olivine and pyroxene minerals. The resulting minerals are anorthite (23%), clinoenstatite 6.1%, fayalite (12.5%) and fosterite (50.9%).

Figure 3.12: Spectrum 3 of the mapping of NWA 11444 (ROI 1). The peaks of Si, Mg and lesser ones of Al, Ca and Fe seem to suggest an olivine.

40 Lunar Meteorites: Origin and Mineralogy 3.3. NWA 11444

Analysis of the spectra of ROI 2

• Spectrum 1 and Spectrum 4: These spectra are in a particular part of the me- teorite, a crack in its surface filled with a mineral (or minerals) that the SEM/EDX detects as bright white. The X-ray is quite complex. It has a peak of Si, a prominent peak of S, another from Sr, medium ones of Al and Ca and then of Ba. Marginally presents Mg and Fe. The minerals could not been identified, in part, because the MINSQ tool did not have any input mineral with Ba nor Sr in its components. Hence, the fissure composition is an anomaly as it as S, Sr and Ba.

• Spectrum 2: This spectrum is located in a granule brighter than the matrix. It has a prominent peak of Si and similar intensity peaks of Mg, Al and Ca. Marginally presents also Ti, Cr and Fe. The element distribution of the peaks suggests augite, which turns out to me the dominant mineral (82.6%). Other secondary minerals include albite (4.8%), labradorite (8.9%) and clinoenstatite (3.7%).

• Spectrum 3: This spectrum belongs to the matrix of the meteorite. As in other spectra, it is characterised by twin peaks of Si and Al and a half intensity peak of Ca. There are other elements detected but remain marginal (Na, Mg and Fe). The dominant mineral is anorthite (89.5%) and the secondary one is augite (9.5%).

• Spectrum 5: This spectrum points to a granule of a grey colour, with cracks. The X-ray presents a prominent peak of Si with similar intensity peaks of Mg, Al, Ca and Fe. Marginally Ti and Mn are also present. There is no particular dominant mineral but the distribution of peaks suggests the presence of orthopyroxenes. The estimated minerals include anorthite (6.6%), augite (20.7%), pigeonite (37.9%), clinoenstatite (10.8%), ferrosilite (7.1%) and labradorite (23.1%).

(a)

Figure 3.13: Spectrum 1 of the mapping of NWA 11444, ROI 2. Observe the different peaks at anomalous elements such as Sr and B, and also the prominent peak of S.

41 Lunar Meteorites: Origin and Mineralogy 3.3. NWA 11444

Analysis of the spectra of ROI 3

• Spectrum 1, Spectrum 2 and Spectrum 3: Spectra 1 and 2 are inside the region of a granule, particular by its bright white colour, while spectrum 3 it is at the limit between the granule and the matrix. According to the X-rays, there is a prominent, much larger than the rest peak of Fe. The rest of elements present small peaks, those include Mg, Al, Si, P, Ca and Ni. The spectrum clearly indicates that it is an iron granule. The secondary mineral is probably fayalite, of an unknown wt %.

• Spectrum 4 and 5: The spectra are located in a region of lighter color belonging to the matrix. There is a prominent Si peak, with less intense ones of Mg, Al, Ca and Fe. There is also the presence of Ti, Cr and Mn. There is no defined dominant mineral. The minerals detected are pigeonite (41.8%), anorthite (14.2%), augite (23.4%), ferrosilite (11.2%) and fayalite (8.2%).

• Spectrum 6 and 7: Both spectra are located on the matrix of the meteorite. There is an intense peak of Si with a lesser but also prominent peak of Al, and then Ca, Mg, Na and Fe. The distribution of minerals discloses a higher prevalence of anorthite but the peaks of Mg, Na and Fe hint the presence of pyroxenes. The resulting minerals are anorthite (69.6%), augite (5.4%), pigeonite (21.6%) and labradorite (3.1%).

• Spectrum 8: This spectrum is located on a lighter grey grain in the matrix. It is similar to the results at Spectrum 4 and Spectrum 5 without the presence of Ti and Cr. There is no dominant mineral and needs further analysis to verify the percentages. The identified minerals are anorthite (28.1%), clinoenstatite (12.5%), ferrosilite (10.3%), fayalite (20.6%), olivine (17.2%) and labradorite (2.3%).

• Spectrum 9: It is located on the matrix. The X-ray spectrum is characterised by twin peaks of Al and Si and a half intensity one of Ca. The dominant mineral is clearly anorthite (92.4%). Secondary minerals include fayalite (1.2%), fosterite (2.5%) and labradorite (3.9%).

• Mapping: As previously explained, for the mapping is key to the SEM/EDX images. It can be clearly seen that the grain is made of iron. In the lateral right part there is the presence of S. Additionally, inside the contour of the granule, almost faded, there is Ni. The combination of both metals, Fe and Ni, suggest the presence of kamacite. If looking attentively to Figure 3.15, the SEM/EDX detects also Cr and P inside the metal grain. The matrix is composed mainly by anorthite (see the brightness in Al, Si and less intense, Ca). The more scattered presence of Mg suggests the intrusions of pyroxenes.

42 Lunar Meteorites: Origin and Mineralogy 3.3. NWA 11444

Figure 3.14: Spectrum 1 of the mapping of NWA 11444 (ROI 3). The peak of Fe makes evident the nature of the granule, rich in iron.

The detailed analysis of each spectrum can be found on Section A.3.4.

43 Lunar Meteorites: Origin and Mineralogy 3.3. NWA 11444 Calcium Phosphorus (e) (j) Silicon Sulfur (i) (d) Cromium Aluminium (h) (c) Niquel Magnesium (g) (b) Oxygen ) Iron (f (a) Figure 3.15: SEM/EDX mapping ofof NWA 11444. S in The granule the of lower iron right stands out part as of a the black spot granule, in bordering all elements with except the for matrix iron. of Note the the concentration meteorite.

44 Lunar Meteorites: Origin and Mineralogy 3.4. RESULTS SUMMARY Ni 1.49 0.00 0.96 e (0) F 07.01 6.22 5.48 Ba 0.00 0.00 2.59 S 0.15 0.07 0.84 ZrO2 0.00 10.56 0.00 Cr2O3 0.08 0.07 0.08 P2O5 0.00 0.27 0.08 MnO 0.07 0.17 0.11 eO Components in wt% F 11.75 8.14 11.90 TiO2 0.23 8.57 0.14 Chemical CaO 9.78 3.13 10.33 K2O 0.00 1.86 0.00 SiO2 46.64 46.62 42.06 Al2O3 16.66 6.00 15.72 MgO 4.75 7.71 9.57 able 3.1: Chemical Components in wt% for sample spectra and averaged spectrum T 0.300.00 1.250.00 27.600.00 33.92 1.570.00 7.86 31.640.00 45.57 4.72 2.770.37 8.93 40.45 0.00 13.230.00 0.00 14.68 89.91 18.12 1.440.00 9.60 41.23 0.00 0.00 4.31 11.890.00 20.85 0.00 32.89 2.650.00 10.35 0.00 03.08 51.17 0.00 0.65 04.08 3.250.34 0.00 44.97 0.00 8.52 0.00 0.00 12.07 12.90 49.59 14.130.00 0.00 9.80 0.00 0.27 20.70 0.56 6.25 0.000.44 6.98 9.40 0.00 11.33 01.03 19.52 14.86 0.00 8.98 0.66 0.00 26.26 14.07 0.00 0.00 0.24 1.51 1.98 11.08 47.98 0.00 0.00 0.46 0.01 0.00 2.84 47.35 0.00 0.00 0.00 0.14 0.00 34.48 39.74 3.56 0.00 11.60 0.00 0.00 0.00 0.00 0.00 8.66 0.00 0.00 44.64 0.00 0.33 0.00 0.00 15.53 0.00 0.46 42.21 0.00 0.00 5.27 0.00 0.00 0.57 0.00 0.00 0.00 0.00 40.40 0.00 0.00 0.00 17.87 20.84 0.00 0.00 4.22 0.00 0.00 0.00 0.00 0.35 0.56 0.00 0.18 0.00 0.00 20.10 0.00 0.49 6.60 0.00 11.69 0.35 0.94 0.00 0.00 0.00 0.00 0.00 0.00 0.00 36.31 0.14 0.00 0.25 0.00 0.00 4.48 0.00 0.87 0.00 0.00 0.27 0.00 0.00 0.00 0.00 0.00 1.68 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.63 0.00 0.00 0.00 6.77 0.00 0.00 0.00 0.00 0.00 0.00 0.00 24.17 0.00 0.00 0.00 0.00 22.29 0.00 7.63 0.29 0.00 0.00 5.84 0.00 8.55 0.00 0.00 0.00 0.07 0.00 0.00 0.940.61 2.950.00 1.320.39 10.65 2.710.99 3.12 9.75 74.65 1.82 21.83 6.46 2.66 37.20 11.72 11.25 1.18 1.33 51.71 0.19 58.30 0.30 1.71 0.36 1.10 2.60 0.00 1.48 6.26 3.74 41.82 0.00 1.19 0.72 0.00 21.17 0.00 0.37 0.00 15.52 1.36 0.46 0.00 1.35 0.00 0.01 0.00 0.00 0.33 0.00 0.00 0.00 0.00 52.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.25 0.00 0.00 0.35 0.80 16.38 0.00 0.00 0.00 0.00 12.16 0.00 0.50 0.00 0.00 0.760.22 5.670.00 1.340.43 12.59 11.14 09.08 0.86 11.08 8.00 82.18 33.87 0.00 51.46 0.00 0.00 4.81 44.91 5.38 0.00 10.59 0.00 0.32 0.61 18.37 37.47 0.00 1.47 08.05 0.00 0.27 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.60 24.72 6.46 0.00 0.00 5.97 0.89 0.00 0.00 0.00 Na2O 0.35 0.59 0.11 ectrums Results Summary Sp 1084 Sp.1, Sp.2 1084 Sp.3, Sp.4 1084 Sp.5, Sp.6 1084 Sp.7, Sp.8 1084 Sp.9 1084 av. 838 Sp.1, Sp.2 838 Sp.3 838 Sp.4 838 Sp.5, Sp.6 838 av. A 11444 ROI 1A Sp.1, 11444 Sp.2 ROI 1A Sp.3, 11444 Sp.4 ROI 1A Sp.5, 11444 Sp.6 ROI 1A Sp.7, 11444 Sp.8 ROI 2A Sp.1, 11444 Sp.4 ROI 2A Sp.2 11444 ROI 2A Sp.3 11444 ROI 2A Sp.5 11444 ROI 3A Sp.1, 11444 Sp.2 ROI 3A Sp.3 11444 ROI 3A Sp.4, 11444 Sp.5 ROI 3A Sp.6, 11444 Sp.7 ROI 3A Sp.8 11444 ROI 3A Sp.9 11444 JaH JaH JaH JaH JaH DHO DHO DHO DHO DHO NW NW NW NW NW NW NW NW NW NW NW NW NW NW DHO NW 3.4

45 Lunar Meteorites: Origin and Mineralogy 3.4. RESULTS SUMMARY ts Commen Inconclusive results. Inconclusive results. also for secondary minerals Secondary minerals need to Secondary minerals need to be Secondary minerals need to be Need to verify secondary mineral Need to verify secondary mineral analysed with Raman Spectroscopy analysed with Raman Spectroscopy Further identification is needed with a be analysed with Raman Spectroscopy There is no dominant primary mineral. There is no dominant primary mineral. There is no dominant primary mineral. Presence of Ba (barium) and Sr (strontium) polarised microscope or Raman Spectroscopy Needs to be analysed with Raman Spectroscopy Needs to be analysed with Raman Spectrometry Needs to be cross-checked with Raman Spectroscopy Needs to be cross-checked with Raman Spectroscopy Needs to be cross-checked with Raman Spectroscopy, There is no strong dominance of the primary mineral. Secondary minerals need to be analysed with Raman Spectrometry Inconclusive results. Needs to be analysed with Raman Spectroscopy Probably the wt% of albite is shared with orthoclase (alkali feldspar) There is no dominant primary mineral. Needs to be cross-checked with Raman Spectroscopy There is no dominant primary mineral. Needs to be cross-checked with Raman Spectroscopy Types (from SEM/EDX) results Mineral Minerals fayalite fayalite fayalite pigeonite pigeonite clinoenstatite anorthite, fayalite Secondary clinoenstatite, pigeonite clinoenstatite, ferrosilite anorthite, ferrosilite, fayalite albite, pigeonite, augite, labradorite Minerals albite albite albite zircon augite ilmenite fosterite anorthite anorthite anorthite anorthite anorthite able 3.2: Primary and secondary minerals for sample spectra and averaged spectrum iron granule iron granule T augite, pigeonite anorthite, fosterite Primary clinoenstatite, labradorite anorthite, fayalite, fosterite anorthite, fayalite, kamacite augite, pigeonite, labradorite augite, pigeonite, labradorite albite, augite, pigeonite, ferrosilite ectra Sp 1084 Sp.1, Sp.2 1084 Sp.3, Sp.4 1084 Sp.5, Sp.6 1084 Sp.7, Sp.8 1084 Sp.9 838 Sp.1, Sp.2 838 Sp.3 838 Sp.4 838 Sp.5, Sp.6 A 11444 ROI 1A Sp.1, 11444 Sp.2 ROI 1 Sp.3, Sp.4 A 11444 ROI 1 Sp.5, Sp.6 A 11444 ROI 1 Sp.7, Sp.8 A 11444 ROI 2A Sp.1, 11444 Sp.4 ROI 2A Sp.2 11444 ROI 2 Sp.3 A 11444 ROI 2 Sp.5 A 11444 ROI 3 Sp.1, Sp.2 A 11444 ROI 3 Sp.3 A 11444 ROI 3 Sp.4, Sp.5 A 11444 ROI 3 Sp.6, Sp.7 A 11444 ROI 3 Sp.8 A 11444 ROI 3 Sp.9 JaH JaH JaH JaH DHO DHO DHO DHO DHO NW NW NW NW NW NW NW NW NW NW NW NW NW NW

46 Lunar Meteorites: Origin and Mineralogy 3.5. CONCLUSIONS

3.5 Conclusions

Considering the results obtained, summarised in tables Table 3.1 and Table 3.2, as well as the comparisons made to known lunar regions (see A.3.1) the following conclusions are extracted for each sample:

• JaH 838: According to the wt % of its primary chemical components for the averaged spectrum, this meteorite is a good candidate for low-mare Ti. A particularly low wt% of Ti with a similar combination of Ca and Fe in addition to low Na and lower than average Mg suggest so. However, if only accepting Spectra 5 and 6 as representative of the meteorite (being the only ones belonging to the matrix) it clearly constitutes a lunar anorthosite. Its primary mineral being plagioclase anorthite and the rest sec- ondary minerals such as kamacite, augite and labradorite2. The particular analysis of this sample best fits with the lunar highlands regarding its composition. However, the Meteoritical Bulletin [2] classifies JaH 838 as mingled regolith breccia due to the presence of mare and KREEPy material, HASP3 glasses and chondritic material. This is not incompatible to belonging to the lunar highlands but reduces the region to specific areas with these characteristic materials.

• DHO 1084: for this meteorite there are no clear composition patterns that hint a moon region. The best fit seems to be high-Ti mare but it must be remarked the heterogeneity of the ROI chosen, with many different areas that are not necessarily common across all the meteorite sample. The ones describing purely its matrix are Spectrum 1 and Spectrum 2. They have a peculiar high amount of Si and K and also Al. As previously described when analysing the SEM/EDX spectrum and taking it as the major component of the sample, this meteorite can be classified as an alkali feldspar, predominantly, an orthoclase (or K-feldspar) with unspecified amount of albite (Na-feldspar). On the other hand, the Meteoritical Bulletin [2] classifies it as lunar anorthosite and not a feldspathic breccia. This differences can be attributed to the properties of this particular sample and the bulk properties of the total 90 g of DHO 1084. However, this makes more difficult to classify the origin of this meteorite as maria or highland. There is only a particular component that seem to point to lunar mare: the presence of P.

• NWA 11444: this particular meteorite has 3 ROIs defined (the fourth being a mag- nified area within ROI 3). For each of the ROIs some of the spectra have been located

2Some secondary minerals need further analysis 3High-Al Si-Poor

47 Lunar Meteorites: Origin and Mineralogy 3.5. CONCLUSIONS

in the matrix of the meteorite: Spectra 1 and 2 for ROI 1, Spectrum 3 for ROI 2 and Spectra 6, 7 and 9 for ROI 3. All of them (see the primary mineral on Table 3.2 for the aforementioned spectra) are identified as anorthite. All of the are charac- terised by ∼30 wt% of Al, ∼30 wt% of Ca and ∼40 wt% of Si making evident the presence of this mineral. This results lead to classify the meteorite as plagioclase anorthite. It must be reminded that the Meteoritical Bulletin [2] has this meteorite classified as impact melt breccia, but also that the sample consists of around 200 different pieces. In all of them plagioclase is a predominant mineral. The presence of anorthositic rocks points to the lunar highlands as the probable origin region.

48 Lunar Meteorites: Origin and Mineralogy

Part II Orbital Dynamics Study

4. Introduction

One of the objectives of this thesis is to determine what influences the transference of lunar material to Earth. The study has been built, taking into account the results and limitations of a previous study1 [21]. In addition, we considered previous works on the exchange of rocks between planetary bodies [19], [18]. Gladman results have been reproduced and re-analysed taking part of a first compara- tive study between different scenarios to obtain correlations between different parameters. Afterwards a series of benchmark runs try to reproduce the trajectories of real, well-known lunar meteorites.

4.1 Software and Databases

For this project it is being used a N-Body integrator created by John E.Chambers [9] written in Fortran. In particular, it is a mixed-variable symplectic integrator a type of integrator faster than conventional N-body algorithms and with no long-term accumulation of energy error (only due to the round-off). Other advantages that exhibits this N-Body integrator is that is based on different solvers: Bulirsh-Stoer, Everhart, hybrid-symplectic methods among others, Thus, making it suitable for integrating systems like the Solar system, the 3 and 4 body problem, etc. See [1] and [9] for a detailed description of the integrator. For the computation of the Solar System data (positions and velocities) has been used the JPL HORIZONS online Solar System Ephemeris [26]. The choice of HORIZONS system is owing to the easy access to solar system parameters, the flexibility in which parameters can be requested (different reference systems, different state vectors that define the position of the body, the output format...) and the accuracy and broadness of the ephemerides. Additionally, a Matlab code has been implemented to automate the routines of the N-Body integrator, as had to be repeated for many different configurations. On the other

1Brett Gladman’s PhD Thesis Delivery of Planetary Ejecta to Earth

49 Lunar Meteorites: Origin and Mineralogy 4.2. PREVIOUS WORKS hand, Matlab has been the programming language choice to analyse and plot the obtained results.

4.2 Previous Works

As stated previously, this work has taken Brett Gladman’s PhD Thesis [21] as starting point and the reader is referred to his work to a detailed analysis on the subject. The following lines give an overview of his study on lunar ejecta. First of all, the origin of the coordinate system is defined at the 3-body barycenter between the Sun, Earth and the Moon using a set of initial conditions based on the JPL ephemerides (in cartesian coordinates: velocity and position). Two different models are implemented according to the location in the Solar System in which the ejected particle is: geocentric orbit or heliocentric orbit. In the geocentric orbit or stage consists of a 4-body problem approach where the particle is considered to be inside the Earth-Moon system. For this reason the model only includes the Earth, Moon and Sun as gravitationally influencing bodies and the lunar ejecta as massless particles moving under their effects. The border between what is considered Earth-Moon system and beyond it is defined by a distance 10 times Earth’s Hill 2 sphere radii. In contrast, the heliocentric phase includes all planets from Mercury to Saturn, analysing the Earth-Moon system as a point particle, hence using its barycenter. It is important to note that the heliocentric stage is not only required when the particles surpass the 10 Hill sphere radii from Earth but also when time scales are of 105 years and beyond, when other planetary influences are not negligible.

2The Hill sphere is the region in which smaller bodies tend to orbit a body. Outside the radius of the defined region, the smaller body will be drawn to orbit around the next larger body which the initial hosting body is orbiting [24]. Earth’s Hill radius is 0.01 AU. Heliocentric phase is considered when the particle is beyond the 0.1 AU from Earth.

50 Lunar Meteorites: Origin and Mineralogy

5. Simulations of Lunar Ejecta

As there is no record of the fall of a lunar ejecta and neither the monitoring of an orbit, there is no empirical data to contrast results directly. This is why Gladman’s work is paramount for this study and its results are taken as reference. This project not only tries to reproduce Gladman’s results but builds on them, giving a deeper insight on the geocentric stage as well as a multiple-scenario analysis on a recorded impact. The simulation of the ejected particles is done with a N-body integrator that is based on a Bulirsh-Stoer algorithm (see Section 4.1). A set of 500 launching sites are randomly generated over the surface of the Moon, with all regions having the same proba- bility 1. The default elevation angle is set at 45º and the limit between the geocentric and heliocentric spaces is maintained at 10 times Earth’s Hill radii. Regarding the maximum time scale that is acceptable for the geocentric phase it has been considered at 104, one order of magnitude below Gladman’s2

Figure 5.1: Geographic map of the Moon showing 500 randomly generated launching sites.

In contrast to Gladman’s work, in this project each launching site corresponds only to one particle and all the launched particles are set at the same elevation and local azimuth. By doing this, variations that result from the direct change in launching parameters are easier to spot and correlate. The process is as follows, for a particular velocity 500 launch- 1See Section A.1.1 for a detailed description of launch sites generation. 2Some meteor shower orbits exhibit changes due to secular perturbations every 3000-4000 years [16].

51 Lunar Meteorites: Origin and Mineralogy ing sites are randomly generated (corresponding each to an ejected particle) with the same local azimuth: towards East, North, West or South. Obtaining four different trial samples for each direction.

(a) Launch towards West, ejection angle 45º (b) Launch towards South, ejection angle 45º

(c) Launch towards West, ejection angle 90º (d) Launch towards South, ejection angle 90º

Figure 5.2: Launching sites and velocities for different directions of launch and ejection angles. Velocity vector not to scale. Ejection angle defined from the local vertical at each point.

Moon coordinates

In order to later correctly interpret some of the results, it is important to give some brief notes on the Moon coordinate system used. For this project the selenocentric coordinates system is the system of choice when referring to cardinal points, latitudes and longitudes from the Moon. This system has its origin in the centre of mass of the Moon and is defined by three ortonormal vectors, two of them contained in the lunar equatorial plane and the other perpendicular to it (and facing northwards). Taking advantage that the equatorial plane of the Moon is only tilted 1º32’ [32] from the ecliptic, the lunar North direction is approximated to the normal vector of the ecliptic plane. The prime meridian (0º longitude) can be imagined

52 Lunar Meteorites: Origin and Mineralogy as a plane that slices the Moon in two halves, defined by the vector that unites the centre of the Earth with the centre of the Moon and the normal vector to the ecliptic. When referring to the direction of the launches, they will be referencing this coordinate system as shown in Figure 5. See Section A.1.2 for a detailed description on the generation of lunar coordinates and reference frames used in the project.

Launch angle

During the geocentric phase some meteoroids do not survive, either by impact with the Earth Figure 5.3: Moon coordinates. Image ex- or the Moon. There is a parameter able to predict tracted from [38], the cardinal points have the particle’s fate, which combines the local ele- been added. Latitude and longitude lines drawn at 10º intervals. vation, azimuth and location of the launch site of the ejecta. This parameter is defined as the angle between the launch velocity vector and Moon’s velocity vector (both seen from the Earth), re- ferred as launch angle.

Figure 5.4: Velocity vectors in mooncentric and geocentric orbits

This angle is interesting for two reasons: allows a side-by-side comparison with Glad- man’s results and on the other hand, provides proof to a qualitative reasoning of why some ejecta escape to heliocentric orbit and why others do not. If the Moon-ejecta system is seen from Earth, the geocentric velocity of the ejected particle will be the vector sum of its launch (mooncentric) velocity vector and the Moon (geocentric) velocity. One must expect from those particles whose angle with respect to the Moon’s orbital velocity is < 90º to exceed the geocentric escape velocity and escape directly to heliocentric orbit. In contrast, seems plausible to expect that particles with opposed direction to the Moon’s orbital velocity (≈ 180º) to be almost at rest with respect to the Moon and remain trapped

53 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS in a geocentric orbit.

5.1 Short transfers

In celestial mechanics, the time scales are several orders of magnitude greater the lifespan of a human being. When referring to transfers as short, it means that the time scales analysed produce reliable predictions with the most simple model, the Sun and the origin system from which the meteoroid was ejected (in this case Earth and Moon system). This 4 body problem, with the fourth mass as massless object (the lunar ejecta), holds until the 104 years after launch. This stage is also referred as geocentric phase. Beyond that point in time perturbations caused by other bodies in the Solar System are no longer negligible and the particle enters the heliocentric stage regime. The study of short transfers is organised in case studies each one with a characteristic velocity ranging from 2.3 to 3.0 km/s in steps of 0.1 km/s. During the different tests some parameters are held constant and others vary in order to unveil tendencies and correlations between them. Firstly, the direction of the launch is studied, then the variation of the ejection angle and eventually the relative position of the system Earth-Moon-Sun. The reference system is set with origin at the Sun, and if not stated otherwise the initial date and configuration is the following:

Geocentric Phase Initial Conditions Parameter Earth Moon M (in solar masses) 3.0034E-06 3.6951E-08 x 3.371107496568450E-01 3.374547808509278E-01 y 9.264949518099805E-01 9.238437009848245E-01 z -3.902460613157016E-05 1.633263894824704E-04 vx -1.645444011529152E-02 -1.589416950978892E-02 vy 5.817832219013652E-03 5.905723819651551E-03 vz 1.760665556639497E-07 -2.585073131750727E-05

Table 5.1: Geocentric Initial Conditions on Julian Date 2457724.5 (December, 2nd 2016)

5.1.1 Variation of launch direction

This study can be considered as a reproduction of Gladman’s results with a further insight on how the launching direction influences the trajectories and particularly impacts on Earth. The key parameters defined are:

• Velocities tested (in km/s): 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0. The velocity is 2.3 km/s is below the lunar escape velocity (2.38 km/s)3. This velocity is tested to check

3 p The lunar escape velocity is 2.38 km/s (= 2GMm/Rm)

54 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

that the results are in accordance to physics predictions and no object escapes the Moon, so ends up impacting its surface.

• Ejection angle [º]: 45

• Time scales (in years): 1, 10, 100, 1000

• Direction of the launch (lunar geography): East, North, West, South

Launch Variation Gladman case study Earth-Moon-Sun Input Reference System Sun barycenter min: 360 Number of particles 500 max:1080 min: 20 Launch sites 500 max: 60 Ejection angle 45º 45º automatically chosen by integration algorithm (Bulirsch-Stoer). Time Step 0.04h Maximum 1 d (1-10 years), 5 d (100-1000 years) Launch of 18 particles from each Launch of one particle for each launch site randomly distributed launching site, randomly distributed Brief description on the surface of the Moon. on the surface of the Moon. Same ejection angle, variable azimuth Same ejection angle and local azimuth

Table 5.2: Comparison of the simulation settings

Tables 5.3 and 5.4 show the results of lunar ejecta numerical simulations. As expected, for a velocity of 2.3 km/s (below the lunar escape velocity of 2.38 km/s) all particles collide with the Moon. At a first glance, a certain ejection velocity produces a maximum amount of particles that impact with Earth; below or above that velocity impacts with Earth become rarer. The same can be said for the Moon, the greater the ejection velocity (above the escape speed) the less amount of particles that collide with it. In fact, there is a considerable drop in lunar impacts from 2.4 km/s (6%) and 2.5 km/s (near 1%). This can be explained as at vl = 2.4 km/s particles escape only at 20 m/s above the lunar escape velocity having almost a null velocity relative to the Moon . These particles end up in a nearly circular orbit around Earth and will become scattered or pulled back again multiple times by the Moon [21].

55 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

Table 5.3: Geocentric-stage simulations in Gladman study. The averaged values have been added for a later comparison. Esc particles refer to those that escape to heliocentric space, Earth are those that impact the Earth and Moon the ones that impact the Moon. The simulations marked with (*) have the initial conditions of the heliocentric simulation (see [21]).

vl [km/s] N Esc [%] [%] Earth [%] Moon 2.3 360 0 0 100 2.4 360 88.1 3.3 8.6 2.4 360 91.7 3.9 4.4 2.4 360 90 3.3 6.7 2.4 720 91.1 2.2 6.7 2.4* 360 90.5 3.1 6.4 2.4 (Average) 432.00 90.28 3.16 6.56 2.5 360 92.8 5.5 1.7 2.6 360 80 18.9 1.1 2.6 720 83.7 16 0.3 2.6* 360 81.7 18 0.3 2.6 (Average) 480.00 81.80 17.63 0.57 2.8 360 81.4 18.1 0.5 2.8 360 77.2 22.5 0.3 2.8* 360 80.2 19.2 0.6 2.8 (Average) 360.00 79.60 19.93 0.47 3 360 95.3 3.9 0.8 3* 360 94.7 5 0.3 3.0 (Average) 360 95 4.45 0.55 3.2 360 100 0 0 3.2 1080 99.3 0.7 0 3.2* 360 99.1 0.6 0.3 3.2 (Average) 600.00 99.47 0.43 0.10 3.5 360 100 0 0

56 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

Table 5.4: Each velocity has a launch direction and the average of the four directions. Results are calculated for a timescale of 100 years and of 1000 years. Esc, Earth and Moon represent escaped velocities to heliocentric space, Earth impacts and Moon impacts respectively. vl [km/s] Direction N Esc [%] 100y Esc [%] 1000y [%] Earth 100y [%] Earth 1000y [%] Moon 100y [%] Moon 1000y 2.3 South 500 0 0 0 0 100 100 2.3 West 500 0 0 0 0 100 100 2.3 East 500 0 0 0 0 100 100 2.3 North 500 0 0 0 0 100 100 2.3 Average 500 0 0 0 0 100 100 2.4 South 500 89 79.2 3.4 14.4 3.2 3.4 2.4 West 500 83.2 69.6 4.4 19.6 8.6 8.8 2.4 East 500 84 72.8 4.8 16.8 7.8 8.2 2.4 North 500 89.6 81.2 3.8 13 3.4 3.6 2.4 Average 500 86.45 75.7 4.1 15.95 5.75 6 2.5 South 500 89.6 82.8 5.8 13.2 0.4 0.6 2.5 West 500 82.2 77 11.4 18 2.4 2.4 2.5 East 500 83 78.2 12.8 17.6 1.2 1.2 2.5 North 500 91.4 85 5.2 10.4 0.4 0.6 2.5 Average 500 86.55 80.75 8.8 14.8 1.1 1.2 2.6 South 500 87.2 84.4 9 12 0.8 0.8 2.6 West 500 72.4 70.8 24.2 26.4 0.4 0.4 2.6 East 500 71 68.4 26.2 29.4 0.8 0.8 2.6 North 500 88 85.6 8.8 11.6 0.6 0.6 2.6 Average 500 79.65 77.3 17.05 19.85 0.65 0.65 2.7 South 500 86.6 84.8 10.8 12.4 0.4 0.4 2.7 West 500 67.2 65.6 30 32 0.6 0.6 2.7 East 500 75 73.8 21.8 22.8 1.2 1.2 2.7 North 500 84.8 84 12.8 13.8 0.2 0.2 2.7 Average 500 78.4 77.05 18.85 20.25 0.6 0.6 2.8 South 500 89.6 88.4 6.8 8.6 0.4 0.4 2.8 West 500 75.2 74.2 22.2 23 0.4 0.4 2.8 East 500 75.6 75.2 20.2 21.4 0.6 0.6 2.8 North 500 87.8 86.6 9.2 10.2 0.2 0.2 2.8 Average 500 82.05 81.1 14.6 15.8 0.4 0.4 2.9 South 500 92.2 93.6 3 3.6 0.2 0.2 2.9 West 500 82 83.8 12.6 13.2 1.2 1.4 2.9 East 500 83 82.2 11.8 12.8 1 1.2 2.9 North 500 90 88.4 7 8.4 0 0 2.9 Average 500 86.8 87 8.6 9.5 0.6 0.7 3.0 South 500 94 95.2 2 2.2 0.2 0.2 3.0 West 500 89.6 92.4 4.4 5.8 0.4 0.4 3.0 East 500 92.2 90 4 6.6 0.6 0.6 3.0 North 500 93.6 95.2 1.8 2.6 0.4 0.4 3.0 Average 500 92.35 93.2 03.05 4.3 0.4 0.4

Interestingly, Table 5.4 makes evident the differences between launching in a specific direction. Specially Earth but also Moon impacts have a higher tendency to occur if the launch is produced Westwards or Eastwards than Northwards or Southwards. This is a predictable result and can be illustrated with a simplified example: as previously said, the particles launched at the opposite direction of the Moon will eventually stabilise in a semi-circular orbit similar to that of the Moon, hence, will encounter the satellite many times and will have a greater chance to end up colliding with it. The particles launched in a perpendicular direction to the velocity of the Moon will describe orbits with steeper inclinations (Moon’s obliquity being 6.68º with respect to the ecliptic) being less susceptible to lunar gravity assists and potential collisions.

57 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

Table 5.5: Comparison of geocentric-stage simulations between Gladman’s work and this project. Go to 5.2 to see the specifications for each simulation

Esc [%] Esc [%] [%] Earth [%] Earth [%] Moon [%] Moon vl [km/s] (Gladman) (100y) (Gladman) (100y) (Gladman) (100y) 2.3 0 0 0 0 100 100 2.4 90.28 86.45 3.16 4.1 6.56 5.75 2.6 81.80 79.65 17.63 17.05 0.57 0.65 2.8 79.60 82.05 19.93 14.6 0.47 0.4 3.0 95.00 92.35 4.45 3.05 0.55 0.4

The Table 5.5 shows a comparison between the averaged percentages of escaped parti- cles, Earth collisions and Moon collisions for velocity values common in both works. The value of the percentages are similar within an acceptable range, with a maximum absolute error of 5.33(%) and a minimal of 0.07(%) (for the 2.8 km/s Earth impacts and Moon impacts respectively). One main difference is that in this study the velocity at which more Earth impacts occur on average is 2.7 km/s (and not 2.8 km/s). As seen in Figure 5.5, when segregating the results by direction of the launch, 2.7 km/s is the one with a higher accumulated percentage of Earth collisions except for launches towards the East direction, being surpassed by launch velocity 2.6 km/s.

(a) Accumulated percentage of Earth impacts after 100 years (b) Accumulated percentage of Earth impacts after 1000 years

Figure 5.5: Variation of Earth impacts with launch velocity. Each line represents a launch direction: blue (West), yellow (East), red (South) and purple (North). Launches at 2.3 km/s have been excluded as all particles collide with the Moon.

In Figure 5.7, one can observe the relation between the launch angle of a particle and the time until it collides with Earth. Note that particles launched at 2.4 km/s are found randomly scattered in both axis, time and launch angle, with an upper limit at 160º, where no more particles result in Earth impact. Particles ejected with a launch angle near 180º barely have any velocity when they leave the Moon system and mostly impact with the Moon or more rarely with Earth. Launch angles ≈ 160º allow the particle to escape

58 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS the Moon system despite their low velocity. Those particles remain inside the Earth- Moon system and are repeatedly perturbed by the Moon’s gravity, eventually colliding or escaping to heliocentric phase (see Figure 5.6). As velocity increases particles get accumulated in a smaller range of angles and time. The launch at 3 km/s presents a few Earth collisions taking place before the first 200 years, 2 Moon impacts between launch angles [120º, 160º] and three outliers beyond 200 years. For a launch velocity of 2.6 km/s particles can be classified into three groups according to the launch angle:

• Range [120º 180º]: particles impact Earth within the first 10 years

• Range [60º 120º]: particles are scattered along time, meaning that they become trapped within the Earth-Moon system

• Below 60º less than 10 particles end up colliding with Earth as most gain enough energy to escape to heliocentric orbit

Figure 5.6: Trajectories of two particles in geocentric orbits. The black halo repre- sents the orbit of the Moon, the pink points represent the trajectory of a lunar ejecta that in 202 days impacts with Earth, the green markers represent the orbit of a lu- nar ejecta that in 24 days impacts with the Moon. Note that the trajectories of the ejecta are contained inside the Hill’s re- gion (0.1 AU). The particle that collides with Earth (pink) performs multiple fly- bys around Earth and a gravity assist of the Moon energises the orbit, but not enough to escape for the heliocentric space. (Earth not to scale).

59 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS Launch towards West at 2.4 km/s Launch towards North at 3.0 km/s (b) (d) Launch towards East at 2.6 km/s Launch towards South at 2.3 km/s (c) (a) Figure 5.7: Evolution ofangles the with meteoroid respect impact to population thewith for geocentric different Earth. velocity velocities of It and the launch isEarth. Moon directions. easy varies with With to time. each see of Red that them triangles different the represent velocities distribution impacts of and with launch the launch Moon directions and will blue yield squares in impacts shorter or longer transfer times between the Moon and the

60 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS Launch towards West at 2.4 km/s Launch towards North at 3.0 km/s (b) (d) Launch towards East at 2.6 km/s Launch towards South at 2.3 km/s (c) (a) Figure 5.8: Evolutionprovides of a the meteoroid different impactmatter perspective of population for days. for the Particularly, differentdistribution for distribution velocities and velocity of 2.6 as and km/s collisions time launch towards increases directions during the it (logarithmic time. East decays scale). shows and a It becomes The linear more is tendency logarithmic noisy. between clear scale launch that angle the and time fastest at particles the are beginning of transferred the to Earth in a

61 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

Finally, the influence of the launch site in the lunar ejecta’s fate is analysed. On the one hand, the launch angle has proven to be a key parameter to predict if a particle will collide with Earth. The next question would be: which is the launching site of that particle? The answer is at least constrained by one parameter: the direction of the launch (see Section 5). For example, a set of particles is launched at 2.7 km/s towards the West. According to Figure 5.7, particles that end up impacting with Earth were launched with a launch angle of ≈120º or higher. As all particles are launched at the same local azimuth and elevation, it provokes that the only sites on the lunar surface that provide those particular launch angles become concentrated on the Far Side of the Moon (approximately between longitudes [120º 180º] and [-120º -180º]). In contrast, for launches towards the East, the particles that eventually collide with Earth concentrate on the Near Side of the Moon, being for those longitudes when the orientation of the launch velocity virtually opposes the velocity of the Moon. Furthermore, observing Figure 5.10.a and Figure 5.10.c there is a symmetry between launches towards the North and the South. For a southwards launch, particles that collide with Earth cluster in northeastern latitudes. At those sites the launch velocity vector is almost the same direction and with opposite orientation to the Moon’s.

(a) Launch towards North (b) Launch towards East

Figure 5.9: Launch angle of particles according to their launch site and their direction of launch. Note that the locations where the angle approaches 120º with the Moon’s velocity most particles will collide with Earth (see the correlation with Figure 5.10). This plot establishes a link between the launch angles and the fate of the particle taking into account its original launching site.

Figure 5.11 shows the distribution of the particles according to their fate with time for a launch velocity of 2.5 km/s towards West. Note the concentration of particles after one year that become trapped in geocentric orbit. The future collisions with Earth (and also the Moon) will be expected from that region. It is also interesting to remark the scattering of Earth collisions in Figure 5.11.d and the clustering in Figure 5.10.d, a behaviour reflected also while plotting the launch angles (Figure 5.4).

62 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS Launch towards East Launch towards West (b) (d) Launch towards North Launch towards South (c) (a) Figure 5.10: Correlation betweenin launching site the and regions Earth collisions whereorientation. with the All varying launch cases launching direction. are velocity Particles for and that a end the launch up Moon’s colliding velocity with of velocity Earth 2.7 (both cluster km/s. seen from the Earth) have virtually the same direction with opposite

63 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS Particle’s fate after 10 years Particle’s fate after 1000 years (b) (d) Particle’s fate after 1 year Particle’s fate after 100 years (a) (c) Figure 5.11: Correlation betweenand launching site particles and are Earth launched collisions towards with the varying West. launch direction at different times. The launch velocity is 2.5km/s

64 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

Until this point, all analysis have focused on the fate of the particle: impact with Earth, impact with the Moon, escapes to heliocentric orbit or remains in geocentric orbit. A matter of interest is the transfer time4 of the particle. Indirectly, this concept has been tackled on Figures 5.7 and 5.8. At a first glance, seems evident that the velocity of the launch is the main responsible of the distribution in time of the particles. Additional graphs have been done to understand better the effects on the transfer time and can be consulted on Section Figures A.1 and A.2. Indeed, the velocity of the launch creates clusters earlier or further in time according to its value but the plots reveal two other trends:

• as time increases the launch angle in which particles collide decreases

• eastward/westward launches present higher clusters at early collisions that north- wards and southwards counterparts.

The second statement can be directly answered by observing Figure 5.9. Launches towards the West and the East have more particles with a favourable (120º or above) launching angle for collision, hence, more will collide during the first year. The first statement can be reasoned in the following way: particles launched at smaller launch angles were more energetic, they could escape to heliocentric orbit or at least remain in geocentric. In any case, to eventually collide with the Earth (or the Moon) more time will be required that those launched at ≈120º. Section 5.1.3 focuses in further detail on the transfer time of the ejecta.

4Referring to transfer time as the time a particle takes from its launch to its impact with Earth.

65 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

5.1.2 Variation of Ejection Angle

The same proceeding used in Section 5.1.1 has been implemented for the ejection angle analysis. To avoid redundant data, tests performed that did not add new information are provided on Annex A.2.2. A total of four additional ejection angles (defined from the local vertical, see Figure 5.4) have been studied: 0º, 22.5º, 67.5º and 90º. Given an ejection angle, all selected velocities5 for each of the launch directions (North, East, South, West) are tested. This analysis goes further than in Gladman’s work, where a set of experiments holding the velocity fixed at 2.4 km/s and varying the angle with respect to the local vertical show no apparent dependence (see [21] pag. 30-31). This table contains the aforementioned results:

Angle Esc (%) Earth (%) Moon (%) 10º 90.5 3.1 6.4 25º 93 2.8 4.2 45º 88.1 3.3 8.6 45º 91.7 3.9 4.4 45º 90 3.3 6.7 45º 91.1 2.2 6.7 45º 90.5 3.1 6.4 45º (average) 90.28 3.16 6.56 60º 91.7 2.2 6.1 75º 91.6 1.7 6.7 89º 90.7 3.3 5.8

Table 5.6: Fate of the lunar ejecta for varying ejection angle and launch speed 2.4 km/s. Retrieved from [21]. The averaged value at 45º has been added to the original table.

Nevertheless, if the study is extended for the eight different velocities the non-dependence shown by 2.4 km/s cannot be extrapolated to the rest. In fact, Figure 5.12 shows a non- dependence for the fate of the particles varying the ejection angle that holds until 2.5 km/s. Abruptly for 2.6 km/s, 2.7 km/s and 2.8 km/s the ejection angle influences the amount of Earth impacts and again with 2.9 km/s and 3.0 km/s the dependence seems to fade. The launch velocities at which more Earth impacts occur are more susceptible of variations of the ejection angle than those that are above or below. For the case of 2.9 km/s and 3.0 km/s the explanation could be the following: particles are ejected with enough energy to escape to an heliocentric orbit regardless of the ejection angle. The following plots in this section explore the different behaviours in relation to the ejec- tion angle.

5Launch velocities respect to the lunar surface used in this project: 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3.0 km/s

66 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

Figure 5.12: Histogram of Earth Impacts as function of ejection angle and ejection velocity. The histogram shows the accumulated percentage of Earth impacts after 100 years have passed. All particles have been launched towards the West. Note that for velocity 2.4 km/s there is no correlation with the ejection angle.

Figure 5.13: Flat view of the four histograms for Earth Impacts as function of ejection angle and ejection velocity. Each of them is a 2-D top view of an histogram like Figure 5.12

Furthermore, the correlation of Earth impacts as function of velocity and ejection angle also depends on the direction of the launch as shown in Figure 5.13. One thing shared by all histograms is that velocities highly susceptible to ejection angle variation are comprised between 2.6 and 2.8 km/s. But the effects of varying the ejection angle seem to provoke

67 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS opposite effects between the West/East groups and North/South groups. First of all, for launches towards the East or West: the minimum value of Earth collisions (for ejection angle 0º) is half of the maximum value for the optimal ejection angle (ejection angle 67.5º) (see Table 5.7), making the difference not negligible. Furthermore, for eastwards and westward launches, the peak occurs at an ejection angle of 67.5º (with the local vertical) smoothly decreasing until reaching 0º and abruptly decreasing if the ejection angle is 90º. In contrast, northwards and southwards launches have a cumulative percentage of Earth impacts more homogeneous and hit a minimum at between 45º and 67.5º of ejection angle. At the two extremes (0º and 90º) the amount of Earth collisions are maximum (see Table 5.7). Let’s focus on two scenarios experimented by the launch velocity 2.6 km/s: the launch towards the East and the launch towards the North. To shed some light on why the cumulative Earth impacts depend on the ejection angle Figure 5.14 compares the results for all angles to the reference angle (45º). For the case of the launch eastwards, the function that better adjusts the distribution is Weibull (note the skewness towards the right). The ejection angles below 45º not only lower the population of Earth collisions but concentrate the launch angles at which collisions occur, consequently decreasing the standard deviation of the distribution. When the ejection angle is above 45º the range of launch angles is broader: for the ejection angle 67.5º the population increases without changing the shape of the distribution (see the global overlay between the two). For an ejection angle of 90º the impact population decreases as well as the value of the mean and the standard deviation increases. If focusing on the plots vs. time one can see a the linear part occurring during extremely short transfers (between 3 and 30 days) and then a scattering across time. This brief lineal tendency appears for 45º, is more prominent for 67.5º and starts to fade at 90º. In the case of the launch northwards the distribution of collisions can be considered normally distributed. Its population reaches a minimum with ejection angles 45º and 67.5º. When the ejection is 90º the distribution’s curve is notably displaced to the left (to a lower mean). The ejection does not seem to affect the scattering of the particles during time.

68 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS Launch at 2.6 km/s towards the North (b) Launch at 2.6km/s towards the North (d) for the probability distribution. A.4 Launch at 2.6 km/s towards the East Launch at 2.6km/s towards the East (c) (a) Figure 5.14: Comparison betweenthe ejection launch angles. angles The (y-axis) fourthe at plots left c) in y-axis and a) d) indicates andscale). respectively the in (only count The b) after and are variation 100 the theits in years right histograms behaviour ejection have y-axis and in passed). angle the the time. produces P.D.F. The probability The x-axis See changes density plots of function Figure in: c) the (P.D.F.) of the and histograms d) population indicate indicate the of the launch Earth angle launch collisions, while angle the distribution shape in time of (in the logarithmic distribution for the collisions and

69 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS vl [km/s] Direction Ejection angle [º] N Esc [%] 100y Esc [%] 1000y [%] Earth 100y [%] Earth 1000y [%] Moon 100y [%] Moon 1000y 2.6 East 45 500 71 68.4 26.2 29.4 0.8 0.8 2.6 East 0 500 78.4 81.4 14 15.6 1.4 1.4 2.6 East 22.5 500 77.4 75.2 19.2 20.8 1 1 2.6 East 67.5 500 62.6 59.2 34.6 38.2 0.4 0.4 2.6 East 90 500 78.8 76.2 18.6 21.2 0.4 0.4 2.6 North 45 500 88 85.6 8.8 11.6 0.6 0.6 2.6 North 0 500 82.6 80.6 14.6 16.4 0.6 0.6 2.6 North 22.5 500 79.8 80.2 15.2 17.2 0.6 0.8 2.6 North 67.5 500 86.4 83.4 9.6 13.6 0.2 0.2 2.6 North 90 500 80.2 79.2 16.2 18 1.4 1.4

Table 5.7: Comparison between ejection angles. The numbers of columns 100y correspond to the results of Figure 5.14. Note that for the eastwards launch, the greatest value of Earth impacts (34.6%) is more than twice the lowest (14 %). As initial populations are the same and Moon impacts remain below 2%, this means that the amount of particles that impact Earth with 67.5º ejection angle are two times those launched with 0º ejection angle. The difference in collision rate between ejection angles seems to be linked to the original distribution on the lunar surface of the particles with > 120º launch angle. For an ejection angle of 0º (which means that is a launch in the local vertical direction), the region with favourable launch angle is twice the region with ejection angle 45º (see Figure 5.15). For this reason, southwards and northwards launches with ejection angle 0º present a larger population of collisions than the rest of ejection angles as this configuration generates a maximum population of ejecta with favourable launching angle. The opposite it is true for eastwards and westward launches, the area with favourable launch angles becomes minimum for ejection angle 0º.

(a) Ejection angle 45º (b) Ejection angle 0º

(c) Ejection angle 90º (d) Ejection angle 0º

Figure 5.15: Launch angle of particles according to their launch site (a) and b) northwards launch, c) and d) eastwards launch). Northwards launch: The region with favourable launch angle for the ejection angle 0º goes from [60º 120º] longitude, to [-30º 30º] latitude. For the ejection angle of 45º the longitude remains the same but the latitude varies from [-60º -30º]. Eastwards launch: for ejection angle 90º any latitude has launch angles > 120º between [-30º 30º] longitude. For ejection angle 0º the region is the same as the launch towards North.

70 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

5.1.3 Variation of Earth-Moon-Sun configuration

Another factor that has been considered as potentially have effects on the lunar ejecta is the relative positions among the Earth, Moon and the Sun. In this analysis there are 4 different case studies each of them with a different starting date, which translates to a different Earth-Moon-Sun configuration. The starting dates are: after 7 days, 14, 21 and 28 days (see Figure 5.16 for each configuration) from the initial date. The time interval of 7 days has been chosen for the sake of simplicity and split the relative position of the Moon with respect to the Earth and the Sun in quarters. The parameters defined are those of Section 5.1.1 for each different initial date:

• Set of test velocities: 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3.0 all in [km/s]

• Ejection angle in [º]: 45

• Time scales (in years): 1, 10, 100, 1000

• Direction of the launch: East, North, West, South

The aim is to detect differences resulting of the change in the configuration of the Earth-Moon-Sun configuration, investigating if:

• There are changes in the percentages of Earth impacts.

• If other parameters vary. Even if the ratio of particles that impact the Earth remains the same with respect the total of launch particles, it is possible that varying the geometric configuration of the problem could affect to the transfer of particles Moon- Earth. The minimum and maximum transfer time that lunar ejecta take to reach Earth will be evaluated and also at which velocities occur for each configuration.

As in the previous studies, the analysis has been cumulative. This means that all previ- ous conclusions have been tested if they held with varying initial configuration, afterwards, other tests were performed on the data.

71 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

(a) Initial Earth-Moon-Sun Configuration. Julian Date 2457724.5

(b) Earth-Moon-Sun Configuration after 7 (c) Earth-Moon-Sun Configuration after 14 days. Julian Date 2457731.5 days. Julian Date 2457738.5

(d) Earth-Moon-Sun Configuration after 21 (e) Earth-Moon-Sun Configuration after 28 days. Julian Date 2457745.5 days. Julian Date 2457752.5

Figure 5.16: Different Earth-Moon-Sun configurations for lunar ejecta launches. The arrows indicate the directions in which the Sun and Moon are heading from the Earth’s perspective. Observe that after 28 days, image (e), the arrows heading towards the Moon and the Sun are not in the exact same position as in image (a). This difference is due to the 7 days increments instead of exactly 7d 9h to complete a synodic month (≈ 29d 12h). The lag is noticeable after a full translation of the Moon around the Earth.

72 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

Figure 5.17: Earth impacts for different velocities and initial dates. Each plot is divided according to the direction of launch. The timescale at which percentages are calculated is 100 years after the initial date. Note that each velocity group has one particular colour indicating the same number of Earth impact [%]. The exception is velocity 2.7 km/s which presents a variation at 7d and 21d, at both eastwards and westward launches.

Observing Figure 5.17, overall, there is no correlation between the position of the Moon with respect to Earth and Sun and the amount of impacts on Earth. In the case of northwards and southwards launches Earth impacts are contained between 0% and 15% regardless of the velocity (with 2.6, 2.7 and 2.8 on the upper side). In eastwards and westward launches the value of the velocity correlates with the % of Earth impacts but not the configuration. Each specific velocity has an homogeneous colour, indicating that the oscillation in Earth impacts does not exceed of a 5% difference. Nevertheless, there is one velocity that proves to be more susceptible to changes in the configuration: launch velocity 2.7 km/s. Supported by the results in Table 5.8, the differ- ence between the minimum and maximum Earth impacts are of 10%. Particularly, seems to exist a peak in collisions for the configurations after 7 days and 14 days respectively. Unlike Figure 5.13, were collisions increased gradually as ejection angle approached 67.5º, in this case peaks seem to have occurred randomly. For this reason, before concluding that configuration after 7 and 14 days has any repercussion on the amount of Earth impacts additional tests have been performed and can be found at Section A.2.2, Figures A.5, A.6 and A.7. These additional tests confirm that velocity 2.7 km/s is the most susceptible to the change in configuration and that there is a maximum 10% difference between the maximum and minimum values, but also that the peaks are randomly distributed and not

73 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

associated with any configuration in particular. vl [km/s] Direction days after JDi N Esc [%] 100y Esc [%] 1000y [%] Earth 100y [%] Earth 1000y [%] Moon 100y [%] Moon 1000y 2.6 East 0 500 71 68.4 26.2 29.4 0.8 0.8 2.6 East 7 500 72.2 68.2 26 28.4 0.6 0.6 2.6 East 14 500 72.8 70.4 23.6 27.2 0.2 0.2 2.6 East 21 500 71.8 70.2 24.6 27.4 0.6 0.6 2.6 East 28 500 74.2 71.6 22 25.6 0 0.2 2.6 average East 500 72.4 69.76 24.48 27.6 0.44 0.48 2.7 East 0 500 75 73.8 21.8 22.8 1.2 1.2 2.7 East 7 500 65.4 63.6 31 32.2 0.8 0.8 2.7 East 14 500 73 71.4 23.6 24.8 1.2 1.2 2.7 East 21 500 67 67.2 29.4 30.4 0.2 0.2 2.7 East 28 500 71.2 69.6 24.8 27.2 1.2 1.2 2.7 average East 500 70.32 69.12 26.12 27.48 0.92 0.92

Table 5.8: Earth impacts for two velocities and different initial dates. Note that the numbers of this table correspond to those that can be found in Figure 5.17 for velocities 2.6 and 2.7 km/s. In particular, it is the data from column % Earth 100y that corresponds to the colour pattern in the aforementioned figure. For 2.6 km/s at any initial date, the colour is green. This is translated to an almost constant value of the percentage of Earth impacts. By comparing the data in the table, it can be observed that the difference between the highest and lowest value is is below 5%. In contrast, for velocity 2.7 km/s the yellowish colours after 7 and 14 days stand out from the rest and looking into the table one can see that the highest value reaches 31%, 9.2% above the lowest value (21.8%) .

Performing additional tests is even more important when analysing the minimum trans- fer time of a particle from the Moon to Earth. The reason is because this minimum value will depend only on one particle, the fastest one, so it is not a ’bulk’ value, averaged from the set of particles. Then, performing additional tests allows to distinguish between outlier values and trends. On average, westwards and eastward transfers are faster than those of north and south launches. Velocities 2.4 and 2.5 km/s produce the slow- est ejecta regardless of the direction of launch and the fastest occur at 3 km/s. But for example, the westwards launch 21 days after JDi at 3 km/s takes around 200 days. The value stands out from the rest launched at the same velocity, which are two orders of magnitude below. Is this particular E-M-S configuration and velocity causing this result or it happens to be an extreme improbable value? Plots A.8, A.9 and A.10, A.11, A.12 and A.13 in Section A.2.2 are proof of its outlier nature. That value is not representative for all launches towards west at 3 km/s passed 21 days. What it is true is that velocities 2.9 and 3 km/s are more heterogeneous and produce more frequently outliers at least an order of magnitude above the average than 2.6, 2.7 and 2.8 km/s velocities. A different way of visualising data of Figure 5.18 is featured in Figure 5.19. The values correspond to the minimum, maximum, mean and median time that takes a particle launched at a particular day to reach Earth. It corroborates that westward and eastward launches are homogeneous and fast (the median time being just 3 days). The most common velocity for the fastest transfer is 3 km/s while 2.4 km/s is the one for the slowest transfers.

74 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

Figure 5.18: Minimum time for a lunar ejecta to impact with Earth, in days. The plot represents the time for the first lunar ejecta to impact with Earth for each velocity and particular launching date. The colour scale is logarithmic to be able to distinguish the different orders of magnitude of ejecta transfers: the fastest take as little as 3 days and the slowest around 700 days. The slowest ejecta are the ones launched at 2.4km/s and the fastest can be found from launching velocity 2.6 km/s and above. For velocity 2.3 km/s the data is empty as all particles collide with the Moon and none transfers to Earth.

Figure 5.19: Minimum time for a lunar ejecta to impact with Earth, in days. These plots display the information in Figure 5.18 in a different way. Red lines indicate the maximum time a particle takes to impact Earth (slowest particle) for that particular launching date. The blue line indicates the same for the fastest particles, so the minimum time. The yellow line indicates the average of all transfer times and the pink line the median value of transfer times, both for a particular date. The numbers on the lines indicate, not the value of the y-axis, but the velocity at which that transfer (minimum or maximum) is taking place. For example, when launching westwards 28 days after the origin date the slowest particle takes 100 days to impact Earth, having been launched at 2.4 km/s.

75 Lunar Meteorites: Origin and Mineralogy 5.1. SHORT TRANSFERS

5.1.4 Summary of results

After studying short transfers varying its launch direction, ejection angle and relative 3-body system position the following conclusions are extracted:

• The launch angle allows to explain qualitatively why ejecta escape to heliocentric orbits or stay in geocentric orbits based on a simple vector sum. If the vectors have the same orientation the particle exceeds the lunar geocentric velocity and escapes the Earth-Moon system, when orientations are near opposite the ejecta will have low kinetic energy and eventually stay in geocentric orbit or collide.

• The effect of velocity on lunar ejecta’s fate is non lineal. There is a velocity (ap- proximately 2.6 and 2.7 km/s) for which a maximum amount of Earth collisions take place (near 20% in both cases), below and above this velocity Earth collisions decline.

• The fate of lunar ejecta, regarding their potential collision with Earth varies also with the change in the ejection angle. However not all velocities have a correlation with the change in ejection angle and same behaviour varies with different directions of launch. Only 2.6, 2.7 and 2.8 velocities (in km/s) seem to display non-negligible differences in Earth collisions for different ejection angles. For example, for 2.6 km/s eastwards launch 34.6% of the total ejecta collide with Earth 6 for ejection angle 67.5º while only 14% collide if the ejection angle is 0º.

• Transfer times do not depend on the 3-body system configuration nor ejection angle. Anomalous values are associated to the random nature of the launch sites and out- liers. As a general rule, 2.4 km/s launches are the slowest (taking approximately 100 days) while 3.0 km/s launches are the fastest (taking an average of 3 days). Velocity 2.7 km/s is particularly more susceptible to variations of the celestial system configu- ration. However, this variations are not associated with any particular configuration. In other words, the initial date (Earth-Moon-Sun configuration) does not alter the percentages of heliocentric escapes, geocentric particles or collisions.

6After 100 years.

76 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

5.2 Long transfers

One of the problems simulating the orbital mechanics of the lunar ejecta are time scales. Assuming our model is able to predict accurately trajectories in the long distant future, where is the limit? An ejected particle can linger inside the Solar System for a million years before colliding with any planet. Perhaps 10 million years, or even more. It is necessary to set a threshold for such calculations and not to forget that as time increases, predictions are less reliable (for example, asteroid populations native in the Solar System are not included in the model while in reality the ejecta could impact with them). The largest time scale for this project has been 100 thousand years. This limit comes mainly due to computational-time constraints but also because has been considered large enough to wipe off any differences generated at the moment of launch. In other words, the effects that launch velocity and launching angle had for short transfers7 will be studied for this larger scale and are expected to fade with time. Furthermore, Gladman’s study goes as far as 10 million years, including a particular analysis at 100 thousands years, making comparison possible. For this extended simulations a different model has been used in which all the planets8 have been included. This is necessary as perturbations provoked by near-by planets on Earth’s orbit are no longer negligible for the ejecta [16] when the time scale surpasses 104 years. There are a total of four case studies that share the following initial conditions:

Parameter Body M x y z v v v (in solar masses) x y z Earth 3.00340000E-06 3.37110750E-01 9.26494952E-01 -3.90246061E-05 -1.64544401E-02 5.81783222E-03 1.76066556E-07 Moon 3.69510000E-08 3.37454781E-01 9.23843701E-01 1.63326389E-04 -1.58941695E-02 5.90572382E-03 -2.58507313E-05 Mercury 1.66013680E-07 3.06792546E-01 -2.69585175E-01 -5.01740804E-02 1.30079179E-02 2.24550720E-02 6.41480903E-04 Venus 2.44783834E-06 7.24898594E-01 2.25084284E-02 -4.15225280E-02 -7.11566366E-04 2.01244228E-02 3.17005125E-04 Mars 3.22715145E-07 1.38731435E+00 -6.41769419E-02 -3.53925269E-02 1.18243370E-03 1.51762865E-02 2.89008930E-04 Jupiter 9.54791938E-04 -5.39466927E+00 -7.99939622E-01 1.24034236E-01 1.01719795E-03 -7.11483672E-03 6.78430814E-06 Saturn 2.85885981E-04 -2.02359336E+00 -9.83659083E+00 2.51523361E-01 5.16120563E-03 -1.14701181E-03 -1.85540337E-04 Uranus 4.36624404E-05 1.83860428E+01 7.72326778E+00 -2.09383649E-01 -1.54998802E-03 3.43593375E-03 3.28512265E-05 Neptune 5.15138902E-05 2.83060262E+01 -9.78283812E+00 -4.50881120E-01 1.00643224E-03 2.97901374E-03 -8.46735486E-05

Table 5.9: Initial parameters for second model bodies. The positions of the planets are referenced taking the origin at the Sun. The lunar ejecta trajectories are calculated from its origin date and launch site doing an N-body integration until the final date, 105 years later. Data retrieved for Julian Date 2457724.5 (December, 2nd 2016). The step size used is chosen by the integrator (See Table 5.2. The step size criteria is preserved with additionally, a maximum of 10 days for the period beyond 1000 years).

7Short transfers refer to those that take place up to the first 1000 years after launch. 8Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.

77 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

Each case study is defined by a set of 500 particles launched from a random location on the lunar surface at a speed of 2.6 km/s and particular launching direction. As in previous cases, 4 different directions of launch are tested: North, East, West and South. The results of the two first are provided in Section A.2.3 and the other two are presented below. Looking at Figure 5.20, one can notice that the launch angle is no longer able to predict if the particle will eventually col- lide or not. Looking back into the con- clusions for short transfers, a launch angle between ≈[120º, 180º] sentenced the parti- cle to collide (mainly with Earth). When the simulation is extended the decreasing trend and scattering in (already displayed for short transfers) is more evident. By the time particles have been 100 thousand years in orbit, collisions have occurred at all values of launching angles. The downward (a) Launch towards West trend confirms the hypotheses of the energy at the moment of launch: the smaller the launch angle the more energy the particle has and the higher the probability to es- cape to heliocentric orbit, hence, the more time required to encounter Earth again and eventually impact. On the other hand, the increasing scattering indicates how other phenomena are more relevant to the parti- cle’s fate than the launch angle parameter. For this reason, to study the particle’s evo- lution it is necessary to study the orbital elements.

(b) Launch towards South

Figure 5.20: Evolution of launch angles for long time scales. Note that in both cases collisions take place for a wider launch angle range as time increases. Par- ticularly, southwards launches present a higher colli- sion density between 104 and 105. Both cases have 2 impacts with Venus approaching the limit of 100 thousand years. 78 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

The following plots show different combinations of orbital elements (following the cri- teria on [21]) for West and South launch directions. The first thing to notice is that by the end of the simulation, the orbital elements distributions look very similar regardless of the differences at the initial instant.

Figure 5.21: Initial orbital parameters. The four plots on the left are for the westwards launch and the for plots on the right correspond to a southwards launch. All particles are represented as no collisions have occured yet.

Figure 5.22: Final orbital parameters, after 105 years. The particles represented are those that have survived collisions. Beware the limits of the semi-major axis which differ from those on the initial orbital elements.

Surviving particles have specific characteristics. They have eccentricities below 0.3, very

79 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS similar to Earth’s and inclinations that not surpass 10º9, having a higher concentration on ≈ 4º. The longitude of the ascending node concentrates between the values 50º and 150º while in contrast the argument of the periapsis is totally free. The change on the semi-major axis and eccentricity requires further insight provided by Figure 5.23.

(a) 1 year after the launch (b) 103 years after the launch

(c) 104 years after the launch (d) 105 years after the launch

Figure 5.23: Semi-major axis vs. eccentricity evolution in time. Note that the particles move along the blue lines and only after 105 years are transferred to the yellow ones. These lines represent the constant perihelia (upper line) and constant aphelia (lower line) for varying a and e, as rp = a(1 − e) and ra = a(1 + e) respectively. The blue lines represent the aphelia and perihelia of particles launched from Earth (value 1 AU), the red ones for Mars (1.524), the yellow ones from Venus (0.723 AU) and the pink ones for Mercury (0.307).

Ejecta’s eccentricity and semi-major axis follow a path defined by two asymptotes. The transport of particles along these lines is not by chance. For a given three-body dynamical system, in which one of the masses is negligible compared to the other two (the system could be the Sun, Earth-Moon barycenter and the massless lunar ejecta) the variation of the orbital elements a, e and i of the ejecta after a close encounter with Earth will be such that the following expression is satisfied [66]: q 1 2 1 q 2 + a0(1 − e0) cos i0 = + af (1 − ef ) cos if = T (5.1) 2a0 2af This constant value, T is known as Tisserand parameter and the maintains the particles

9The lunar orbit inclination is approximately of 5º.

80 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS travelling along these lines. The perturbations of other planetary bodies in the vicinity of Earth disrupt these trajectories, particularly the ones caused by Venus are important after 104 years and beyond.

Figure 5.24: Lunar ejecta survivor population after 105 years. The black dots represent the orbits of the first four planets: Mercury, Venus, Earth and Mars. The coloured markers (except the one in the centre which is the Sun) are the location of the survivor population of lunar ejecta. Each colour corresponds to a particular direction of launch.

Figure 5.24 clearly shows the non-dependence between the direction of launch of the particles and their fate. The ejecta that manage to survive the first 1000 years after launch start scattering inwardly and outwardly from Earth’s, to Venus and towards Mars, respectively. Table 5.10 shows that as time advances the collisions with Earth balance out the differ- ence initially created by different launch directions. This balancing effect is also evident for different launch velocities. Table 5.11 shows the averaged value for all launching di- rections with velocity 2.6 km/s and the results for two other different tests with launch velocities 2.4 km/s and 3 km/s. The launch at 3 km/s presents no collisions with Venus. Even though this can be the product of a particular case, it is expected that more energetic particle require larger time scales to eventually being perturbed by the neighbouring planets. In the study of Gladman after 10 million years ([21] Table 3.5) almost a 12% of the launched particles

81 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

Table 5.10: Fate of the particle with direction of the launch. Note that only after 105 collisions with Venus are possible, and no longer the direction of the launch seems to affect the rate of collision with the neighbouring planet.

Iteration [%] Esc. Helio [%] Earth [%] Moon [%] Venus Southwards launch after 103 years 85.8 11 0 0 after 104 years 81.4 16.6 0.2 0 after 105 years 67.2 30.6 0.4 0.4 Westwards launch after 103 years 69 27.8 1.6 0 after 104 years 62 35.2 1.6 0 after 105 years 52.2 44.8 2 0.4 Eastwards launch after 103 years 68.4 30.4 0.2 0 after 104 years 62.8 36.2 0.2 0 after 105 years 54.8 44.8 0.2 0 Northwards launch after 103 years 83.8 12.6 0.8 0 after 104 years 78.6 19.6 0.8 0 after 105 years 65.8 32 1 0.6

Iteration [%] Esc. Helio [%] Earth [%] Moon [%] Venus Average 2.6 after 103 years 76.75 20.45 0.65 0 after 104 years 71.2 26.9 0.7 0 after 105 years 60 38.05 0.9 0.35 Average 2.4 after 103 years 78.33 14.33 6.33 0 after 104 years 57 36 6.67 0 after 105 years 43.33 49.67 6.67 0.33 Average 3.0 after 103 years 93.67 3 0.33 0 after 104 years 92.67 5.67 0.33 0 after 105 years 84 15 0.33 0

Table 5.11: Fate of particles for different launch velocities. Test for 2.4 km/s and 3 km/s differ from the rest. A total of 300 particles have been launched but only from 75 different launch sites, meaning that 4 particles have been launched from the same spot. Each particle has been launched in one of the preferential directions: North, East, South and West.

82 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS at 3 km/s have impacted with Venus. On the other hand, launch velocity 2.4 km/s was characterised by lower % of Earth impacts than velocity 2.6 km/s until 103 years (short transfers). When studying the particles for the long transfer regime, launch velocity 2.4 km/s becomes the one with more Earth collisions.

Figure 5.25: Accumulated impacts %.

Finally, the long transfer study allows to make a comparison with the real data from retrieved meteorites. Even thought that for a side-by-side comparison it is necessary to extend the simulation several orders of magnitude further (at least until 10 million years), obtained results are in accordance to Figure 1.10. According to CREA data, the % of accumulated Earth impacts that have spent in orbit for 104 years is of 17% and for those that have spent 105 years, 46%. It must be noted that CREA data has been constructed after the study of the isotopes of the meteorite, hence, there is no way to know at which original velocity they were launched and most probably, the meteorites of the sample were launched in different crater formation events. The fact that Figure 5.29 approaches the empirical data suggests that the range of velocities for lunar ejecta is constrained and similar to 2.6 km/s.

83 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

5.2.1 Case study: Meteorite Impact on the Moon

After studying the dynamics of lunar ejecta for artificially created scenarios, this section will focus on a real event that took place on the surface of the Moon and will explore the variability of possibilities for the fate of the theoretically produced ejecta. On September 11 of 2013, at 20h07m28s.68 UTC two telescopes at the observatory of Sevilla, Spain (37.34611ºN, 5.98055ºW) with CCD video cameras recorded a flash pro- voked by the impact of a meteoroid on the surface of the Moon [40]. According to the subsequent analysis performed on the data retrieved by both telescopes the impact loca- tion was discovered to belong to the west region of the Mare Nubium (see Figure 5.27). Thanks to the multiple detection it was possible to obtain complete observed data and estimated values for the impact characteristics, which are summarised in Table 1 of José M.Madiedo et al. [40] article. Part of this data has provided a solid basis for the modelling of the ejecta: it has been used alongside an online tool for calculating impact effects and cratering10 developed by K.A. Holsapple [28] and to support some assumptions taken in this case study regarding the ejection of lunar material.

Target properties Impactor Properties Table 5.12: Properties of Geology Type Lunar Regolith Meteorite Type unknown target and impactor. Data 3 3 Density 2.3 g/cm Density 3.7 g/cm extracted from [40] for the 2 Surface Gravity 1.668 m/s Diameter 0.61 m Impact Calculator [28]. Pressure 0 atm Total mass 440 kg Velocity 25 km/s Entry Angle 45 º Energy 0.016 kt of TNT

Figure 5.26: On the left, definition of variables for the impact-cratering-ejecta process (extracted from [27]). On the right, plot of the ejected mass (in kg and in %) when the ejecting velocity is greater than v (the total mass ejected being 3.95E5 kg). The data points have been created introducing different velocities in the ejecta field of the Impact calculator [28]. For a velocity above 2.3 km/s a 0.027% of the total mass is ejected (97.53 kg) and for a velocity greater than 3 km/s a 0.019% or 70.904 kg.

10For further reading on the topic of crater excavation by meteorite impacts see [25] and [27].

84 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS . It is Oceanus Procellarium Mission data). The location of the impact is the west Clementine W of the selenogrpahic coordinates. The landing site of Apollo 11 has been shown as reference. The º located in the southern hemisphere of the Moon, particularly at the southeast of the lunar mare is a Mare Nubium , at 17.2 º S 20.5 5.27: Detailed map of the Moon surface (image extracted from [ 30 ], from one of the oldest lunar basins and was formed by several impacts [ 42 ]. Mare Nubium region of the Figure

85 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

For this case study, the impact site on the Moon is the only launching point for the lunar ejecta. A total of 360 particles are launched at a specific local azimuth, evenly distributed across an arc of 360º (see Figure 5.28). All particles are ejected at 45º with respect to the local vertical and with launch velocity 2.6 km/s. Each particle has an identifier (M###) when comparing the the evolution of its orbital elements, propagated until 104 years.

Figure 5.28: Impact point and directions of launch for the lunar ejecta. Only 12 of the ejecta have been represented for clarity. The identification number of the meteor starts at the direction towards West and increases counterclockwise from 0º to 360º.

Figure 5.29: Distribution of lunar ejecta after 104 years. Some of the ejecta are labelled and display a red contour to distinguish them from the rest.

86 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

Figure 5.29 is the aftermath at the last instant of the simulation while Figure 5.28 presents the configuration that the ejecta have at the initial instant. Only by observing the distribution of colour, it is evident that survivors present all the range of launching angles. On the other hand, the distribution of the launching angles appears to be random. The labelling of the ejecta confirms this. Ejecta M30 position is virtually the opposite than M45, while their azimuthal difference in launch was only of 15º. In contrast, M90 and M285 end up in a similar position while the difference of their launching angles has been of 205º, M90 launched southwards and M285 virtually northwards. The characteristics of the survivor ejecta are equivalent to those discussed in the previ- ous section and are not presented here. The only difference is a more prominent clustering in the inclination and semimajor axis values. But these are due to an order of magnitude less for the simulation end time (104 years). Data can be seen in Section A.2.5 in Figure A.16. Instead, Figure 5.30 explores the orbital elements of the ejecta that have collided during the 104 years.

(a) (b)

(c) (d)

Figure 5.30: Orbital elements at collision instant.

87 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

As the orbital elements of the surviving population do not offer much information, Figure 5.30 focuses on the orbital elements of those ejecta that collide. The elements investigated are the semi-major axis, the eccentricity, inclination and time of collision. Plots against time (of a and e) do not show any particular correlation between the time of collision and the value of these elements. However, both plots show that the lower the value of e and a the greater the inclination is. But the most important tendency is the one described in Figure 5.30 which clearly reveals a smooth line between the semi-major axis and the eccentricity of those that collide. The plot has been reproduced changing the axis to obtain a function:

Figure 5.31: Orbital elements at collision instant. The colorbar indicates the years passed from the initial date and the inclination is represented by the relative size of the markers. Note: the colorbar on the previous figure represents the inclination.

The points follow a tendency line that has been modelled analytically as:

b f(x) = d − a · b(x − c)π(b−1) · e−a·(x−c) (5.2)

a b c d Coeff. 1.298 1.186 0.608 0.803 CI 95% lower bound 1.122 1.132 0.571 0.783 CI 95% upper bound 1.473 1.241 0.646 0.822

Table 5.13: Coefficient values for the analytical model.

88 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

The drawback of this plot is that a and e values correspond to the last recorded by Mercury 6, that is the orbital elements at the instant of the collision. The problem is that these can change drastically in a matter of hours and do not represent the average values of the orbital elements during the transfer period of the particle. For example, take particle M184 depicted in the upper right corner of Figure 5.31. Its a = 5.6 and e = 0.83 at the time of collision (in days) JDcol = 2456581.2951. On the other hand, the last recording of its trajectory11 the values are a = 1.06, e = 0.07 at last recorded date JDlast = 2456580.35 (days). The time difference between these two recordings is of only 0.9451 days (22.6824 h). Figure 5.32 presents the evolution of M184’s orbital elements during its 33-day transfer.

Figure 5.32: Orbital elements evolution of M184. The peaks at 3 days and 19 days correspond to flybys with Earth. Te blue colour of the lines indicate the ejecta remains continuously in geocentric orbit.

Note the range of a, e and i, virtually constant for all the transfer period. Notice the sharp contrast with the orbital elements of M184 eventually at collision (Figure 5.31). Eventually, Figure 5.33 compares the time evolution of different particles: M0, M36, M320 and M160. Each of them represents a very different scenario: M0 survives the 104 years, M36 collides by the end of the simulation (7400 years), M160 barely takes 1.65 years and M320 16 years.

11Mercury 6 gives two outputs. The file with the trajectory of the body and a file with the interaction of the particle with another body. The latter records the accurate, specific time and orbital elements at the collision. In contrast, the trajectory file saves the particle’s orbital elements at specific data-output intervals specified by the user (not to confuse with time step of the integration), which do not include the exact date of collision.

89 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS (b) (d) . (c) (a) 5.33: Time evolution of the orbital elements for different ejected particles. The parts in blue indicate that the particle is in geocentric phase (inside 10 times Earth’sgeocentric Hill stages region) during while time.geocentric those phase in Period (caused yellow of by indicate stabilitybut, Earth in are and M0 heliocentric coincidental Moon survives phase. with flybys). whileby heliocentric However, M0 M36 short-period both phase and collides patterns perturbations while M36 after are caused peaksonly are 7400 very by geocentric particles in years. similar the at that and the M160 the proximity seem alternate orbital corresponds moment of not heliocentric elements to of to the and correspond a launch indicate Earth with and different purely and the fates return geocentric the for for stage Moon. the impact. ejecta. ejecta Notice M320 Its the can orbital constant be elements value considered are of a characterised M320’s purely orbital elements heliocentric while particle in as heliocentric it stage. is Figure

90 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

Finally, the table with the percentages respect the original population are presented. For this particular launch site with 2.6 km/s launch velocity there is no ejecta that impact the Moon. All of them collide with Earth during the 104 years period.

Iteration [%] Esc. Helio [%] Earth after 1 year 93.61 6.39 after 10 years 86.39 13.61 after 100 years 85 15 after 1000 years 83.06 16.94 after 10000 years 76.11 23.89

Table 5.14: Percentage of ejecta in heliocentric orbit and collided with Earth.

The Table 5.14 Earth collision % are complemented by Figure 5.34. This figure shows the accumulated impacts for an interval of time. It can be easily seen that during the first year is when most of the impacts will occur and as time increases the flux of ejecta arriving to Earth decreases by the same order of magnitude12

Figure 5.34: Histogram of Earth collisions. The height of the bar indicates the amount of collisions (also indicated by the number on the bar itself) and its width corresponds to the period of time in which collisions occur. Intervals are defined in the following way: between [10−2, 10−1] intervals are of 10−2, between [10−1, 1] of 10−1, between [1, 10] of 1, between [10, 102] of 10 [...] always dividing the interval in 10 parts.

12From 10 years onwards the number of collisions given a time interval is restricted between 6 and 1. However, the bars are plotted with varying width (which corresponds to the time interval). This means that the number of particles, even though sharing the same number, accumulate in time intervals that last differently. As the number of collisions stabilises for time spans greater than 10 years this means that ejecta reaching Earth become more and more seldom.

91 Lunar Meteorites: Origin and Mineralogy 5.2. LONG TRANSFERS

5.2.2 Summary of results

The study of ejecta evolution during long transfers has yielded the following conclusions:

• Parameters that in short transfers indicated the fate of the ejecta (eg. launching angle) are no longer useful for the case of long transfers. Instead, the orbital elements of the ejecta are analysed as they offer the complete description of the particles orbits.

• The conclusions extracted for the launch velocity during short transfers are only valid for a limit time scale of 1000 years. The launch velocity with more Earth impacts for short transfers was comprised between 2.6 and 2.7 km/s. For long transfers, 2.4 km/s becomes the velocity with more Earth impacts accumulated.

• Orbital elements tend to cluster with time to particular ranges and values. While the argument of the periapsis is completely random the rest present constraints. Eccen- tricity values are contained below e = 0.3, the semimajor axis clusters in a = 1AU and inclination clusters in i = 4º (for a simulation time of 105 years). Addition- ally, a and e values vary maintaining constant aphelion or constant perihelion only perturbed from both asymptotes by neighbouring planets.

• Orbital elements show greater perturbations when the ejecta is on geocentric orbit and display stability periods during the heliocentric stage. However, there is no patter that indicates if collision is imminent. Therefore, there is a lack of distinction between the survival population and the collided one.

92 Lunar Meteorites: Origin and Mineralogy

6. Conclusions

This project has been motivated by the importance that nowadays has a complete and detailed prospection of the Moon. For this reason, the work focuses on the characterisation of the origin of meteorites in two very different fields, mineralogy and orbital dynamics. The first, analyses the chemical, mineral and geological composition of the meteorite pro- viding information that could be linked to certain lunar regions. The second, studies how these particles initially ejected from the lunar surface could possibly reach Earth. While mineralogical studies are a window to the past, orbital dynamics offer the opportunity of both reconstructing an orbit back to its origin or predict its fate. Together, the combina- tion of mineralogy and orbit dynamics can give answers to future lunaite findings alongside their recorded meteor observation. The main conclusions for the mineralogy part are:

• The strict analysis of the three samples allows the basic characterisation of the main constituents of the three studied meteorites: JaH 838 and NWA 11444 as anorthosite and DHO 1084 as alkali feldspar. However, the results of the Meteoritical Bulletin differ, most probably, because the Meteoritical Bulletin results are based on the anal- ysis of the total sample mass for each of the meteorite as well as the usage of different techniques, not uniquely SEM/EDX.

• Based on the analysis only of the 3 samples of this project, it is possible to associate them with a lunar region, nevertheless, with uncertainty. For JaH 838 and NWA 11444, identified as anorthosites, they are associated with the lunar highlands. On the other hand, DHO 1084 is unclear and only the (marginal) presence of P could relate the sample to the lunar maria.

• Despite having a sample from a lunar rock (in this case coming from a meteorite), for obtaining reliable results are necessary several analysis with different techniques and an exhaustive study of the data obtained, which can take years. This project has lasted for approximately 4 months and only SEM/EDX was performed. For a complete analysis it will be necessary to perform at least additional observations using other techniques like eg.: ICP-MS and ICP-AES(to infer bulk elemental composition), microprobe, X-ray diffraction (XRD) and Raman Spectroscopy (for mineralogical characterisation) and radiometric dating.

• Even if the lunaite classification agrees with the one given by the Meteoritical Bulletin,

93 Lunar Meteorites: Origin and Mineralogy

associating anorthosites with lunar highlands does not give enough information for the origin region of the meteorite. Even if the sample presents specific elements of very particular regions of the Moon (KREEP, see Figure 1.9) the original impact is still contained in a region of hundreds of km. Summarising, the mineralogy analysis might allow a broad classification of the lunar meteorites but has limited results associating a lunar meteorite with its origin region.

The orbital dynamics study main conclusions are the following:

• When predicting the fate of the lunar ejecta there are differences between short trans- fers (up to 1000 years) to long transfers (studied beyond 1000 years until 100,000 years).

• In the case of short transfers there are two principal parameters that influence on the fate of the ejecta are: velocity and launch angle.

– The launch velocity there is a value in which the amount of collisions is maxi- mum and below or beyond that value less impacts occur. After 100 years, for velocities of 2.6 - 2.7 km/s the average value of Earth collisions of the initial ejecta population is nearly 20%, while for 2.4 km/s is of 4% and for 3 km/s of 3%. After 1000 years impact % remain the same except for 2.4 km/s, increasing to 15%. – The launch angle is able to determine if the particle will escape to heliocentric orbit or will stay in geocentric and eventually impact. Those particles with a launch angle ≈120º or above may impact as fast as 3 days after ejection. As time passes launch angles at which collisions occur can reach values below 90º. – Another parameter that influences collisions with Earth is the ejection angle. The default is considered 45º and its change only affects the most "efficient"1 velocities. Increasing the percentage of impacts by 15% in velocities 2.6 and 2.7 km/s and having no influence in 2.4 km/s launch velocity.

• Long transfers pose two problems: previous parameters to predict the fate of the ejecta are no longer valid and no other parameter has been found as substitute.

– Beyond 1000 years a particle with any launch angle is able to collide with Earth. In the case of launch velocity, those that produced more collisions in short trans- fers (2.6 and 2.7 km/s) fall behind 2.4 km/s by 10% of impacts. – Studies on the evolution of orbital elements do not provide any combination or characteristic values before imminent collision. The case study analysed proofs

1The ones that provoke more collisions.

94 Lunar Meteorites: Origin and Mineralogy

that two particles ejected at the same velocity and similar launch angles can have completely different fates (take as example M36 and M320).

In other words, for long transfers particles with different ejection velocities and launch angles are indistinguishable from one another (regarding their future evolution).

Both mineralogy and orbit dynamics studies have broad and open solutions when char- acterising a meteorite. However, at this moment, mineralogy studies are able to provide more hints to link a lunar meteorite with a particular region of the Moon than by studying orbital dynamics. Combining them does not necessarily imply better predictions. First, to use both methods implies a sample of the rock and an observation: as a recorded impact on the lunar surface or as meteor entering Earth’s atmosphere. On the other hand, according to the conclusions the dynamical study should be limited to transfers contained in the first 1000 years after ejection. The limitations for each scenario are the following:

• If a retrieved (lunar) meteorite has also been observed (and recorded) as meteor, it could be possible to calculate the orbital elements at the atmospheric entry and subsequently, reconstruct the orbit. However, if isotope dating analysis concludes that the ejecta spent tens of thousands of years in space before collision, no tracing back can be done. Time will have completely erased any characteristics from launch. Recording the meteor fall and being a short transfer reduces the odds. Only two meteorites from Table 1.5 (DHO 026 and ALH 81005) have been dated a T4π of the order of 1000 years, and none has been observed falling.

• If an impact on the Moon is recorded, ideally with images of ejected material in order to limit the local azimuth angle, a traceable impact can be expected within the following 100 to 1000 years. This case is far from ideal and only useful if particles are able to reach Earth in less than a century (considering the lifespan of a human and the acceleration on science and technology). Additionally, the meteorites will need to be isotope dated to ensure their time in space corresponds to the recorded event.

95 Lunar Meteorites: Origin and Mineralogy

7. Future Work

This project deals with the identification problems from both mineralogy and orbit dynamics. Mineralogy analysis are restricted by the different techniques applied and the knowledge about the different lunar regions. Both leave open different lines of investigation but particularly, orbital dynamics:

• The meteorite samples are required to be observed under an optical microscope and to perform a Raman Spectroscopy analysis. By performing these techniques sec- ondary minerals and specific minerals that MINSQ is not able to distinguish from the SEM/EDX data could be determined. It is also interesting performing a nano- indentation test, to our knowledge never performed before on lunar meteorites.

• Long transfers need further studying: do all the characteristics from the launch in- stant fade beyond 1000 - 10,000 years? This project gives an overview on the major parameters for three different velocities, without varying ejection angle. For complete- ness, it should be tackled in all its complexity and detail. The different variations (8 different velocities, change in the ejection angle and change in the Earth-Moon- Sun configuration) would be interesting to analyse for long transfers. Despite some of them lacking a major impact in short transfers, it is important to verify if those results hold beyond 1000 years.

• The properties of orbital elements at Earth’s collision should be further analysed with Mercury 6 or another software that allows to reduce the time step when approaching the body before collision. Current results present a gap of several hours between the last recorded point in the orbit and the final orbital elements at the moment collision. Could a certain combination of orbital elements trigger a non-return orbit for the ejecta or is it only due to its proximity to Earth regardless of a, e and i?

96 Lunar Meteorites: Origin and Mineralogy and general project. Dynamics , Mineralogy 8.1: Gantt Diagram. The different tasks of the project were divided in the categories of Planning Figure 8.

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