3D Modelling of Near-Earth Asteroids using Lightcurve Database by Jonatan Michimani Garcia

Thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN SPACE SCIENCE AND TECHNOLOGY

at the Instituto Nacional de Astrof´ısica, Optica´ y Electr´onica

February 2019

Tonantzintla, Puebla

Under the supervision of: Jos´eRam´on Vald´es Parra, INAOE Jos´eSilviano Guichard Romero, INAOE

c INAOE 2019 The author hereby grants to INAOE permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part.

Abstract

The record of catastrophic impacts of asteroids towards the Earth, indicates that such phenomena will, to a certainty, occur at some time in the future. Given this threat, the only convenient approach to elaborate a mitigation strategy is to know, as much as possible, the characteristics of the objects with high probability of striking the planet: Near-Earth Asteroids (NEAs). This work focuses on the asteroid characteristics that can be obtain through the synthesis of photometric data i.e. period of rotation, amplitude of the lightcurve, shape and direction of the spin axis or pole. The NEAs (25916) 2001 CP44, (1627) Ivar, (1036) Ganymed (1866) Sisyphus and (450894) 2008 BT 18 were selected to be observed during the months of March, April and May. Subsequent, lightcurve analysis was per- formed by means of the software MPO Canopus, and last, with the lightcurves available in the ALCDEF data base and the own data, the inversion method was run in MPO LCInvert software. Accordingly, first it is presented lightcurves of the observed objects as well as period of rotation and amplitude of the lightcurve. Asteroids (25916) 2001 CP44, (1627) Ivar, (1036) Ganymed and (1866) Sisyphus show results that are consistent with others previously published, however as- teroid (450894) 2008 BT 18, due to its binary nature, did now show conclusive results. Shortly it is also presented the outcomes of the inversion process. For as- teroids (25916) 2001 CP44, (1627) Ivar, (1036) Ganymed, the pole direction and shape are close to its true solution, on the other hand, the presented pole and shape of (1866) Sisyphus (450894) 2008 BT 18 are the best fit with the available data and further observations are needed to improve the solution. The results of the characterization process shows that the Schmidt Camera is a suitable instru- ment for asteroid photometry and hence, INAOE should keep on contributing to the effort of NEAs characterization.

I II Contents

1 Introduction 1 1.1 Asteroids ...... 1 1.1.1 DefinitionandMainCharacteristics ...... 1 1.1.2 OrbitalElements ...... 4 1.1.3 AsteroidPopulations ...... 4 1.2 Photometry ...... 10

2 The Impact Hazard of Near-Earth Asteroids 13 2.1 ARecordofImpacts ...... 13 2.2 DefendingPlanetEarth ...... 15 2.2.1 DetectionandTracking...... 17 2.2.2 Cataloguing and Orbital Parameters Calculation ...... 19 2.2.3 Mitigation...... 20 2.2.4 Characterization ...... 20 2.3 Conclusion...... 22

3 Objectives and Methodology 23 3.1 Objectives...... 23 3.2 Methodology ...... 24 3.2.1 Selection...... 24 3.2.2 Observations ...... 27 3.2.3 Photometry ...... 28 3.2.4 ShapeDetermination ...... 29

4 Observations, Image Reduction and ALCDEF 31 4.1 Observations...... 31 4.1.1 SchmidtCamera ...... 31 4.1.2 SelectedAsteroidsandImageReduction ...... 33 4.2 AsteroidLightcurvePhotometryDatabase ...... 35

5 Results 39 5.1 Lightcurves ...... 39 5.1.1 (25916)2001CP44 ...... 40 5.1.2 (1627)Ivar ...... 46

III IV CONTENTS

5.1.3 (1036)Ganymed ...... 48 5.1.4 (1866)Sisyphus ...... 51 5.1.5 (450894)2008BT18...... 52 5.2 TheinversionMethod ...... 55 5.3 MPOLCInvertResults...... 58 5.3.1 (25916)2001CP44 ...... 58 5.3.2 (1627)Ivar ...... 61 5.3.3 (1036)Ganymed ...... 65 5.3.4 (1866)Sisyphus ...... 70 5.3.5 (450894)2008BT18...... 73

6 Conclusion and Future Work 77 Bibliography ...... 79 List of Figures

1.1 From left to right: First picture: Asteroid (25143) Itokawa, vis- ited by the Japanese spacecraft Hayabusa in 2005 and the first one from where material samples were brought to Earth. Credit: NASA/JPL. Second picture: model representation of a radar ob- servation from Asteroid (216) Kleopatra. Credit: Stephen Ostro et al. (JPL), Arecibo Observatory, NSF, NASA ...... 2 1.2 Geometry of an elliptical orbit in one (a) and three (b) dimensions. The Sun is found at one focus. For solar system objects, the ref- erence plane is the ecliptic (Adapted from Lissauer & de Pater, 2013)...... 5 1.3 (a) Histogram of asteroids versus semi-major axis shows primary Kirkwood gaps in the Asteroid Main-Belt (credit: Alan Chamber- lain, JPL/Caltech). (b) Location of Jupiter’s Troyan asteroids at theLagrangianpointsL4andL5(Kutner,2003)...... 7 1.4 Orbital representation of the different groups of NEAs (Adapted fromJPL,CNEOS)...... 9 1.5 Lightcurveofasteroid(1627)Ivar...... 11

2.1 (a) Full Moon and (b) Mercury, showing scars of large giant im- pacts that are remnants from the Late Heavy Bombardment pe- riod, about 3.3 billion years ago. Credits: (a) Galileo spacecraft (NASA), (b) University of Arizona/LPL/Southwest Research In- stitute...... 14 2.2 Location of inland known craters on the surface of the Earth (Koe- berl,2013)...... 15

V VI LIST OF FIGURES

2.3 Examples of impact craters on Earth. (a)Tswaing (Saltpan)-crater in South Africa (1.2 km in diameter, 250,000 years old); (b) Wolfe Creek crater in Australia (1 km in diameter, 1 Ma old); (c) Meteor Crater in Arizona, U.S. (1.2 km in diameter, 50,000 years old); (d) Lonar crater, India (1.8 km in diameter, age ca. 50,000 years); (e) Mistastin crater in Canada (28 km in diameter, age ca. 38 Ma); (f) Roter Kamm crater in Namibia (2.5 km in diameter, age ca. 4 Ma); (g) Clearwater double crater in Canada (24 and 32 in km diameter respectively, age ca. 250 Ma); (h) Gosses Bluff crater in Australia (24 km in diameter, age 143 Ma); and (i) Aorounga crater in Chad (18 km in diameter, younger than ca. 300 Ma), (Koeberl,2013)...... 16 2.4 (a) Effects on the Siberian forest by the Tunguska asteroid explo- tion, one of the largest recent impacts. Credit: Leonid Kolik. (b) The Chelyabinsk bolide in 2013 renew the awareness of asteroid impacts. Credit: Footageofanamateurvideo...... 17 2.5 NEOs current population estimate: Number(N) of objects as a function of absolute magnitud H. Average impact interval scale (right), impact energy released in megatons (MT) of TNT for an assumed velocity of 20 km per second (top), and NEOs diameters determined assuming an average value of albedo of 14% (bottom). (Adapted from Defending Planet Earth, National Research Council). 19 2.6 Number of NEA discoveries per year by Survey. (JPL, Center for NearEarthObjectStudies) ...... 20 2.7 Cumulative number of known Near-Earth Asteroids versus time. Here is shown the total of NEAs of all sizes discovered by all de- tection surveys differentiating them from the total of NEAs larger than 140 m and larger than 1 km in diameter. Potentially Haz- ardous Asteroids and Near-Earth Comets are also shown. (JPL, CenterfotNearEarthObjectStudies) ...... 21

3.1 Potential Lightcurve Targets search format from Minor Planet Center...... 24 3.2 Example of the associated lightcurves to a certain asteroid, dis- played by the Asteroid Lightcurve Photometry Database site. .. 26 3.3 GraphicenviromentofMPOCanopus...... 28 3.4 Graphic interface of the Inversion Wizard from MPO LCInvert. . 29

4.1 SchmidtCameraatINAOE...... 32

5.1 ...... 40 5.2 ...... 40 5.3 Field of view around (25916) 2001 CP44 on April 14th, 2018. . .. 41 5.4 Field of view around (25916) 2001 CP44 on April 16th, 2018. . .. 41 5.5 ...... 41 LIST OF FIGURES VII

5.6 ...... 41 5.7 ...... 42 5.8 ...... 42 5.9 Field of view around (25916) 2001 CP44 on April 20th, 2018. . .. 43 5.10 Field of view around (25916) 2001 CP44 on April 21st, 2018. ... 43 5.11 ...... 43 5.12 ...... 43 5.13 ...... 44 5.14 ...... 44 5.15 Field of view around (25916) 2001 CP44 on May 26th, 2018. . .. 45 5.16 Field of view around (25916) 2001 CP44 on May 28th, 2018. . .. 45 5.17 ...... 45 5.18 ...... 45 5.19 ...... 46 5.20 ...... 46 5.21 Field of view around (1627) Ivar on March 17th, 2018...... 47 5.22 Field of view around (1627) Ivar on March 27th, 2018...... 47 5.23 ...... 47 5.24 ...... 47 5.25 ...... 48 5.26 ...... 48 5.27 ...... 48 5.28 Field of view around (1036) Ganymed on March 19th, 2018. . .. 49 5.29 Field of view around (1036) Ganymed on March 20th, 2018. . .. 50 5.30 Field of view around (1036) Ganymed on March 21st, 2018. . .. 50 5.31 ...... 50 5.32 ...... 50 5.33 ...... 51 5.34 Field of view around (1866) Sisyphus on March 25th, 2018. .... 51 5.35 ...... 52 5.36 ...... 52 5.37 ...... 53 5.38 ...... 53 5.39 Field of view around (450894) 2008BT18 on the first session of March24th,2018...... 54 5.40 Field of view around (450894) 2008BT18 on the second session of March24th,2018...... 54 5.41 Field of view around (450894) 2008BT18 on the first session of March29th,2018...... 54 5.42 Field of view around (450894) 2008BT18 on the second session of March29th,2018...... 54 5.43 ...... 54 5.44 ...... 54 5.45 ...... 58 VIII LIST OF FIGURES

5.46 4-Vane model view from the pole solution λ = 60.0, β = +90.0 of (25916)2001CP44...... 59 5.47 Ecliptic model view from the pole solution λ = 60.0, β = +90.0 of (25916)2001CP44...... 59 5.48 Equator model view from the pole solution λ = 60.0, β = +90.0 of (25916)2001CP44...... 59 5.49 4-Vane model view from the pole solution λ = 240.0, β = +90.0 of (25916)2001CP44...... 60 5.50 Ecliptic model view from the pole solution λ = 240.0, β = +90.0 of(25916)2001CP44...... 60 5.51 Equator model view from the pole solution λ = 240.0, β = +90.0 of(25916)2001CP44...... 60 5.52 ...... 62 5.53 ...... 62 5.54 ...... 63 5.55 ...... 63 5.564-Vanemodelview ...... 63 5.57 (1627)Ivareclipticmodelview...... 64 5.58 (1627)Ivarequatormodelview...... 64 5.59 ...... 65 5.60 4-Vane model view from the pole solution λ = 178.697, β = −76.671 of(1036)Ganymed...... 66 5.61 Ecliptic model view from the pole solution λ = 178.697, β = −76.671of(1036)Ganymed...... 66 5.62 Equator model view from the pole solution λ = 178.697, β = −76.671of(1036)Ganymed...... 67 5.63 4-Vane model view from the pole solution λ = 179.176, β = −76.726 of(1036)Ganymed...... 67 5.64 Ecliptic model view from the pole solution λ = 179.176, β = −76.726of(1036)Ganymed...... 68 5.65 Equator model view from the pole solution λ = 179.176, β = −76.726of(1036)Ganymed...... 68 5.66 4-Vane model view from the pole solution λ = 178.479, β = −76.755 of(1036)Ganymed...... 69 5.67 Ecliptic model view from the pole solution λ = 178.479, β = −76.755of(1036)Ganymed...... 69 5.68 Equator model view from the pole solution λ = 178.479, β = −76.755of(1036)Ganymed...... 69 5.69 4-Vane model view from the pole solution λ = 15.0, β = 15.0 of (1866)Sisyphus...... 70 5.70 Ecliptic model view from the pole solution λ = 15.0, β = 15.0 of (1866)Sisyphus...... 71 5.71 Equator model view from the pole solution λ = 15.0, β = 15.0 of (1866)Sisyphus...... 71 LIST OF FIGURES IX

5.72 4-Vane model view from the pole solution λ = 75.0, β = 15.0 of (1866)Sisyphus...... 71 5.73 Ecliptic model view from the pole solution λ = 75.0, β = 15.0 of (1866)Sisyphus...... 72 5.74 Equator model view from the pole solution λ = 75.0, β = 15.0 of (1866)Sisyphus...... 72 5.75 ...... 73 5.76 4-Vane model view from the pole solution λ = 75.0, β = 15.0 of (450894)2008BT18...... 74 5.77 Ecliptic model view from the pole solution λ = 75.0, β = 15.0 of (450894)2008BT18...... 74 5.78 Equator model view from the pole solution λ = 75.0, β = 15.0 of (450894)2008BT18...... 75 5.79 4-Vane model view from the pole solution λ = 75.0, β = 15.0 of (450894)2008BT18...... 75 5.80 Ecliptic model view from the pole solution λ = 75.0, β = 15.0 of (450894)2008BT18...... 76 5.81 Equator model view from the pole solution λ = 75.0, β = 15.0 of (450894)2008BT18...... 76 X LIST OF FIGURES List of Tables

1.1 Asteroid taxonomic classes (Adapted from Dymock, 2010; and Lis- sauer&dePater,2013)...... 3 1.2 Orbital elements (Adapted from Dymock, 2010) ...... 5 1.3 Near Earth Asteroids groups (Adapted from JPL, CNEOS) . . . . 10

2.1 Approximate average impact interval and impact energy of NEOs. (Adapted from Defending Planet Earth, National Research Council). 18

4.1 Primarymirrorcharacteristics ...... 32 4.2 Fieldflatteninglenscharacteristics ...... 32 4.3 Correctorlenscharacteristics...... 33 4.4 CCDDetectorcharacteristics ...... 33 4.5 Orbital elements of observed asteroids at Epoch 2,458,200.5, 2018- Mar-23.0. (Source: JPL Small-Body Database Browser) ...... 33 4.6 Selected physical parameters of observed asteroids...... 34 4.7 Observational circumstances for observed asteroids ...... 34 4.8 ALCDEFlightcurvesfor(25916)2001CP44...... 35 4.9 ALCDEFlightcurvesfor(1866)Sisyphus...... 35 4.10 ALCDEF lightcurves for (450894) 2008 BT18...... 36 4.11 ALCDEFlightcurvesfor(1627)Ivar...... 36 4.12 ALCDEFlightcurvesfor(1036)Ganymed...... 37

5.1 Rotation period and brightness amplitude of the observed asteoids 39 5.2 Comparison stars data from the April 14th, 2018 session . . ... 40 5.3 Comparison stars data from the April 16th, 2018 session . . ... 41 5.4 Comparison stars data from the April 20th, 2018 session . . ... 42 5.5 Comparison stars data from the April 21st, 2018 session . . ... 42 5.6 Comparison stars data from the May 26th, 2018 session ...... 44 5.7 Comparison stars data from the May 28th, 2018 session ...... 44 5.8 Comparison stars data from the March 17th, 2018 session . .... 46 5.9 Comparison stars data from the March 27th, 2018 session . .... 46 5.10 Comparison stars data from the March 19th, 2018 session ..... 49 5.11 Comparison stars data from the March 20th, 2018 session ..... 49 5.12 Comparison stars data from the March 21st, 2018 session ..... 49 5.13 Comparison stars data from the March 25th, 2018 session ..... 52

XI XII LIST OF TABLES

5.14 Comparison stars data from the March 24th, 2018 first session . . 53 5.15 Comparison stars data from the March 24th, 2018 second session. 53 5.16 Comparison stars data from the March 29th, 2018 first session . . 53 5.17 Comparison stars data from the March 29th, 2018 second session. 53 5.18 Coarse Search resultsfor(25916)2001CP44 ...... 58 5.19 Periodsearchresultsfor(1627)Ivar ...... 61 5.20 Coarse Search resultsfor(1627)Ivar ...... 61 5.21 Fine Search resultsfor(1627)Ivar...... 62 5.22 Period search results for (1036) Ganymed ...... 65 5.23 Fine Search resultsfor(1036)Ganymed ...... 66 5.24 Coarse resultsfor(1866)Sisyphus...... 70 5.25 Coarse resultsfor(450894)2008BT18...... 73 Chapter 1

Introduction

This chapter is divided into two main parts. The first is a general outlook of asteroids, some of the most fascinating, mysterious and abundant bodies in the solar system. Along with their definition and main characteristics, a description of the existing groups of asteroids is also presented, succeeded by a more extensive picture of Near-Earth Asteroids (NEAs) and Potentially Hazardous Asteroids (PHAs). The aim of this section is to make a clear distinction between the objects of study of this work and other solar system bodies. The second part reviews the astronomical technique of photometry as the principal source of data for the fulfilment of the present thesis.

1.1 Asteroids

1.1.1 Definition and Main Characteristics

As the discovery of celestial bodies increased, especially in the region beyond Nep- tune, it became difficult to know with certainty which objects could or could not be defined as planets, as well as a clear distinction between other solar system ob- jects. This recognition thus provoked the B5 Resolution, adopted at the XXVIth General Assembly of the International Astronomical Union (IAU) in 2006. Res- olution which states that the planets and other bodies, except satellites, in our solar system are defined into three distinct categories: 1. A planet is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces, so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the vicinity around its orbit.

1 2 CHAPTER 1. INTRODUCTION

Figure 1.1: From left to right: First picture: Asteroid (25143) Itokawa, visited by the Japanese spacecraft Hayabusa in 2005 and the first one from where material samples were brought to Earth. Credit: NASA/JPL. Second picture: model representation of a radar observation from Asteroid (216) Kleopatra. Credit: Stephen Ostro et al. (JPL), Arecibo Observatory, NSF, NASA

2. A “dwarf planet” is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces, so that it assumes a hydrostatic equilibrium (nearly round) shape, (c) has not cleared the vicinity around its orbit, and (d) is not a satellite. 3. All other objects, except satellites, orbiting the Sun shall be collectively referred as “Small Solar System Bodies”. By this resolution, asteroids and comets are included in the “Small Solar System Bodies” category. In this respect, the difference between asteroids and comets is their composition. While asteroids are generally constituted by metal or rock, comets are composed mostly of water ice and dust particles; therefore, as they approach the Sun, comets lose material—to the vaporization of the ice they are build with—forming a tail. Ranging in radius from a few meters to more than 1,000 km, asteroids are also re- ferred as minor planets. The Encyclopedia of the Solar System defines an asteroid as “a rocky carbonaceous or metallic body, smaller than a planet and orbiting the Sun” (2007, p.920). Contrary to popular belief, asteroids are not all solid bodies, usually, asteroids with diameters smaller than 100-150 m are solid and called monoliths, while larger ones, i.e. 150-300 m, are regularly rubble piles (Dymock, 2010). As will be discussed in detail in the next subsection, and according to Lissauer & de Pater (2013), the asteroid families in the Main Belt indicate a violent colli- sional environment. While it is true that catastrophic collisions lead to formation 1.1. ASTEROIDS 3

Table 1.1: Asteroid taxonomic classes (Adapted from Dymock, 2010; and Lissauer & de Pater, 2013).

Bus-DeMeo Description Examples class B Uncommonclassofcarbonaceousaster- (2) Pallas, (431) oids, found mainly in the outer Main Nephele, (704) Belt. Spectra show the presence of Interamnia and clays, carbon and organics. (25143) Itokawa. C, Cb, Cg, Carbonaceous type common in the (1) Ceres (10) Cgh, Ch outer Main Belt. Hygeia, (19) For- tuna, (45) Eugenia, (90) Antiope, (253) Mathilde, (324) Bamberga, (379) Huenna and (2060) Chiron. A RareinnerMainBeltasteroids. Spec- (246) Asporina and tra indicate presence of olivine. (289) Nenetta. Q InnerMainBeltasteroids. Spectrain- (1862) Apollo. dicate presence of olivine and pyroxene. R Moderatelybright,innerMainBeltas- (349) Dembowska. teroids with presence of olivine, pyrox- ene, and plagioclase. K Silicaceous or stony uncommon Main (221) Eoa and Belt asteroids. Spectra indicate pres- (233) Asterope. ence of olivine and orthopyroxene. L Uncommon asteroids with featureless (387) Aquitania spectra. and (728) Leonisis. S, Sa, Sr, Sq Moderately bright, stony, chondritic as- (6) Hebe, (15) Eu- teroid class dominating the inner Main nomia and (433) Belt. Eros. X,Xe, Xc, Xk Metallic asteroids. Spectra indicate (16) Psyche, (44) presence of troilite (iron sulphide), en- Nysa, (64) An- statite, and hypersthene. gelina, (87) Sylvia, (216) Kleopatra and (2867) Steins. T LowalbedoinnerMainBeltasteroids (114) Kassandra. of unknown composition with feature- less, moderately red spectra. D SpectrumoftheseouterMainBeltob- (624) Hektor and jects may indicate presence of organic (944) Hidalgo. rich carbon and anhydrous silicates, and possibly ice. O - (3628) Boznemcova V SimilartoS-classbutcontainingaform (4) Vesta. of pyroxene known as augite. 4 CHAPTER 1. INTRODUCTION of these families, more frequent but less energetic impacts result in bodies frac- tured or shattered. Considering the history of perpetual encounters, asteroids shapes can be diverse and nearly always irregular (see Fig. 1.1), though, aster- oids are characterized by elongated shapes (Harris et al., 2014). The so called “potato shape” is due to asteroids that are not as massive to achieve hydrostatic equilibrium and hence aquire round shapes. The study of the composition of asteroids, comets and other small objects is particularly important, because they are debris left over from the formation of the Sun and the planets—around 4.5 billion years ago. Apart from their collisions, asteroids have practically remained unchanged, thus their study is essential to understand the origins of the solar system. Asteroid composition data is obtained by the examination of meteorites—which are believed to be pieces of asteroids and of which there are limited samples of material taken by spacecrafts in their costly missions—and the shapes of their reflectance spectra made radiation reflect from their surfaces. Through spectrometry, it was possible the implementation of a taxonomy, which has prominently evolved from the first one put in action more than 50 years ago. Nowadays, the Bus-DeMeo (DeMeo et al., 2009) taxonomy has 25 classes based on the analysis of the visible and near-IR spectral data, spanning wavelength from 0.45 to 2.45 microns. Table 1.1 shows the most representative of these classes.

1.1.2 Orbital Elements

It is necessary to define a number of terms that will be used constantly hereafter. In point of fact, all bodies in the solar system travel on conic section orbits around the Sun. While some comets have parabolic orbits, planets, dwarf planets and asteroids move along elliptical orbits with the Sun in one of the two ellipse foci. In this regard, every orbit is characterized by six orbital parameters or elements, described and shown in Table 1.2 and Figure 1.2, respectively. Another essential term is the semi-minor axis of an elliptic orbit, which is denoted by letter “b”. In contrast to perihelion (q), aphelion (Q) is the farthest point on the orbit to the Sun; both perihelion and aphelion lay on the major axis. Finally, the “Epoch” is the date on which the orbital parameters are calculated. For this purpose, astronomers use the Julian Date system (JDT), which is a count of days and fractions of days since noon Universal Time (UT) on January 1, 4713 BC.

1.1.3 Asteroid Populations

Taxonomic classes and asteroid families are defined, respectively, by physical and orbital characteristics. However, the fundamental form of asteroid grouping is 1.1. ASTEROIDS 5

Figure 1.2: Geometry of an elliptical orbit in one (a) and three (b) dimensions. The Sun is found at one focus. For solar system objects, the reference plane is the ecliptic (Adapted from Lissauer & de Pater, 2013).

Table 1.2: Orbital elements (Adapted from Dymock, 2010)

Name Notation Description Units Semi-majoraxis a Half the length of the long axis of the au elliptical orbit represents a measure of the size of the orbit. Eccentricity e Definestheshapeoftheorbit,itcom- - putes the orbit’s variation from a circle (e=0). Inclination i / Incl The angle between the plane of the or- deg bit and the ecliptic. Longitude of the Ω/Node Determines the angle between the ver- deg ascending node nal equinox—first point of Aries—and the ascending node (where the orbital plane intersects the plane of the eclip- tic) pointing “northward”. Meananomaly M The angular distance from the deg perihelion—which is the closest point of the orbit to the Sun denoted by the letter “q”—to the current body’s location, which is measured in the direction of motion. Argument of the ω/P eri Defines the angle between the ascend- deg perihelion ing node and the perihelion, which is measured counter-clockwise along the plane of the orbit. 6 CHAPTER 1. INTRODUCTION due to their distribution within the solar system. In this manner, the groups of asteroids are:

• Trans-Neptunian objects (TNOs),

• Centaurs,

• Trojans,

• Main Belt asteroids, and

• Near-Earth asteroids (NEAs).

Trans-Neptunian objects (TNOs), the group at the top of the list, possess the greatest distance from the Sun, whereas the shortest is hold by Near-Earth as- teroids (NEAs). Before a description of each asteroid group, it is necessary to explain the key concept of orbital resonances; according to Moltenbrey (2016), “Orbital resonances happen when two orbiting bodies exert a regular and periodic gravitational influence on each other. This is the case when their orbital periods are related by a ratio of two integers” (p. 6). That is to say, the gravitational interaction causes unstable orbits, as it can be seen in the resonant perturbation from Jupiter, which has cleared gaps within the asteroid Belt. Daniel Kirkwood was the first one to notice that the 4:1, 3:1, 7:3 and 2:1 resonances are regions almost empty from asteroids, so these gaps are named after him (Lissauer & de Pater, 2013).

TNOs

Since the discovery of Pluto by Clyde Tombaugh in 1930, many astronomers— among them Frederick Charles Leonard (1896-1960)—came to the hypothesis that beyond Neptune’s orbit there might be “debris left over from the formation of the planets” (Dymock, 2010, p.26). Later on, Kenneth Essex Edgeworth (1880-1972) and Gerard Kuiper (1905-1973) proposed that a large number of small bodies could have formed in that remote area—later known as the Edgeworth-Kuiper belt—through the disk of planet-forming material. Even though the discovery of TNOs is constant—to the extent that by January 2018 the Minor Planet Center reports 1,910 TNOs—the region beyond Neptune is not as densely populated as the Main Belt. TNOs are also subdivided according to orbital parameters and to the areas of the solar system where they orbit, which can be Kuiper Belt, Scattered Disk or the Oort cloud. Consequently, the subgroups of TNOs are: plutinos, plutoids, classical Kuiper belt objects, scattered disk objects (SDOs), and detached objects also known as inner Oort cloud objects. In other words, an object that orbits the Sun with a semi-major axis greater than Neptune’s (30.047 au) is a trans-Neptunian object. 1.1. ASTEROIDS 7

Figure 1.3: (a) Histogram of asteroids versus semi-major axis shows primary Kirk- wood gaps in the Asteroid Main-Belt (credit: Alan Chamberlain, JPL/Caltech). (b) Location of Jupiter’s Troyan asteroids at the Lagrangian points L4 and L5 (Kutner, 2003).

Centaurs

Named after the Greek mythological creatures—hybrids of horse and human— Centaurs are small solar system bodies with semi-major axis similar to those of the outer planets, i.e. between Jupiter and Neptune (from 5.5 to 29 au). Centaurs possess unstable orbits due to gravitational domination of the above mentioned planets. They are an interesting group because of the occasional resemblance to comets, like the display of the traditional coma around them, though, sometimes they do behave like normal asteroids. (10199) Chariklo, with a 260 km in diam- eter, was the first Centaur discovered, found by Charles Kowal in October 1977, after which and until January 2018, a total of 741 objects of this class have been discovered.

Trojans

Trojan asteroids are an exceptional type. They share orbit with a parent planet, which in 1:1 mean motion resonance with it, and this is possible because they are located around the Lagrangian points L4 and L5—somewhere 60◦ ahead and 60◦ behind the planet (Fig. 1.3). It is believed that the number of Jupiter Trojans may equal the number of asteroids in the Main Belt, reaching a total of 6,701 according to the Minor Planet Center (MPC). Besides Jupiter’s Trojans, and although their population is not as large, Earth and Uranus have one Trojan, Mars has 9 Trojans and there are 17 Neptune’s Trojans discovered so far. 8 CHAPTER 1. INTRODUCTION

Main Belt asteroids

Lying between the orbits of Mars and Jupiter, the Main Belt spans from 2.1 to 3.3 au from the Sun. Almost all of the known asteroids orbit inside this area (about 600,000). Estimations suggest that asteroids larger than 1 km in diam- eter may be up to a number between 1.1 and 1.9 million within the Belt, and “many million or perhaps billions of smaller asteroids also orbit in the main belt” (Elkins-Tanton, 2006, p.92). The Belt is divided into three zones: zone I (inner) stretches from 2.1 to 2.5 au, zone II (central) extends from 2.5 to 2.8 au, and zone III (outer) lengthens from 2.8 to 3.3 au. In 1918, Kiyotsugu Hirayama discov- ered orbital similarities among most of the Main Belt asteroids, thus he defined families according to orbital characteristics, e.g. Flora, Eos, Koronis and Themis (Hirayama, 1918). By 2015, a total of 122 families had been calculated (Nesvorny et al., 2015) using a method described in Zappala et al. (1990, 1994). Finally, it is worth remembering that the Main Belt encloses the previously defined Kirkwood gaps (Fig. 1.3), corresponding to orbital resonances with Jupiter, i.e. 4:1, 3:1, 5:2, and 2:1. These gaps are not totally empty but barely populated.

Near Earth Asteroids (NEAs) and Potentially Hazardous Asteroids (PHAs)

Near Earth Objects (NEOs) are asteroid and comets with a perihelion distance (q), less than 1.3 au. Near Earth Comets (NECS) are limited to short-period comets with an orbital period less than 200 years, Near Earth Asteroids (NEAs) are divided according to orbital elements, into four groups: Atira, Aten, Apollo, and Amor. On the other hand, Potentially Hazardous Asteroids (PHAs) are defined on two parameters, Earth Minimum Orbit Intersection Distance (MOID) and the absolute magnitude (H); both are a measure to the possibility for the asteroid to make a dangerous approach to the Earth. Table 1.3 and Figure 1.4 display characteristics of NEAs. As for PHAs defining parameters, Earth MOID can be described as the minimum distance between the orbit of the Earth and the asteroid, and indicates the closest possible approach of these objects. All asteroids with an Earth MOID of 0.05 au (7,480,000 km) or less are PHAs. As Ted Bowell and Bruce Koehn from the Lowell Observatory point, the MOID can act as an early warning indicator for collision. Due to planetary gravitational perturbations, asteroid orbits can change with time and, as a consequence, MOID also changes. A valid generalization of this change is of 0.02 au per century, hence, if the Earth MOID of a PHA is small, it must be under constant track. Meanwhile, the absolute magnitude H is defined as the brightness of asteroids, as seen at 1 au from the Sun and Earth, and at a zero phase angle (Boehnhardt, 2009). In addition, there is a direct relationship between magnitude H and the 1.1. ASTEROIDS 9

Figure 1.4: Orbital representation of the different groups of NEAs (Adapted from JPL, CNEOS) diameter size of an asteroid (Harris & Harris, 1999) given by:

− − d = 100.5[6.259 log10 a 0.4H] (1.1)

Where a is the albedo and d the diameter of the asteroid in kilometers. According to the Center for Near Earth Objects Studies, together with a MOID of 0.05 au, asteroids bigger than about 140 m—brighter than H = 22.0 with a 14% assumed albedo—are considered PHAs. According to Dymock (2010), two mechanisms rule the way asteroids from the Main Belt become NEA’s. In both mechanisms Kirkwood gaps play a crucial role. In the first one, two asteroids collide, and as a result, one, both or (a) frac- tion(s) of either may drop in one of the previously mentioned gaps. In the second mechanism, asteroids no larger than 20 km of diameter progressively move—a movement that usually lasts several millions of years—into the orbit resonances with Jupiter, and this progressive movement is caused by the Yarkovsky effect. The former occurs as follows, as asteroids transit around the Sun and rotate about their spin axis, they absorb and reradiate sunlight incident to them. This reradiation process modifies the asteroid’s orbit. In the case where asteroids have a prograde motion, the Yarkovsky effect accelerate them, moving them away from the Sun. In an asteroid with retrograde motion, the Yarkovsky force acts the other way around, decreasing its velocity and bringing it closer to the Sun. Once the asteroid has shifted unto one of the Kirkwood gaps, its orbit gets altered 10 CHAPTER 1. INTRODUCTION

Table 1.3: Near Earth Asteroids groups (Adapted from JPL, CNEOS)

Atiras Named after (163693) Atira. Atiras have a semi-major axis (a) and an aphelion distance (Q) less than 1.0 au and 0.983 au, respectively, and their orbits are contained entirely within the orbit of the Earth. Atens Named after (2062) Aten. Like Atiras, Atens have a semi-major axis (a) less than 1.0 au, but an aphelion distance (Q) greater than 0.983 au. Apollos Named after (1862) Apollo. They possess a semi-major axis (a) greater than 1.0 au and a perihelion distance (q) less than 1.017 au. Amors As Apollos, Amors have a semi-major axis (a) greater than 1.0 au and their perihelion distance (q) lies between 1.017 and 1.3 au. They were named after (1221) Amor. PHAs A NEAs whose Minimum Orbit Intersection Distance (MOID) with the Earth is 0.05 au or less, and H ≤ 22. by Jupiter’s gravity, with an outcome of eccentricity increment. Thus, sooner or later the asteroid turns into a Mars crosser and subsequently lands around the Earth’s neighborhood—making it a near-Earth asteroid or NEA. After planetary perturbations reduced the eccentricity, this secures the NEA to be kept in the proximity of Earth.

1.2 Photometry

As stated in Romanishin (2006), most of the astronomical information that comes to us, does so in some form of electromagnetic radiation. In this respect, as- tronomers are able to study a wide range of wavelength of the electromagnetic spectrum, i.e. from radio to gamma rays. Thus, analysing every range of ra- diation emitted by celestial objects provides essential information, not only of the composition of their bodies, or their temperature, but also about the whole history and evolution of the universe. The optical region of the spectrum—0.32 µm to 1.00 µm—stands out in impor- tance for two main reasons. The first one is that stars and galaxies emit a con- siderable quantity of their energy in its range or wavelength, the second reason is that the atmosphere of the Earth is, to a certain degree, transparent to the optical region. Consequently, and following the goal of observational astronomy—which is to make measurements of the electromagnetic radiation of celestial objects as precise as possible—several techniques have been developed to monitor these ob- jects. One of these techniques is photometry, which is according to Gallaway (2016), “one of the key observation pillars of astrophysics” (p.129). 1.2. PHOTOMETRY 11

Figure 1.5: Lightcurve of asteroid (1627) Ivar.

Photometry, in general terms, refers to the measurement of the amount of energy over a broad wavelength band of radiation (Romanishin, 2006), amount also designated as flux or brightness. By another side, a lightcurve is a plot of the resulting data of observations, generally magnitude—a measure of the brightness of the object—or flux versus time or phase (see Figure 1.5). The computation of brightness or other parameters variation—caused by the rotation of an object such as asteroids (Warner, 2003)—as well as the corresponding analysis of the data is called “Lightcurve Photometry.” Therefore, given that asteroids, as previously stated, only re-emit energy from the Sun, it is possible to observe them with a technique such as photometry.

It has been mentioned that the variations in brightness, as can be observed in Figure 1.5, are caused by the rotation of the asteroid. The time that an asteroid takes to complete one revolution around its own axis, is called rotation period, and “phase” represents a portion of that period that the asteroid has completed.

To obtain a lightcurve is necessary to use a method called differential photometry, which means to find the difference—in magnitude—between a target and a set of comparison stars or the average of those comparisons. From a lightcurve is possi- ble to deduce a number of characteristics of an asteroid, i.e. a lightcurve can tell us the period of rotation and the amplitude of the lightcurve (A), which measures if the relation between minimum and maximum cross sections (CSmin/CSmax) of the asteroid (see Equation 1.2) (Harris et al., 2014). A single lightcurve can also determine if the asteroid is rotating about a single fixed axis or if it is “trum- bling”; it can also be inferred if the asteroid has a satellite and measure the distance between both. As more lightcurves of minor planets are obtained, it 12 CHAPTER 1. INTRODUCTION is possible, to deduce an approximation of the shape and the orientation of the asteroid’s spin axis (Warner, 2003).

A = −2.5log(CSmin/CSmax) (1.2) Chapter 2

The Impact Hazard of Near-Earth Asteroids

The objective of the present chapter is to justify the study and determination of Near-Earth Asteroids physical parameters. Undoubtedly, many reasons exist to make science out of NEAs, all of them self-sufficient to stand an investigation, nevertheless, the emphasis is made on the impact hazard of these minor planets on Earth.

2.1 A Record of Impacts

Among the scientific community there is a consensus that the formation of the solar system—Sun, planets and minor planets—was completed around 4.5 billion years ago. The chaotic environment left over by that age led to an epoch were planetesimals—that were not incorporated into planets—essentially became pro- jectiles that bombarded surfaces of planets. Traces of that epoch, known as the Late Heavy Bombardment period (LHB), are still visible today (Figure 2.1) as craters on the surfaces of Mercury, the Moon and Mars (Ivanov, 2008). The end of the Heavy Bombardment period, around 3.3 billion years ago, was followed by a relatively slow evolution of the orbits of small solar system bodies. The slow evolution was characterized by less frequent impact between bodies and other alterations in their orbits. As a result, there was a constant bombardment rate, which was much lower than the one from LHB but which is distinguished in the consequent craters on planets, including the Earth (Ivanov, 2008). The dynamics of solar system bodies kept evolving and even though space envi- ronment is not as rough as in the LHB period, nowadays our planet is subjected to a constant flow of extraterrestrial material at a rate of approximately 40,000 tons per year—most of which reaches the atmosphere with sizes that range from

13 14 CHAPTER 2. THE IMPACT HAZARD OF NEAR-EARTH ASTEROIDS

(a) (b) Figure 2.1: (a) Full Moon and (b) Mercury, showing scars of large giant im- pacts that are remnants from the Late Heavy Bombardment period, about 3.3 billion years ago. Credits: (a) Galileo spacecraft (NASA), (b) University of Ari- zona/LPL/Southwest Research Institute. micron to centimeters (Brownlee, 2001).

Internal core-mantle crust dynamics and continuous extraterrestrial large im- pacts moulded the history of Earth, since they, “triggered seismic, tectonic, vol- canic and tsunami processes as well as several mass extinction of species” (Glik- son, 2013,p.1). However, and unlike the Moon, Mercury and some satellites of the outer planets—where craters of antique impacts are still visible—tectonic- magmatic processes on Earth erased the majority of that historical evidence. Fortunately, a considerable number of archaic impact craters were form on the young surface of our planet and some still exist. Nowadays, an estimated number of 180 impact structures have been recognized all over the globe (Figure 2.2). The largest impact structures found have diameters up to almost 300 km and, from a morphological point of view, two forms are recognisable: simple craters with diameters of ≤2–4 km, and complex craters, which are larger and have diameters of ≥2–4 km (Figure 2.3).

In 1980 Luis Alvarez, Nobel Laureate, established a connection between the impact of a kilometer-sized asteroid—occurred approximately 65 million years ago—and the end-Cretaceous mass extinction. Event which corresponds to the second largest mass extinction of species, when about 46% of living genera were extinguished—including dinosaurs. The crater located underneath the Yucatan Peninsula in the Gulf of Mexico, as can be seen in Figure 2.2, is a 180 km in diameter impact structure called Chicxulub, which was caused by the collision of a 5-15 km asteroid. Therefore, in 2011, a group of 41 experts from 33 institutions concluded that, as Alvarez originally proposed, the Chicxulub impact triggered the mass extinction at the Cretaceous-Tertiary (K-T) boundary (Glikson, 2013).

Another remarkable event caused by a cosmic object occurred on June 30th, 1908, 2.2. DEFENDING PLANET EARTH 15

Figure 2.2: Location of inland known craters on the surface of the Earth (Koeberl, 2013). in Tunguska, on the Siberian taiga, when a small asteroid—of approximately 100 m in diameter—exploted, releasing energy of 5-20 Mt TNT above the ground. The result was the devastation of some 2,000 km2 of forest, as well as environmental effects that reached as far as London (Figure 2.4, (a)). One of the latest significant events of the entrance of a cosmic object into the Earth occurred on 15th February 2013, when an asteroid of 20 meters in diam- eter and 11,000 metric tons exploded 23.3 kilometres above the Russian city of Chelyabinsk (Figure 2.4, (b)). The energy released by the explosion was more than 30 times bigger than the Hiroshima atomic bomb, still, pieces of the bolide were recuperated for further analysis. The Chelyabinsk impactor approached Earth from the direction of the Sun, thus, it could not have been seen by any telescope on Earth and hundreds of people were injured by broken windows due to the shock wave hit. The previous examples of impacts show clear evidence of the danger—for the Earth itself and its living organisms—from the collision of cosmic objects. Hence, mankind must find—as far as possible—a solution for the problem of defending planet Earth.

2.2 Defending Planet Earth

From the previous section we conclude that, since the formation of the solar system, collisions of cosmic objects on Earth have been constant. Given this hazardous environment, mankind has no other option than to face the threat and therefore use, to its utmost, all the scientific and technological capabilities to develop hazard mitigation strategies. In this respect, in 2010 The National Re- 16 CHAPTER 2. THE IMPACT HAZARD OF NEAR-EARTH ASTEROIDS

Figure 2.3: Examples of impact craters on Earth. (a)Tswaing (Saltpan)-crater in South Africa (1.2 km in diameter, 250,000 years old); (b) Wolfe Creek crater in Australia (1 km in diameter, 1 Ma old); (c) Meteor Crater in Arizona, U.S. (1.2 km in diameter, 50,000 years old); (d) Lonar crater, India (1.8 km in diameter, age ca. 50,000 years); (e) Mistastin crater in Canada (28 km in diameter, age ca. 38 Ma); (f) Roter Kamm crater in Namibia (2.5 km in diameter, age ca. 4 Ma); (g) Clearwater double crater in Canada (24 and 32 in km diameter respectively, age ca. 250 Ma); (h) Gosses Bluff crater in Australia (24 km in diameter, age 143 Ma); and (i) Aorounga crater in Chad (18 km in diameter, younger than ca. 300 Ma), (Koeberl, 2013). search Council, a U.S. institution, published the report: Defending Planet Earth: Near-Earth Object Surveys and Hazard Mitigation Strategies, which denotes that the only objects to be considered potentially capable of striking Earth, at least for the next century, are comets and asteroids whose orbital parameters belong to the near-Earth object category (1.1.3). Moreover surveys have found that at least 20% of NEOs have orbits that pass within 0.05 astronomical units of Earth and thus are classified as Potentially Hazardous Objects/Asteroids.

Defending Planet Earth was initiated after two mandates the U.S. Congress es- tablished for the search of NEOs by NASA. The first, in 1998, referred to as the Spaceguard Survey, “called for the agency to discover 90 percent of NEOs with a diameter or 1 kilometer of greater within 10 years”; the second mandate, in 2005, known as the Geoge E. Brown Jr. Near-Earth Object Survey, “called for NASA 2.2. DEFENDING PLANET EARTH 17

(a) (b)

Figure 2.4: (a) Effects on the Siberian forest by the Tunguska asteroid explotion, one of the largest recent impacts. Credit: Leonid Kolik. (b) The Chelyabinsk bolide in 2013 renew the awareness of asteroid impacts. Credit: Footage of an amateur video. to detect 90 percent of NEOs 140 meters in diameter or greater by 2020”. In summary, based on the approximate damage produced by the impact of NEOs of certain diameter (Table 2.1) and their size distribution (Figure 2.5), the report emphasizes the achievement of two tasks: • 1: NEO Survey To detect, track, catalogue, and characterize the physical characteristics of at least 90% of potential hazardous NEOs larger than 140 meters in diameter by the end of 2020. • 2: NEO Hazard Mitigation To produce an optimal approach to developing a deflection capability, in- cluding options with a significant international component. Despite the U.S. origin of the mandates, various institutions decided to take a step forward and other organisms have been created to support one or more of the duties needed to fulfill these two tasks. A single organization is not capable of performing the detection, tracking, cataloguing and characterization of the asteroid, and subsequently of the elaboration of mitigation strategies. It is not a goal of this work to mention every institution dedicated to each duty, however, it is important to refer the most prominent, which will be covered in the following section.

2.2.1 Detection and Tracking

• Lowell Observatory Near-Earth-Object Search (LONEOS) was located at Flagstaff, Arizona, and used a 0.6-meter-diameter telescope. LONEOS dis- covered 289 NEOs when it was active between 1993 and 2008. 18 CHAPTER 2. THE IMPACT HAZARD OF NEAR-EARTH ASTEROIDS

Table 2.1: Approximate average impact interval and impact energy of NEOs. (Adapted from Defending Planet Earth, National Research Council).

Type of Event Characteristic Di- Approximate Approximate ameter of Impacting Impact Energy Average Impact Object (MT) Interval (yrs) Airburst 25m 1 200 LocalScale 50m 10 2,000 Regionalscale 140m 300 30,000 Continentalscale 300m 2,000 10,0000 Below global 60m 20,000 200,000 catastrophe threshold Possible global 1km 100,000 700,000 catastrophe Above global 5km 10million 30million catastrophe threshold Massextinction 10km 100million 100million

• Near-Earth-Asteroid Tracking (NEAT) colaborated using a 1-meter-telescope on Haleakala, Maui, Hawai. It was the first fully automated asteroid-search telescope. Between 1996 and 2007, NEAT discovered 442 NEOs. • Catalina Sky Survey (CSS) is a high rate NEO discoverer. CSS is a system of 3 telescopes, one located in the Siding Spring Observatory in Australia and the other two placed in Arizona. The CSS has discovered more than 8,500 NEOs so far. • Lincoln Near Earth Asteroid Research Program (LINEAR) is a MIT pro- gram, it consists of a pair of telescopes in Socorro, New Mexico. LINEAR has discovered 2,641 NEOs. • Spacewatch is a project by the University of Arizona, whose operations started in 1984 with a 0.9-meter-diameter telescope in Kitt Peak, Arizona. Almost a thousand NEOs have been discovered by this project. • Wide-field Infra-red Survey Explorer for Near-Earth Objects (NEOWISE) is a NASA spacecraft mission. NEOWISE produces images of the sky in four infrared wavelength bands using a 0.4-meter-diameter telescope always 90 degrees from the Sun. Since 2010, NEOWISE has already discovered more than 250 NEOs. • Panoramic Survey Telescope and Rapid Response System (PanSTARRS) was developed and is operated by the Institute for Astronomy at the Uni- versity of Hawaii. Located in Haleakala, Maui, PanSTARRS has discovered 2.2. DEFENDING PLANET EARTH 19

Figure 2.5: NEOs current population estimate: Number(N) of objects as a func- tion of absolute magnitud H. Average impact interval scale (right), impact energy released in megatons (MT) of TNT for an assumed velocity of 20 km per sec- ond (top), and NEOs diameters determined assuming an average value of albedo of 14% (bottom). (Adapted from Defending Planet Earth, National Research Council).

more than 4,000 NEOs.

2.2.2 Cataloguing and Orbital Parameters Calculation

• Minor Planet Center (MPC) The MPC operates at the Smithsonian Astrophysical Observatory, it re- ceives and distributes astrometric measurements of minor planets, comets and irregular satellites of major planets. The identification, designation and orbital computation of minor planets is a responsibility of the MPC, which is sponsored by the International Astronomical Union (IAU). • Center for Near-Earth Object Studies (CNEOS) The CNEOS is a Jet Propulsion Laboratory center dedicated to the com- putation of orbits for NEOs in support of NASA’s Planetary Defence Co-

2.2. DEFENDING PLANET EARTH 21

Figure 2.7: Cumulative number of known Near-Earth Asteroids versus time. Here is shown the total of NEAs of all sizes discovered by all detection surveys differ- entiating them from the total of NEAs larger than 140 m and larger than 1 km in diameter. Potentially Hazardous Asteroids and Near-Earth Comets are also shown. (JPL, Center fot Near Earth Object Studies) number of NEAs larger than 1 km in diameter is 981±19. Figure 2.5 shows that the Spaceguard mandate of detecting 90% of all 1 km in diameter NEAs has already been met. On the other hand, the estimated number of NEAs with a diameter larger than 140 m is ∼13,200±1,900 (Mainzer et al., 2011), of which surveys have found more than 8,000 (Figure 2.7). Thus, the George E. Brown Jr. Near-Earth Object Survey is on the way to be accomplished.

With regard to cataloguing, the MPC is in charge of the asteroid provisional designation and the subsequent naming. Both the MPC and JPL compute orbital parameters and possess large databases that make this information available to the international community, which is based in the characterization previously gathered from asteroids.

Characterization of NEAs means that through observational or radar astronomy the physical quantities of asteroids, such as size, mass, shape, spin state, and whether the asteroid is metallic, stony or carbonaceous, solid, fractured or a “rubble pile” type, can be obtained. Observations suggest that future impacts cannot be avoided and will affect Earth as they had in the past, for this reason, characterization is essential in two respects. The first one is related to the miti- 22 CHAPTER 2. THE IMPACT HAZARD OF NEAR-EARTH ASTEROIDS gation strategies. When facing an imminent threat of an asteroid, SMPAG group must develop a series of plans to avoid the impact: slow-push or pull methods, kinetic impact or nuclear detonation. All of these mitigation strategies need the whole characteristic group of the target asteroid to be performed. The second aspect refers to the calculation of long-term orbital parameters. Grav- itational interaction modifies the orbits of asteroids as they approach Earth, hence, regular astrometric measurements are required to constrain these orbital parameters, but non-gravitational forces also play a key role in the long term evo- lution of the orbit. The first of two major non-gravitational forces was already described in Chapter 1, and is the so-called Yarkovsky effect—which changes the semi-major axis of objects and depends on the object’s distance from the Sun, spin state, size, mass, shape and thermal properties. The second non-gravitational al- teration comes from the YORP effect, which slowly modifies the spin rate of asteroids with irregular shape. Remitted photons apply a recoil force normal to the surface and if the body is not perfectly symmetrical, the sum of these forces produces a thermal torque, therefore, the effect strongly depends on the body’s shape.

2.3 Conclusion

Models of formation and evolution of the solar system always consider the role played by asteroids as crucial, furthermore, they are linked to the delivery of water and organic material to Earth and thus are a key element for the development of life. It is evident that all kind of resources—water and minerals mainly— have been over-exploited by humanity and now are in risk of running out, for that reason, asteroids’ mining is a project that soon will be accomplished. In addition, asteroids are characterized by the diversity of their composition, some of them being repositories of water, giving cause for companies like Planetary Resources and Deep Space Industries to develop technology to mine asteroids. The study of asteroids will help scientists to understand evolutionary processes within the solar system and explore our possible points of supply of some natural resources, moreover, research and characterization of asteroids is the only way humanity has to prevent and mitigate the asteroid impact hazard. Unfortunately, characterization “is falling well behind discovery, forming a bottleneck in science” (Elvis et al., 2013, p.2). Either for accurate long-term orbital calculation or for planning of mitigation strategies, a need exist to organize observing campaigns than can potentially generate enough photometric, spectrometric, and astrometric data obtained from the physical characteristics of the highest number of NEAs. Chapter 3

Objectives and Methodology

3.1 Objectives

General Purpose:

To obtain physical properties—period of rotation, amplitude of lightcurve, shape and spin axis orientation—of selected near-Earth asteroids (NEAs) through the synthesis of self-generated and public available photometric data.

Specific Aims:

1. Select asteroid targets and plan observations.

2. Perform photometric observation with the 77 cm Schmidt telescope of the Instituto Nacional de Astrof´ısica, Optica´ y Electr´onica (INAOE [National Institute of Astrophysics, Optics and Electronics]) at Tonantzintla Puebla, Mexico.

3. Build asteroid lightcurves and determine rotation periods and amplitudes of selected asteroids using the Minor Planet Observer (MPO) Canopus soft- ware.

4. Extract data set from the Asteroid Lightcurve Photometric Database (AL- CDEF).

5. Obtain the shape and spin axis orientation through lightcurve inversion method already implemented in MPO LCInvert software.

23 24 CHAPTER 3. OBJECTIVES AND METHODOLOGY 3.2 Methodology

3.2.1 Selection

The first stage of asteroid characterization is the object selection, which is based on three criteria. The first criteria has to do with the availability of an asteroid to be observed at a certain location. For this purpose, the MPO has made available tools that make possible the generation of a target list of observation opportunities. An acceptable acquisition of a target’s lightcurve, according to Warner, is “obtained when the asteroid is at significant different aspect angles (or viewing angles). This is not for just one apparition, i.e., the period of a few weeks or moths spanning opposition or brightest appearance, but for several different apparitions. With each apparition, the spin axis of the asteroid likely has a different angle from the line of sight to the observer”(2003, p.7). The selection process begins using the Potential Lightcurve Targets’ CALL home- page (http : //www.minorplanet.info/call.html) utility, which performs a quest— limited by a number of search parameters, such as asteroid family or group, range of magnitude, maximum diameter and declination range, among others—for as- teroids reaching brightest during a chosen month and year (Figure 3.1). Usually, the date of brightest and opposition are a few days apart of one another.

Figure 3.1: Potential Lightcurve Targets search format from Minor Planet Center. 3.2. METHODOLOGY 25

The search restriction parameters (Figure 3.1) are: • year and month of observation: March, April and May 2018 for the present work; • NEA group; • Favorable Only Status, meant for asteroids with favorable brightest appari- tions; • Ignore Call Status, parameter needed when working simultaneously on a certain asteroid; • Asteroid Lightcurve Database (LCDB) Status of U < 2, which means that the possible targets have a period reported; • (0,18) Magnitude Range, given that fainter objects will be impossible to detect with the Schmidt Camera and; • (-10,90) Dec Range since, according to the latitude and longitude of the observatory, objects with declination beyond -10 will be very hard to observe for a long period of time. • Diameter range is not a restriction, thus 5000 km is appropriate. Once the search has been restricted through the desired parameters, the CALL site returns a list of objects and their corresponding characteristics i.e. opposition date, opposition magnitude (V), date of brightest, brightest magnitude, period and amplitude, to name but a few. Therefore, the next step is the formulation of the asteroids’ ephemerides—right ascension and declination—for which, it is necessary to enter longitude, latitude and elevation of the observation as well as select the asteroids of interest. The CALL ephemerides provide right ascension, declination, phase angle, magnitude (V), distance to the Earth and the Sun from the asteroid, and other orbital parameters each day for thirty days after setting a date. The analysis of right ascension and declination indicate whether the asteroid is visible from our location and, if so, the time the asteroid will be available for its observation in the sky. The magnitude (V) indicates how brilliant the asteroid appears to the observer, the optical and electronic capabilities of the telescope in use, as well as the quality of the sky in the observatory location; these are parameters that establish a limit for the magnitude of the asteroid to observe. In reference to the results here presented, the magnitude limit for the telescope – affected mostly by weather conditions – is 17 mag. Differential photometry, as it has been mentioned in section 1.2, compares de brightness of the asteroid and stars, thus, in general terms, the brighter the asteroid the better. The second selection criterion is the period. As a requirement for the further shape determination, the period must be known precisely (Minor Planet Observer, 2009), hence, the aim is to observe asteroids whose period is already known to add a degree of accuracy. According to the schedule or the availability of time of 26 CHAPTER 3. OBJECTIVES AND METHODOLOGY a telescope, it is convenient to consider to choose asteroids with a period that, beyond atmospheric conditions, will be certain to complete in a few nights. In this regard, the recommendation is to choose asteroids whose period is no longer than 12 hours, in order for the full period to be observed in no more than 3 or 4 nights. Furthermore, databases show that there is a significant proportion of asteroid periods between 4 and 8 hours. The third criterion are the lightcurves that are publicly available on the Aster- oid Lightcurve Photometry Database (ALCDEF). The inversion method needs a minimum of 6 or 7 lightcurves obtained at different phase angles, not just from one apparition. The reason for this requirement is that at different apparitions, “the spin axis of the asteroid likely has a different angle from the line of sigh to the observer” (Warner, 2003, p.8).

Figure 3.2: Example of the associated lightcurves to a certain asteroid, displayed by the Asteroid Lightcurve Photometry Database site.

The ALCDEF site (http://alcdef.org/) is a repository for minor planet basic information, whose purpose is to allow researchers upload and download observa- tional data—lightcurves—for the modelling of shapes and spin axis. The database has a simple user interface, it only requires the input of the name or number of asteroid and it will display—if any—the lightcurves uploaded in a tabular format (Figure 3.2). Along with the date, the table shows the filter used, the author and the phase angle of observation, so that it can be compared with the ephemerides generated in the CALL site, and make sure that future observation contributes to the coverage of different phase angles. In addition to the table shown in Figure 3.2, the ALCDEF provides a summary of basic information of the asteroid, i.e. family, spectral class, diameter, H magnitude, G parameter, albedo, period and other information, all associated with a corresponding reference. In respect to period, most of the times there is more than one source reporting different periods of rotation, consequently each line carries a value (U) that judges the quality of the period solution (Warner et al., 2009). This value spans from 1 to 4 , 1 to 3 depending on the minor or major accuracy of the reported period, 3.2. METHODOLOGY 27 and 4 accounting for a pole solution. For the process of precessing the period, it is considered best to give greater importance to references with value ‘3’.

3.2.2 Observations

After the selection of the target asteroids, the second stage is the observation. It is explicit that every step of the characterization is crucial, however, the process of taking images of asteroids stands out in importance. The observation procedure consists of taking 4 types of images: 1. Light frames: the actual images of the asteroids. 2. Dark frames: used to remove the noise within the Charge-Coupled Device CCD. It is a measure of the dark current accumulated during the exposure time of light frames. 3. Flat frames: which account for the differences in sensitivity of all CCD pixels. 4. Bias frames: used to remove the noise in the image due to the CCD elec- tronics (dark current). In the first images type—light frames—the goal is to “catch” enough photons from the asteroid and the comparison stars without reaching the saturation of the CCD camera, which means to have a high signal-to-noise ratio (SNR) in order to get the needed photometric precision. Despite several references in photometry advice to take exposure of about 1% or 2% of the period, it is better to take images of different exposures times and look for the one best result for our purpose. For this same purpose, it is important to take into account the apparent faster movement of NEAs against Main-Belt asteroids. Consequently, and in order to get an optimal count value, a NEA and a Main-Belt asteroid with the same magnitude will have different exposure time. It is also a good practice to have delays between images, if the exposure time is in the order of 30 to 60 seconds— to avoid the excess of data—on the other hand, with longer exposure time, the delay is not necessary. Lastly, the total observation time of one session must be at least 1.5 or 2 times the period. Continuing with Dark frames, these are taken with the shutter closed, and have the same exposure time as the light frames. Flat frames, on the other side, can be taken with the evening or morning sky, or with the help of a white screen illuminated by a halogen lamp—taking into account that a good Flat frame must show a signal of approximately 85% of saturation level. Finally, the Bias frames, which are images taken with zero exposure time and the shutter closed. It is recommended to take Dark, Bias and Flat frames every night of observation at a similar temperature as the Light frames, it is also advisable to take more than 10 of each frame for the posterior image reduction. 28 CHAPTER 3. OBJECTIVES AND METHODOLOGY

Figure 3.3: Graphic enviroment of MPO Canopus.

3.2.3 Photometry

Once the object images are taken, the following step is to remove the electronic readout noise, thermal electrons, and pixel-to-pixel difference introduced in the CCD camera. The previous process of taking calibration images—Bias, Flat and Dark frames—is then necessary to execute the so-called cosmetic reduction. With the Image Reduction and Analysis Facility (IRAF), the reduction procedure consists in the creation of a Zero frame by averaging all the individual bias frames. In the same way, a Master Dark and a Master Flat are created, averaging all the Dark and Flat frames to finally substract the Zero frame or Master Dark from each Light frame dividing them by the normalized Master Flat.

After the Light frames have been corrected, what follows is to capture the pho- tometric measurements of the images, the lightcurve construction and the period analysis, which is denominated as lightcurve photometry. This process is per- formed using MPO Canopus—a software developed by Brian Warner, Director of the Palmer Divide Observatory, which incorporates the Fourier analysis algo- rithm for period determination elaborated by Alan Harris. Canopus provides a Lightcurve Wizard that helps the user in every stage of the lightcurve construc- tion, beginning with the astrometry, the selection of the target and comparison stars and the individual measurement of the magnitude differences, to the Fourier analysis and the result presentation: period and lightcurve amplitude. 3.2. METHODOLOGY 29

3.2.4 Shape Determination

The final stage is the shape and spin axis determination. The present work makes use of the software MPO LCInvert—also developed by Brian Warner—which is based on the algorithms and code of Mikko Kaasalainen and Josef Durech (Kaasalainen et al., 2014). MPO LCInvert is in essence, an implementation of the lightcurve inversion method (Kaasalainen et al., 2001; Kaasalainen & Torppa, 2001; Kaasalainen & Durech, 2007), which derives the shape and spin axis co- ordinates from lightcurve data. The software presents to the user an Inversion Wizard (Figure 3.4) that guides step-by-step the entire process of converting the lightcurves into a 3-D model. The Wizard requires the input, of the downloaded ALCDEF lightcurves of the target asteroid and the lightcurves generated by one’s own observation in a compatible file type. The results of observations, period de- termination and shape are to be displayed in the next chapters.

Figure 3.4: Graphic interface of the Inversion Wizard from MPO LCInvert. 30 CHAPTER 3. OBJECTIVES AND METHODOLOGY Chapter 4

Observations, Image Reduction and ALCDEF

This chapter focuses on the observations made with the Schmidt Camera, there- fore, a sketch of the main characteristics of the telescope is presented. Asteroid targets and the corresponding orbital elements, physical features and observa- tional circumstances are introduced as well, along with tables of lightcurves ob- servation dates of the selected asteroids available on the Asteroid Lightcurve Photometry Database.

4.1 Observations

4.1.1 Schmidt Camera

Located in Tonantzintla, the Schmidt camera was inaugurated in February 1942 as the principal scientific instrument of the Observatorio Astrof´ısico Nacional de Tonantzintla (OANTON [National Astrophysical Observatory of Tonanzintla]) (Cardona et al., 2011) paved the way for modern Astrophysics in Mexico for two main reasons: the dimension of its mirror (D = 77.4 cm) and its location at 19- degrees, latitude north. Both features have provided the outstanding discoveries made with this telescope, such as: Herbig-Haro objects, UV Cet-Type Flare Stars, T-Tauri stars, blue stars, planetary nebulae, blue galaxies and quasars (Vald´es et al., 2016). Due to several circumstances—mostly technological updating—the Schmidt Cam- era has had a series of modifications in its mount, image acquisition system and in its electronics in general, nevertheless, the optic system has remained original (Cardona et al., 2009). System which is constituted by by a corrector lens of 66.04 cm of diameter and a spherical primary mirror with a diameter of 77.4 cm.

31 32 CHAPTER 4. OBSERVATIONS, IMAGE REDUCTION AND ALCDEF

Figure 4.1: Schmidt Camera at INAOE.

To be able to use the Tonantzinta Schmidt Camera with CCD detectors, it was necessary to install a field flattening lens to reduce the field of view of the tele- scope. Nowadays, the Schmidt Camera possesses a modern Telescope Control System—developed by the physicist Sergio Noriega Nieblas—a CCD SBIG STF- 8300 and a five position filter wheel with the BVRI Johnson photometric system already installed . Tables 4.1 to 4.3 show the characteristics of the optical com- ponents of Schmidt Telescope.

Table 4.1: Primary mirror characteristics

Diameter D=77.4cm Effective Diameter De = 76.2 cm Radius of curvature Rc = 4,314.82 mm Focallength F=2,157.4mm FocalRatio F/Dc=3.25 PlateScale 95.6arcsec/mm

Table 4.2: Field flattening lens characteristics

Diameter D=190mm Radius of curvature C1 = -1,455.3095 mm Radius of curvature C2 = 1,455.3095 mm 4.1. OBSERVATIONS 33

Table 4.3: Corrector lens characteristics

Diameter Dc = 66.04 cm Thickness 2.2352 cm

Table 4.4: CCD Detector characteristics

Model SBIG STF-8300 / 5 Filter Wheel Imaging / Pixel Array 3,326 x 2,504 CCDSize 17.96x13.52mm PixelSize 5.4micron Imagescale(s) 95.6arcsec/mm FOV 28.9x21.76arcmin Imagescale(s) 0.52arcsec/pix

4.1.2 Selected Asteroids and Image Reduction

Through the Minor Planer Center tools, it was possible to produce a target list of observation opportunities for the months of March, April and May of 2018. As a result, five Near-Earth Asteroids were chosen under the criteria described in Chapter 3. Orbital elements and selected physical parameters of those asteroids are shown in Table 4.5 and Table 4.6, respectively.

Table 4.5: Orbital elements of observed asteroids at Epoch 2,458,200.5, 2018-Mar-23.0. (Source: JPL Small-Body Database Browser)

Name a(au) e i(deg) Ω(deg) M(deg) ω (deg) (25916) 2001 CP44 2.5613 0.4979 15.7454 94.7004 329.1712 199.6622 (1627)Ivar 1.8630 0.3965 8.4503 133.1382 306.5688 167.7429 (1036) Ganymed 2.6629 0.5335 26.6933 215.5521 183.3611 132.4535 (1866) Sisyphus 1.8933 0.5384 41.2022 63.4966 161.5984 293.0906 (450894)2008BT18 2.2217 0.5935 8.1337 107.6630 344.0186 139.2867

Given their orbital parameters, 3 of the selected NEAs belong to the Amor group: (25916) 2001 CP44, (1627) Ivar, (1036) Ganymed. The other two belong to the Apollo group: (1866) Sisyphus and (450894) 2008 BT18. Table 4.7 shows the dates of observations and other observational circumstances. Given the variations of the Spring weather conditions and the contrasting bright- ness of the asteroids, the integration times varied between 30 and 210 s. After the Bias and Flat-field correction process, the images were ready to be used in MPO Canopus, where the differential photometry and period analysis were per- formed. Canopus performs first the astrometry and then the photometry. For the photometry, 4 to 5 comparison stars were selected, verifying that they were solar analogs non-variable comparison stars, within the same field of view and near the path covered by the asteroid during the observations. 34 CHAPTER 4. OBSERVATIONS, IMAGE REDUCTION AND ALCDEF

Table 4.6: Selected physical parameters of observed asteroids.

Asteroid Ha Taxonomic Diameter(km) Albedo (mag) class (25916)2001CP44 13.6 Sb 5.683±0.030f 0.262±0.047f (1627)Ivar 13.2 Sc 8.370±0.075f 0.134±0.025f (1036)Ganymed 9.45 Sb 37.675±0.399f 0.238±0.048f (1866)Sisyphus 9.45 Sd 6.597±0.189f 0.255±0.049f (450894)2008BT18 18.3 Ve Binary: 0.600 and 0.20g > 0.200g aFrom the JPL HORIZONS online solar system data and ephemeris computation service. bLin, et al. (2018) cCarry, et al. (2016) dThomas, et al. (2014) eReddy, et al. (2008) f Mainzer, et al. (2016) gBenner, et al. (2008)

Table 4.7: Observational circumstances for observed asteroids

Asteroid Date(UT) RA(J2000.0) DEC(J2000.0) Delta r α (de- V (UA) (UA) grees) (mag) (25916) 2001 CP44 2018 Apr. 14.36 16h41m45.5s +03◦31′′27′′.0 0.841 1.675 27.2 15.6 2018 Apr. 16.33 16h43m19.0s +03◦39′′11′′.0 0.819 1.663 26.9 15.5 2018 Apr. 20.26 16h46m08.5s +03◦53′′19′′.0 0.776 1.640 26.2 15.3 2018 Apr. 21.31 16h46m49.7s +03◦56′′42′′.0 0.765 1.634 26.0 15.3 2018May26.10 16h50m44.6s +01◦52′′56′′.0 0.468 1.450 17.1 13.7 2018May28.15 16h49m49.6s +01◦20′′33′′.0 0.455 1.441 16.6 13.6 (1627)Ivar 2018Mar. 17.26 15h08m07.2s -02◦07′′19′′.0 0.893 1.708 26.71 14.8 2018 Mar. 27.23 15h15m17.8s -00◦19′′43′′.0 0.778 1.654 24.3 14.4 (1036) Ganymed 2018 Mar. 19.10 10h43m02.0s -18◦54′′38′′.0 3.166 4.083 6.2 15.4 2018 Mar. 20.10 10h42m18.7s -18◦46′′40′′.0 3.168 4.083 6.2 15.4 2018 Mar. 21.20 10h41m31.5s -18◦37′′42′′.0 3.170 4.083 6.2 15.4 (1866)Sisyphus 2018Mar. 25.32 13h26m02.8s +53◦01′′21′′.0 2.222 2.893 16.7 17.3 (450894) 2008 2018 Mar. 24.41 13h27m51.6s +45◦01′′10′′.0 0.207 1.143 41.3 16.8 BT18 2018 Mar. 29.24 13h57m09.3s +51◦31′′01′′.0 0.184 1.107 49.8 16.7 4.2. ASTEROID LIGHTCURVE PHOTOMETRY DATABASE 35 4.2 Asteroid Lightcurve Photometry Database

The ALCDEF repository—which provides data in the public domain—previously reported characteristics and lighcurve entries for the 5 observed asteroids. For the asteroid (25916) 2001 CP44, the ALCDEF reports 12 lightcurve entries in two different opposition dates, 2014 and 2018, with a phase angle coverage from +14.83 to +37.96. The asteroid (1627) Ivar has 46 entries in various opposition dates: 2009, 2012, 2015 and 2018; and a phase angle coverage from +14.62 to +61.20. (1036) Ganymed posses 141 lightcurve entries with a phase angle cover- age from +1.04 to +52.55, and the dates of observation that are from the 2009, 2011, 2012 and 2015 oppositions. (1866) Sisyphus was observed in the 2011, 2016 and 2018 oppositions, has 32 lightcurve entries and the coverage of phase angle spans from +9.64 to +19.42. The last asteroid, (450894) 2008 BT18, has 20 en- tries with a coverage from +20.47 to +60.55, which correspond to the dates of opposition of 2008 and 2018.

Table 4.8: ALCDEF lightcurves for (25916) 2001 CP44.

Mid-Date Phaseangle Mid-Date Phaseangle 2014-03-16 11:54:00 +37.32 2018-04-21 09:29:00 +26.00 2014-03-17 11:54:00 +37.48 2018-04-23 09:41:00 +25.62 2014-03-19 12:00:00 +37.80 2018-04-25 09:57:00 +25.23 2014-03-19 12:00:00 +37.96 2018-04-25 09:57:00 +14.87 2018-04-17 10:05:00 +26.68 2018-06-07 09:34:00 +14.86 2018-04-19 08:52:00 +26.36 2018-06-08 07:25:00 +14.83

Table 4.9: ALCDEF lightcurves for (1866) Sisyphus.

Mid-Date Phase Mid-Date Phase Mid-Date Phase 2011-05-10 06:21:00 +10.18 2011-05-30 05:01:00 +14.91 2016-05-22 07:03:00 +18.32 2011-05-12 08:28:00 +9.78 2011-05-30 07:54:00 +14.99 2016-05-23 06:58:00 +18.59 2011-05-13 05:50:00 +9.66 2011-06-04 07:16:00 +18.17 2016-05-24 07:01:00 +18.87 2011-05-13 11:16:00 +9.64 2011-06-05 07:17:00 +18.83 2016-05-25 07:00:00 +19.15 2011-05-21 05:32:00 +10.52 2016-05-13 07:31:00 +16.07 2016-05-26 06:54:00 +19.42 2011-05-21 09:03:00 +10.57 2016-05-16 07:20:00 +16.77 2018-04-04 07:39:00 +17.19 2011-05-22 05:04:00 +10.86 2016-05-17 07:19:00 +17.02 2018-04-05 05:34:00 +17.25 2011-05-22 08:42:00 +10.91 2016-05-18 07:38:00 +17.27 2018-04-08 04:35:00 +17.43 2011-05-28 05:06:00 +13.74 2016-05-19 07:44:00 +17.53 2018-04-09 07:21:00 +17.51 2011-05-28 08:15:00 +13.81 2016-05-20 07:00:00 +17.79 2018-04-10 07:15:00 +17.58 2011-05-29 08:20:00 +14.40 2016-05-21 06:35:00 +18.05 36 CHAPTER 4. OBSERVATIONS, IMAGE REDUCTION AND ALCDEF

Table 4.10: ALCDEF lightcurves for (450894) 2008 BT18.

Mid-Date Phase Mid-Date Phase Mid-Date Phase 2008-07-18 13:49:00 +57.50 2008-07-21 16:35:00 +44.25 2018-03-25 10:42:00 +43.03 2008-07-18 14:05:00 +57.43 2008-07-21 16:57:00 +44.21 2018-03-26 05:59:00 +44.38 2008-07-18 14:18:00 +57.37 2008-07-21 17:02:00 +44.20 2018-03-26 09:14:00 +44.61 2008-07-18 14:36:00 +57.29 2008-07-21 18:58:00 +43.97 2018-03-27 06:03:00 +46.12 2008-07-18 15:11:00 +57.13 2008-07-21 19:01:00 +43.96 2018-03-27 10:32:00 +46.45 2008-07-18 15:42:00 +57.00 2008-07-26 13:13:00 +34.36 2018-03-28 06:11:00 +47.94 2008-07-18 16:18:00 +56.84 2008-07-26 16:30:00 +34.16 2018-03-28 09:25:00 +48.19 2008-07-18 16:59:00 +56.66 2008-07-26 19:10:00 +33.99 2018-03-28 11:47:00 +48.37 2008-07-18 17:52:00 +56.44 2008-07-29 11:47:00 +30.45 2018-03-29 05:47:00 +49.78 2008-07-18 18:28:00 +56.28 2008-07-30 10:15:00 +29.38 2018-03-29 09:38:00 +50.08 2008-07-18 19:09:00 +56.11 2008-08-01 10:25:00 +27.32 2018-03-29 12:05:00 +50.28 2008-07-18 19:40:00 +55.98 2008-08-01 15:50:00 +27.10 2018-03-30 05:38:00 +51.70 2008-07-21 11:41:00 +44.85 2008-08-02 11:15:00 +26.35 2018-03-30 08:08:00 +51.90 2008-07-21 11:55:00 +44.82 2008-08-04 11:32:00 +24.67 2018-03-30 09:14:00 +52.00 2008-07-21 12:44:00 +44.72 2008-08-08 10:40:00 +21.97 2018-03-30 11:10:00 +52.16 2008-07-21 13:24:00 +44.64 2008-08-09 10:42:00 +21.41 2018-04-03 05:58:00 +60.11 2008-07-21 13:50:00 +44.58 2008-08-11 09:29:00 +20.47 2018-04-03 07:50:00 +60.29 2008-07-21 15:14:00 +44.41 2018-03-24 07:36:00 +41.21 2018-04-03 10:38:00 +60.55 2008-07-21 15:26:00 +44.39 2018-03-25 06:29:00 +42.74

Table 4.11: ALCDEF lightcurves for (1627) Ivar.

Mid-Date Phase Mid-Date Phase Mid-Date Phase 2008-09-05 10:00:00 +43.47 2008-12-04 06:00:00 +16.66 2013-06-20 10:33:00 +60.80 2008-09-06 10:00:00 +43.11 2008-12-07 05:30:00 +17.80 2013-06-22 10:10:00 +61.20 2008-09-07 10:00:00 +42.74 2008-12-29 06:00:00 +24.14 2013-08-14 10:17:00 +51.96 2008-10-02 10:00:00 +31.08 2009-01-01 05:00:00 +24.69 2013-08-15 10:21:00 +51.43 2008-10-07 10:00:00 +28.17 2009-01-02 05:00:00 +24.86 2013-08-16 10:22:00 +50.89 2008-10-08 08:00:00 +27.61 2009-01-03 04:00:00 +25.02 2013-10-05 08:49:00 +18.18 2008-10-09 10:30:00 +26.94 2009-01-15 04:40:00 +26.42 2015-01-02 10:59:00 +17.65 2008-10-22 09:00:00 +18.78 2009-01-16 04:30:00 +26.49 2015-01-03 11:07:00 +17.38 2008-10-23 08:00:00 +18.18 2009-01-18 04:30:00 +26.62 2015-01-04 11:14:00 +17.10 2008-10-24 09:00:00 +17.54 2009-01-28 04:00:00 +26.93 2015-01-06 10:55:00 +16.53 2008-10-25 09:00:00 +16.93 2009-01-29 04:00:00 +26.94 2015-01-07 11:12:00 +16.22 2008-10-26 09:30:00 +16.31 2009-01-30 04:45:00 +26.94 2018-04-14 09:44:00 +19.22 2008-10-27 08:00:00 +15.76 2009-02-02 05:00:00 +26.90 2018-04-15 09:03:00 +18.98 2008-10-29 08:00:00 +14.62 2013-06-01 09:52:00 +55.37 2018-05-08 22:53:32 +19.7 2008-12-01 06:30:00 +15.49 2013-06-02 09:57:00 +55.70 2008-12-03 07:00:00 +16.29 2013-06-03 09:53:00 +56.02 4.2. ASTEROID LIGHTCURVE PHOTOMETRY DATABASE 37

Table 4.12: ALCDEF lightcurves for (1036) Ganymed.

Mid-Date Phase Mid-Date Phase Mid-Date Phase 2008-12-03 12:00:00 +14.60 2011-07-10 23:45:00 +46.23 2011-10-10 07:00:00 +25.06 2008-12-29 11:00:00 +13.95 2011-07-11 23:00:00 +46.46 2011-10-11 07:00:00 +23.77 2009-01-01 11:15:00 +13.73 2011-07-15 07:00:00 +47.25 2011-10-12 05:30:00 +22.55 2009-01-08 11:00:00 +13.10 2011-07-16 07:00:00 +47.48 2011-10-12 07:00:00 +22.47 2009-01-15 10:30:00 +12.31 2011-07-16 23:00:00 +47.63 2011-10-12 10:30:00 +22.28 2009-01-18 10:15:00 +11.93 2011-07-17 07:00:00 +47.71 2011-10-13 05:30:00 +21.23 2009-01-28 09:30:00 +10.52 2011-07-17 23:00:00 +47.86 2011-10-13 10:00:00 +20.98 2009-01-29 09:20:00 +10.37 2011-07-19 07:00:00 +48.16 2011-10-14 05:00:00 +19.92 2009-01-30 09:20:00 +10.22 2011-07-20 23:00:00 +48.53 2011-10-14 10:00:00 +19.63 2009-02-01 09:10:00 +9.91 2011-07-23 00:00:00 +48.96 2011-10-17 07:00:00 +15.73 2009-02-02 09:00:00 +9.76 2011-07-27 07:00:00 +49.83 2011-10-18 07:00:00 +14.36 2009-02-03 07:00:00 +9.62 2011-07-27 23:40:00 +49.96 2011-10-19 07:00:00 +12.99 2009-02-19 08:00:00 +7.47 2011-08-03 07:00:00 +51.05 2011-10-20 07:00:00 +11.63 2009-03-16 04:40:00 +7.73 2011-08-03 23:00:00 +51.15 2011-10-21 07:00:00 +10.27 2009-03-17 04:30:00 +7.84 2011-08-04 23:00:00 +51.30 2011-10-22 07:00:00 +8.92 2009-03-18 05:40:00 +7.97 2011-08-06 23:30:00 +51.58 2011-10-23 07:00:00 +7.59 2009-03-19 05:30:00 +8.10 2011-08-08 00:20:00 +51.71 2011-10-24 07:00:00 +6.27 2009-03-21 05:20:00 +8.36 2011-08-11 00:30:00 +52.04 2011-10-28 07:00:00 +1.47 2009-03-24 05:30:00 +8.77 2011-08-12 00:30:00 +52.14 2011-10-29 07:00:00 +1.04 2009-03-25 05:15:00 +8.92 2011-08-12 23:00:00 +52.22 2011-10-30 05:00:00 +1.63 2009-03-27 05:00:00 +9.20 2011-08-13 23:00:00 +52.29 2011-10-30 10:00:00 +1.83 2009-03-28 05:00:00 +9.35 2011-08-15 07:00:00 +52.38 2011-10-31 07:00:00 +2.74 2009-03-29 05:00:00 +9.50 2011-08-17 23:00:00 +52.51 2011-11-03 07:00:00 +5.97 2009-04-22 04:30:00 +12.68 2011-08-21 23:15:00 +52.55 2011-11-04 06:00:00 +6.97 2011-05-16 09:00:00 +35.14 2011-08-23 07:00:00 +52.53 2011-11-06 06:00:00 +8.97 2011-05-17 09:00:00 +35.26 2011-08-24 00:00:00 +52.50 2011-11-15 06:00:00 +16.50 2011-05-19 09:30:00 +35.53 2011-08-25 07:00:00 +52.44 2011-11-17 05:00:00 +17.84 2011-05-21 09:00:00 +35.79 2011-08-26 00:00:00 +52.40 2011-11-21 04:00:00 +20.24 2011-05-29 07:00:00 +36.97 2011-09-10 23:00:00 +49.12 2011-11-24 07:00:00 +21.88 2011-06-01 08:00:00 +37.47 2011-09-12 23:00:00 +48.33 2011-11-26 07:00:00 +22.82 2011-06-05 07:00:00 +38.17 2011-09-16 23:10:00 +46.42 2011-11-27 07:00:00 +23.26 2011-06-09 09:30:00 +38.94 2011-09-19 00:20:00 +45.26 2011-11-28 05:00:00 +23.65 2011-06-10 09:30:00 +39.14 2011-09-23 23:00:00 +41.93 2011-12-12 03:00:00 +27.87 2011-06-11 09:30:00 +39.34 2011-09-24 02:00:00 +41.83 2011-12-15 03:00:00 +28.46 2011-06-15 08:00:00 +40.16 2011-09-27 05:00:00 +39.29 2011-12-17 02:00:00 +28.79 2011-06-19 07:00:00 +41.03 2011-09-28 22:50:00 +37.72 2012-01-08 04:00:00 +30.49 2011-06-22 08:00:00 +41.73 2011-09-29 01:30:00 +37.62 2012-01-10 04:00:00 +30.50 2011-06-23 09:00:00 +41.97 2011-09-29 03:20:00 +37.55 2012-01-12 02:00:00 +30.50 2011-06-24 00:00:00 +42.12 2011-10-02 22:20:00 +33.74 2012-01-18 04:00:00 +30.38 2011-06-25 07:00:00 +42.43 2011-10-03 00:50:00 +33.63 2015-04-29 07:15:00 +6.16 2011-06-27 09:00:00 +42.92 2011-10-03 03:05:00 +33.53 2015-04-30 08:43:00 +5.81 2011-07-02 07:30:00 +44.12 2011-10-04 22:55:00 +31.52 2015-05-01 06:41:00 +5.52 2011-07-02 08:00:00 +44.13 2011-10-05 00:10:00 +31.46 2015-05-02 08:13:00 +5.21 2011-07-07 07:30:00 +45.34 2011-10-05 03:15:00 +31.31 2015-05-03 07:51:00 +4.94 2011-07-07 23:00:00 +45.50 2011-10-06 23:05:00 +29.18 2015-05-07 08:09:00 +4.25 2011-07-08 23:15:00 +45.74 2011-10-07 01:15:00 +29.07 2015-05-08 07:14:00 +4.21 2011-07-09 23:25:00 +45.99 2011-10-07 03:20:00 +28.97 2015-05-09 07:59:00 +4.23 38 CHAPTER 4. OBSERVATIONS, IMAGE REDUCTION AND ALCDEF Chapter 5

Results

This chapter is divided into three parts, the first one presents the results of the observations made with the Tonantzintla Schmidt Camera (TSC). The explana- tion of the Lightcurve Inversion Method is found in the second section and the results obtained by means of LCInvert are presented in the third part of the chapter.

5.1 Lightcurves

Table 5.1 resumes the results of the TSC observations, i.e. total time observed, period, amplitude of the lightcurve and so on. It was found that most of the lightcurves had an amplitude less than 0.2-0.3 mag. According to Harris et al. (2014) the best Fourier fit for those lightcurves is a 4th or 6th fit, whereas the cross section rate was calculated using the equation 1.2. The particulars of every asteroid can be found in the following subsections.

Table 5.1: Rotation period and brightness amplitude of the observed asteoids

Asteroid Observedtime(hrs) Period(hrs) Amplitude(mag) Fourier fit CSmin/CSmax (25916)2001CP44(a) 6.21 4.6000±0.0030 0.24 6th 0.80 (25916)2001CP44(b) 9.31 4.6080±0.0030 0.26 6th 0.79 (25916)2001CP44(c) 11.43 4.6000±0.0008 0.23 6th 0.81 (1627)Ivar 8.86 4.7954±0.0002 0.90 4th 0.44 (1036)Ganymed 14.25 10.2940±0.0120 0.13 6th 0.89 (1866)Sisyphus 3.62 2.3900±0.0030 0.12 6th 0.90 (450894)2008BT18 6:98 2.7920±0.0030 0.14 6th 0.88

39 40 CHAPTER 5. RESULTS

5.1.1 (25916) 2001 CP44

Asteroid (25916) 2001 CP44 was observed in six different occasions between April and May 2018. Due to the small variations on the phase angle, it was possible to group the observation into three pairs of nights. For every pair, a period search was performed. ALCDEF data base reports a period of 4.6021 h, which conforms with the present findings.

(a)

On April 14th (UT), images were collected between 08:52:12 - 11:39:26 UT while on April 16th (UT), exposures began at 08:00:08 UT and finished at 11:26:3 UT, hence, the total time of observation was of 6.21 hours. Figures 5.1 and 5.2 show the raw data plots of both nights without attempts to fit the data to a certain period.

Figure 5.1 Figure 5.2

Five comparison stars were selected in every session. The observation fields, where the asteroid and the stars laid, are shown in figures 5.3 and 5.4. Tables 5.2 and 5.3 contain the data of the selected star for every session. The analysis found a period of P = 4.600 ± 0.003 hours with an amplitude of A = 0.24 mag using a 6th-order Fourier fit (Figure 5.5). The RMS scatter on the fit is 0.0253 mag (Figure 5.6).

Table 5.2: Comparison stars data from the April 14th, 2018 session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 164134.83+033403.7 16:41:34.83 +03:34:04.0 14.120 14.505 0.678 0.385 2 164143.91+033401.6 16:41:43.94 +03:34:01.9 14.248 14.648 0.711 0.400 3 164200.50+033509.9 16:42:00.51 +03:35:10.1 15.282 15.686 0.718 0.404 4 164125.09+032921.0 16:41:25.08 +03:29:20.9 15.015 15.381 0.641 0.366 5 164121.55+033715.1 16:41:21.56 +03:37:15.2 14.011 14.436 0.761 0.425

42 CHAPTER 5. RESULTS

(b)

On April 20th (UT), the beginning of observation took place at 06:21:55 UT and ended at 11:34:52 UT. On April 21st, observations began at 07:25:45 UT and finished at 11:32:17 UT. Thus the total time of observation from these two nights was 9.31 hours. Figures 5.7 and 5.8 show the raw data plot of the aforementioned nights.

Figure 5.7 Figure 5.8

Table 5.4: Comparison stars data from the April 20th, 2018 session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 164550.21+035748.3 16:45:50.19 +03:57:48.2 14.890 15.255 0.639 0.365 2 164628.01+035342.1 16:46:28.02 +03:53:42.0 14.655 15.014 0.627 0.359 3 164631.03+035401.7 16:46:31.04 +03:54:01.7 14.413 14.889 0.861 0.476 4 164604.71+035326.5 16:46:04.74 +03:53:27.0 14.610 15.071 0.830 0.461

Table 5.5: Comparison stars data from the April 21st, 2018 session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 164717.00+040127.1 16:43:55.29 +03:44:04.4 14.304 14.736 0.776 0.432 2 164720.34+040157.7 16:43:37.60 +03:35:59.8 14.419 14.804 0.678 0.385 3 164645.62+035854.7 16:43:14.68 +03:42:11.7 15.081 15.560 0.870 0.479 4 164704.76+035549.7 16:44:03.34 +03:40:49.6 14.542 14.882 0.590 0.340 5 164651.43+035528.1 16:43:32.74 +03:36:25.3 14.542 14.967 0.759 0.425

Four comparison stars were selected for the April 20th session (Figure 5.9 and Table 5.4) and five stars were selected for the April 21st session (Figure 5.10 and Table 5.5). Analysis indicate a period of P = 4.608 ± 0.003 hours with an amplitude of A =0.26 mag using a 6th-order Fourier fit (Figure 5.11). The RMS scatter on the fit is 0.0261 mag (Figure 5.12).

44 CHAPTER 5. RESULTS

Table 5.6: Comparison stars data from the May 26th, 2018 session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 165037.83+015122.0 16:50:37.86 +01:51:22.3 13.761 14.242 0.871 0.481 2 165025.97+015008.4 16:50:25.96 +01:50:08.4 13.094 13.505 0.731 0.411 3 164959.47+015525.2 16:49:59.47 +01:55:25.4 13.428 13.835 0.724 0.407 4 165003.79+014955.8 16:50:03.79 +01:49:56.2 13.156 13.541 0.680 0.385 5 164956.65+015002.0 16:49:56.64 +01:50:02.0 13.722 14.088 0.641 0.366

Table 5.7: Comparison stars data from the May 28th, 2018 session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 164922.76+011928.4 16:49:22.75+01:19:28.3 12.491 12.935 0.799 0.444 2 164927.70+011432.6 16:49:27.72+01:14:32.6 12.940 13.326 0.681 0.386 3 164953.80+011430.2 16:49:53.80+01:14:30.3 12.724 13.033 0.530 0.309 4 164916.34+012128.0 16:49:16.34+01:21:28.0 12.464 12.881 0.743 0.417 5 165013.94+011312.9 16:50:13.95+01:13:12.6 13.100 13.401 0.515 0.301

(c)

On May 26th (UT), the observation began at 03:29:18 UT and ended at 9:28:43 UT, whereas on May 28th (UT) observations started at 03:42:23 UT and finished at 09:09:14 UT. The total time of observation from these two nights was 11.43 hours. Figures 5.13 and 5.14 show the raw data plot of the aforementioned nights.

Figure 5.13 Figure 5.14

Five comparison stars were selected for the sessions of May 26th (Figure 5.15 and Table 5.6) and May 28th (Figure 5.16 and Table 5.7). Analysis indicate a period of P = 4.6000 ± 0.0008 hours with an amplitude of A = 0.23 mag using a 6th-order Fourier fit (Figure 5.17). The RMS scatter on the fit is 0.0171 mag (Figure 5.18).

46 CHAPTER 5. RESULTS

5.1.2 (1627) Ivar

Observation of (1627) Ivar were carried out during the nights of March 17th (UT) and March 27th (UT). On the first night observations began at 06:20:44 UT and finished at 12:03:59 UT, while on the second night observations were performed between 05:31:42 and 08:40:44 UT. The total time of observation was 8.86 hours. Figures 5.19 and 5.20 show the raw data of both nights.

Figure 5.19 Figure 5.20

Five comparison stars were selected for the session of March 17th session (Figure 5.21 and Table 5.8) as well as the March 27th session (5.22 and Table 5.9). Analysis indicate a period of P = 4.7954 ± 0.0002 hours with an amplitude of A = 0.90 mag using a 4th-order Fourier fit (Figure 5.23). The RMS scatter on the fit is 0.0340 mag (Figure 5.24).

Table 5.8: Comparison stars data from the March 17th, 2018 session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 150832.80-020434.4 15:08:32.81 -02:04:34.6 14.742 14.742 0.667 0.379 2 150747.83-020317.8 15:07:47.84 -02:03:17.6 14.136 14.136 0.721 0.406 3 150754.72-020950.5 15:07:54.73 -02:09:50.7 14.472 14.472 0.694 0.392 4 150802.34-020604.8 15:08:02.34 -02:06:05.3 15.067 15.067 0.673 0.381 5 150805.28-020554.3 15:08:05.31 -02:05:54.0 14.643 14.643 0.643 0.367

Table 5.9: Comparison stars data from the March 27th, 2018 session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 151449.03-001500.7 15:14:49.04 -00:15:01.0 13.976 14.302 0.563 0.326 2 151457.22-001543.1 15:14:57.20 -00:15:43.3 13.973 14.417 0.797 0.444 3 151505.07-002042.8 15:15:05.07 -00:20:42.7 13.674 14.158 0.612 0.351 4 151501.76-001132.3 15:15:01.77 -00:11:32.3 13.674 13.995 0.552 0.321 5 151514.24-001011.6 15:15:14.26 -00:10:11.7 13.075 13.413 0.585 0.338

48 CHAPTER 5. RESULTS

5.1.3 (1036) Ganymed

Due to the previously reported long period (P = 10.297 hours, ALCDEF), the asteroid (1036) Ganymed was observed during three consecutive nights in or- der to ensure that the period was fully covered. On March 19th (UT), the ob- servation began at 02:24:32 UT and finished at 06:56:50 UT. On March 20th (UT),observations were performed between 02:27:49 and 08:34:16 UT. On the last day of observation, March 21st (UT), the data gathering started at 04:52:57 UT and ended at 08:29:55 UT. The time of observation between three night was 14.25 hours. Raw data from these three nights are shown in Figures 5.25, 5.26, and 5.27.

Figure 5.25 Figure 5.26

Figure 5.27

The comparison stars from March 19th, 20th and 21st are shown in Figures 5.28, 5.29 and 5.30, respectively, and Tables 5.10, 5.11 and 5.12 show the data obtained from them. The Fourier analysis indicates a period of P = 10.294 ± 0.012 hours with an amplitude of A = 0.13 mag using a 6th-order Fourier fit (Figure 5.31). The RMS scatter on the fit is 0.0306 mag (Figure 5.32).

52 CHAPTER 5. RESULTS

Table 5.13: Comparison stars data from the March 25th, 2018 session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 132552.14+530532.1 13:25:52.13 +53:05:32.1 16.170 16.551 0.616 0.381 2 132612.10+530704.3 13:26:12.14 +53:07:04.5 15.808 16.179 0.653 0.371 3 132524.45+530839.5 13:25:24.43 +53:08:39.3 15.968 16.338 0.551 0.370 4 132535.64+525624.8 13:25:35.64 +52:56:25.1 15.120 15.533 0.718 0.413 5 132619.78+525901.7 13:26:19.78 +52:59:01.5 16.047 16.490 0.664 0.443

Figure 5.35 Figure 5.36

5.1.5 (450894) 2008BT18

Observations of (450894) 2008BT18 were carried out during the nights of March 24 (UT) and March 29th (UT). The first night the observations began at 08:45:02 UT and finished at 11:57:51 UT, while on the second night observations were performed between 05:41:55 and 09:30:21 UT. The total time of observation was 6.98 hours. Figures 5.37 and 5.38 show the raw data of both nights. Due to the fast apparent movement of the asteroid against the sky, it was necessary to divide every night of observation in two sessions, given that the object did not stay in the same field of view during the night. Depending on the availability of solar analogs, four to five comparison stars were selected for the sessions of March 24th (Figures 5.37 and 5.38 and Tables 5.14 and 5.15) and the same number of star (four to five) for the March 29th sessions (Figures 5.39 and 5.40 and Tables 5.16 and 5.17). Analysis indicates a period of P = 2.790 ± 0.003 hours with an amplitude of A = 0.14 mag using a 6th-order Fourier fit (Figure 5.43). The RMS scatter on the fit is 0.0340 mag (Figure 5.44). 5.1. LIGHTCURVES 53

Figure 5.37 Figure 5.38

Table 5.14: Comparison stars data from the March 24th, 2018 first session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 132715.66+445845.7 13:27:15.65 +44:58:45.8 14.114 14.590 0.861 0.476 2 132648.91+445813.5 13:26:48.89 +44:58:13.7 15.480 15.907 0.762 0.427 3 132650.14+445724.2 13:26:50.11 +44:57:24.3 14.855 15.349 0.898 0.494 4 132729.86+450026.1 13:27:29.86 +45:00:25.9 14.144 14.618 0.858 0.474

Table 5.15: Comparison stars data from the March 24th, 2018 second session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 132804.52+450911.2 13:28:04.50 +45:09:11.3 15.260 15.611 0.612 0.351 2 132749.46+450447.5 13:27:49.46 +45:04:47.4 14.344 14.731 0.683 0.387 3 132823.72+450545.8 13:28:23.73 +45:05:45.9 14.012 14.346 0.577 0.332 4 132839.09+450625.6 13:28:39.07 +45:06:25.5 14.303 14.756 0.816 0.453 5 132857.25+450651.3 13:28:57.28 +45:06:51.0 14.012 14.498 0.881 0.486

Table 5.16: Comparison stars data from the March 29th, 2018 first session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 135724.95+513624.9 13:25:52.13 +53:05:32.1 14.712 15.151 0.787 0.439 2 135836.85+514201.2 13:26:12.14 +53:07:04.5 15.042 15.455 0.736 0.413 3 135755.05+514430.4 13:25:24.43 +53:08:39.3 14.529 14.836 0.527 0.307 4 135713.34+514422.2 13:25:35.64 +52:56:25.1 15.104 15.519 0.600 0.415

Table 5.17: Comparison stars data from the March 29th, 2018 second session

Comp Name-MPOSC3 RA(J2000) Dec(J2000) Magnitude(Inst) V B-V V-R 1 135749.01+514751.9 13:57:49.01 +51:47:52.0 15.474 16.476 0.615 0.387 2 135817.89+514743.0 13:58:17.90 +51:47:42.8 14.807 15.698 0.564 0.327 3 135836.84+514201.1 13:58:36.78 +51:42:01.4 15.042 16.191 0.736 0.413 4 135830.32+514859.0 13:58:30.33 +51:48:58.9 15.643 16.990 0.876 0.471 5 135824.47+514846.5 13:58:24.54 +51:48:46.6 15.714 16.601 0.532 0.355

5.2. THE INVERSION METHOD 55 5.2 The inversion Method

The next step in the characterization process, once the lightcurve photometry has been completed, is to obtain a 3D Shape of the asteroids observed. In the present case, the aim is to get a convex representation of the asteroid, which is only an approximation of the real shape, as it is known that an asteroid is not totally convex. To fulfill this objective, the inversion method already implemented in the MPO LCInvert software was used. Due to the use of this software, it is possible to obtain the 3D model approximation of the asteroid and the orientation of the pole of rotation in terms of the coordinates λ and β, i.e. longitude and latitude of the pole. The complete lightcurve inversion method is fully described in Kaasalainen et al. (2001), Kaasalainen & Torppa (2001) and Kaasalainen & Durech (2007). The intention of this section is not to reproduce those papers literally, however, but to provide a simple description of the method stages along with an explanation of those stages in the MPO LCInvert software. In order to do this, the inversion process can be divided into five stages: 1. Orbital Elements The load orbital elements, in the case of LCInvert, is done by a file that contains all asteroid orbital elements data from the Minor Planet Center, and thus this file must be updated constantly. 2. Import of Lightcurves Once the orbital elements of the asteroids are set, the next step is to import the lightcurve data. Usually, this data comes in different formats, such as MPO Canopus or ALCDEF, nevertheless, all of these formats contain the same information about photometric observations, the main difference is the way the information is presented, i.e. the arrangement of the data. As mentioned before, LCInvert has an inversion wizard that allows the conversion of the files in MPO Canopus, Generic and ALCDEF format to Kaasalainen format. This format contains the lightcurve data and the corresponding geometry, i.e. the epoch in JD, the brightness in intensity units and the ecliptic astrocentric Cartesian coordinates x,y,z of the Sun and of the Earth in AU. Following the conversion, the files are loaded again into the wizard. 3. Period Search When the period is not known with enough accuracy, LCInvert provides a period “finder”. Finding the right period is the most important step in the inversion method. The period search begins with a number of initial trial periods contained within an interval previously stated and selects the period that gives the lowest χ2 value. The number of trial periods within 56 CHAPTER 5. RESULTS

the period interval [P0,P1] is:

2∆t(P1 − P0) 1 Nper = (5.1) P0P1 p

where ∆t is the complete epoch rang of the lightcurve data, and the coeffi- cient p of the period step, which is always set to p< 1. 4. Inversion Routine At this stage, the program computes the shape, spin and scattering model that gives the best fit to the input of lightcurves. The shape computation obtains a convex polyhedron, i.e. the areas of the facets of the polyhedron and the fixed normals pointing outward the facets. The program calculates 2 and writes down values of χrel (Eq. 5.2), which basically compares the input lightcurves with a modeled or “synthetic” lightcurves. Every group of synthetic lightcurves represent a pair of pole coordinates trial, λ and β, that the program generates to fit to the original data.

(i) 2 L L(i) χ2 = obs − (5.2) rel X (i) (i) i Lobs L

(i) (i) Where Lobs and L are observed and modeled lightcurves, and they are (i) (i) renormalized through the average brightness Lobs and L . In LCInvert, the pole and shape search can be done by three different ap- proaches according to the precision wanted and the time available given that some searches can last up to several days. The Coarse approach searches for 84 pole positions with steps of 30◦ both in longitude, λ and latitude, β. That means that the program begins the search with the λ), β pair (0.0, 2 -90.0) and writes down the value of χrel obtained, then the next pair is 2 (0.0, -60.0) and again writes down the χrel value. The second approach is called Medium and searches for 312 pole positions with steps of 15◦ both in longitude and latitude. The last option is the Fine search, which finds 49 possible poles solution and uses ±30◦ in 10 steps for a given longitude and latitude. When the search is completed, a plot called “Pole search plot” is shown and presents the pole solutions using gradations between blue and red. Blue color is assigned to the best result and red to the worst. 5. 3D Shape The lowest χ2 value is used as an input for the “Minkowski” procedure, which reconstructs the convex polyhedron corresponding to given facet areas and surface that are normal to this areas. The output polyhedral model contains the number of vertices and facets, together with the vertex x,y,z coordinates. 5.2. THE INVERSION METHOD 57

The 3D Shape in MPO LCInvert is shown in three different modes or views. “Equator” mode displays the model as seen “when the observe is directly over the equator of the asteroid, at local noon, and 0◦ rotation. The ”sun” would be directly behind the observer.”(Minor Planet Observer, 2009, p.32). “Ecliptic” mode “places the observer on the plane of the ecliptic looking directly at the center of the asteroid. The asteroid is at either ascending or descending node, so that the observer is not “peeking” over the asteroid. The sun is directly behind the observer, on the plane of the ecliptic.”(Bdw Publishing, 2009, p.33). “4-Vane” view shows four fixed views of the model: from over the north pole, from over the south pole, from above the equator at local noon, and from the equator at the sunrise line. 58 CHAPTER 5. RESULTS 5.3 MPO LCInvert Results

5.3.1 (25916) 2001 CP44

The interval used for the period search was between 4.590 and 4.607 hours. Ide- ally, the lowest χ2 value should be at least 10% lower than the second lowest, in this case, more than 1 period lay within the 10% limit. The lowest χ2 period value found was P = 4.59777 hours (χ2 = 0.67628), this period was used for the search of the spin axis. The pole search method used was a Coarse Search (Figure 5.45).

Figure 5.45

According to the LCInvert manual, when there is not a clear “right” period, a Medium Search or a Fine Search become useless, and the possible outcomes of that searches will not provide a singular result. The most feasible solutions are the two lowest χ2 poles from the Coarse Search shown in Table 5.18. For asteroids orbiting near the plane of the ecliptic, there are two possible poles with the same β and λ ±180◦, the λ = 60.0, β = +90.0 and λ = 240.0 and β = +90.0 agreed to the rule. The two pole solutions were converted into a 3D shape and can be appreciated in Figures 5.46 - 5.51

Table 5.18: Coarse Search results for (25916) 2001 CP44

λ β Chi-squared value Period 60 +90 0.679268 4.59777 240 +90 0.679268 4.59777 5.3. MPO LCINVERT RESULTS 59

Figure 5.46: 4-Vane model view from the pole solution λ = 60.0, β = +90.0 of (25916) 2001 CP44.

Figure 5.47: Ecliptic model view from the pole solution λ = 60.0, β = +90.0 of (25916) 2001 CP44.

Figure 5.48: Equator model view from the pole solution λ = 60.0, β = +90.0 of (25916) 2001 CP44. 60 CHAPTER 5. RESULTS

Figure 5.49: 4-Vane model view from the pole solution λ = 240.0, β = +90.0 of (25916) 2001 CP44.

Figure 5.50: Ecliptic model view from the pole solution λ = 240.0, β = +90.0 of (25916) 2001 CP44.

Figure 5.51: Equator model view from the pole solution λ = 240.0, β = +90.0 of (25916) 2001 CP44. 5.3. MPO LCINVERT RESULTS 61

5.3.2 (1627) Ivar

The period search was performed using an interval between 4.7947 and 4.7980 hours. Table 5.19 contains the top five periods found with the lowest chi-squared values. Table 5.19: Period search results for (1627) Ivar

Period Chi-squared value 4.79516 1.49699 4.79488 5.56558 4.79488 6.79769 4.79544 6.79769 4.79516 6.95170

In this case, there is a clear minimum in the Chi-squared values, hence, the period P = 4.79516 hours could be used as input to the Pole Search. The Pole Search was made in two stages. During the first stage, the Coarse Search indicated that the solution for the spin vector direction, with the lowest Chi-squared associated, was λ = 330.0 and β = +30.0. Table 5.20 shows the top five lowest Chi-square pole solutions. In Figures 5.52 and 5.53 it can also be noted the difference in Chi-squared values between the Pole solutions.

Table 5.20: Coarse Search results for (1627) Ivar

λ β Chi-squared value 330.0 +30.0 2.395543 0.0 +60.0 4.282726 120.0 +30.0 5.119674 330.0 +60.0 5.526873 120.0 +60.0 9.610955

During the second stage, the λ = 330.0 and β = +30.0 values and the period P = 4.79516 hours were used as initial parameter for the Fine Search. The top five lowest Chi-squared value Pole solution are shown in Table 5.20. Figures 5.54 and 5.55 also show the Fine Search results. The outcome solution with the lowest Chi-squared value was λ = 335.425 and β = +36.993, with the period P = 4.79516 hours. In the particular case of (1627) Ivar, the Pole solution can be compared to two entries in the DAMIT data base. The fist one (Kaasalainen et al., 2004) shows a Pole orientation of λ = 336.0, β = +39.0 and the period P =4.795170. The second entry (Hanuˇset al., 2015) indicates a pole solution of λ = 334.0, β = +39.0 and period P =4.79516 hours. Once the Pole Search was made, the process of converting the model data into a 3-D representation takes place. The result of this process can be appreciated in Figures 5.56, 5.57 and 5.58. 62 CHAPTER 5. RESULTS

Figure 5.52

Figure 5.53

Table 5.21: Fine Search results for (1627) Ivar

λ β Chi-squared value 335.425 +36.993 1.433516 335.657 +37.932 1.485482 335.475 +38.024 1.492897 336.510 +39.424 1.505810 335.066 +36.872 1.532027 5.3. MPO LCINVERT RESULTS 63

Figure 5.54

Figure 5.55

Figure 5.56: 4-Vane model view 64 CHAPTER 5. RESULTS

Figure 5.57: (1627) Ivar ecliptic model view.

Figure 5.58: (1627) Ivar equator model view. 5.3. MPO LCINVERT RESULTS 65

5.3.3 (1036) Ganymed

The interval used for the period search was between 10.296 and 10.332 hours, and Table 5.22 shows the five least Chi-squared value periods. As can be easily noted, the period P = 10.312837 hours is 10% lower (in Chi-squared terms) than the second period.

Table 5.22: Period search results for (1036) Ganymed

Period Chi-squared value 10.312837 2.58998 10.312835 2.94841 10.314802 3.12594 10.311149 3.2629 10.311097 3.33813

Figure 5.59

After performing a Coarse Search, the results indicated that the solution remained around β = −90.0. The following step was to perform a Fine Search around β = −90.0, where 3 shape-pole solutions with very similar Chi-squared values and pole coordinates where found (Table 5.23). The 3D shape of the λ = 178.696, β = −76.671 solution is shown in Figures 5.60, 5.61 and 5.62, in the same way, the λ = 179.176, β = −76.726 solution is presented in Figures 5.63, 5.64 and 5.65, and Figures 5.66, 5.67 and 5.68 show the λ = 178.479, β = −76.755 solution. However, Hanuˇs et al. (2015) reports a pole solution of λ = 190.0, β = −78.0 and Viikinkoski et al. (2017) reports a pole solution of λ = 195.0, β = −79.0. 66 CHAPTER 5. RESULTS

Table 5.23: Fine Search results for (1036) Ganymed

λ β Chi-squared value 178.697 -76.671 2.256175 179.176 -76.726 2.260153 178.479 -76.755 2.261635

Figure 5.60: 4-Vane model view from the pole solution λ = 178.697, β = −76.671 of (1036) Ganymed.

Figure 5.61: Ecliptic model view from the pole solution λ = 178.697, β = −76.671 of (1036) Ganymed. 5.3. MPO LCINVERT RESULTS 67

Figure 5.62: Equator model view from the pole solution λ = 178.697, β = −76.671 of (1036) Ganymed.

Figure 5.63: 4-Vane model view from the pole solution λ = 179.176, β = −76.726 of (1036) Ganymed. 68 CHAPTER 5. RESULTS

Figure 5.64: Ecliptic model view from the pole solution λ = 179.176, β = −76.726 of (1036) Ganymed.

Figure 5.65: Equator model view from the pole solution λ = 179.176, β = −76.726 of (1036) Ganymed. 5.3. MPO LCINVERT RESULTS 69

Figure 5.66: 4-Vane model view from the pole solution λ = 178.479, β = −76.755 of (1036) Ganymed.

Figure 5.67: Ecliptic model view from the pole solution λ = 178.479, β = −76.755 of (1036) Ganymed.

Figure 5.68: Equator model view from the pole solution λ = 178.479, β = −76.755 of (1036) Ganymed. 70 CHAPTER 5. RESULTS

5.3.4 (1866) Sisyphus

The period search was set with a period interval between 2.395 and 2.425 hours. The lack of lightcurve data at a different phase angle did not allowed LCInvert to find a clear period solution. Nevertheless, the period with the lowest Chi- squared value, P = 2.40529 hoursa was used as an input to perform a Coarse Search and explore for possible shape and spin axis solutions. Table 5.24 shows the two lowest Chi-squared values retrieved . These two possible solutions where converted into 3D shapes and are shown in Figures 5.69, 5.70, 5.71 5.72, 5.73 and 5.74.

Table 5.24: Coarse results for (1866) Sisyphus

λ β Chi-squared value 15.0 15.0 0.421997 75.0 15.0 0.423210

Figure 5.69: 4-Vane model view from the pole solution λ = 15.0, β = 15.0 of (1866) Sisyphus. 5.3. MPO LCINVERT RESULTS 71

Figure 5.70: Ecliptic model view from the pole solution λ = 15.0, β = 15.0 of (1866) Sisyphus.

Figure 5.71: Equator model view from the pole solution λ = 15.0, β = 15.0 of (1866) Sisyphus.

Figure 5.72: 4-Vane model view from the pole solution λ = 75.0, β = 15.0 of (1866) Sisyphus. 72 CHAPTER 5. RESULTS

Figure 5.73: Ecliptic model view from the pole solution λ = 75.0, β = 15.0 of (1866) Sisyphus.

Figure 5.74: Equator model view from the pole solution λ = 75.0, β = 15.0 of (1866) Sisyphus. 5.3. MPO LCINVERT RESULTS 73

5.3.5 (450894) 2008BT18

The binary nature of the asteroid made the inversion process complicated. The results obtained confirmed that as with (1866) Sisyphus, more lightcurve data was necessary to get a better result. Even so, the inversion process was perform with the available data. Through the period search process, a period interval was defined between 2.725 and 2.272 hours. The period with the lowest Chi-squared value was P = 2.72532 hours. This period was used in a Coarse Search, where two possible solutions with the lowest Chi-squared were found and are shown in Table 5.25 and Figure 5.75. (450894) 2008BT18 orbits near the plane of the ecliptic, hence, the 2 pole-shape results with lowest Chi-squared value were found with same β and λ ± 180◦. Figures 5.76, 5.77, 5.78, 5.79, 5.80 and 5.81 show the 3D representation of these two possible results.

Table 5.25: Coarse results for (450894) 2008BT18

λ β Chi-squared value 300.0 0.0 1.377566 120.0 0.0 1.377759

Figure 5.75 74 CHAPTER 5. RESULTS

Figure 5.76: 4-Vane model view from the pole solution λ = 75.0, β = 15.0 of (450894) 2008BT18.

Figure 5.77: Ecliptic model view from the pole solution λ = 75.0, β = 15.0 of (450894) 2008BT18. 5.3. MPO LCINVERT RESULTS 75

Figure 5.78: Equator model view from the pole solution λ = 75.0, β = 15.0 of (450894) 2008BT18.

Figure 5.79: 4-Vane model view from the pole solution λ = 75.0, β = 15.0 of (450894) 2008BT18. 76 CHAPTER 5. RESULTS

Figure 5.80: Ecliptic model view from the pole solution λ = 75.0, β = 15.0 of (450894) 2008BT18.

Figure 5.81: Equator model view from the pole solution λ = 75.0, β = 15.0 of (450894) 2008BT18. Chapter 6

Conclusion and Future Work

Certainly, there is more than one scientific reason to study asteroids, however, the present work emphasises that these objects—specially Near-Earth Asteroids— represent an impact hazard to the planet. There is evidence that catastrophic collisions between asteroids and planet Earth has happened in the past and will happen in the future. Against this threat, the only possible way to prevent this kind of event is to identify and characterize Near-Earth Asteroids, thus, a plan to mitigate damages can be elaborated. This thesis focuses on asteroid characterization, but in the particular way characteristics that can be obtained through the synthesis of photometric observations. The methodology followed was divided into three main parts. During the first part of this work, the imaging of a selected number of NEAs took place. Asteroids (25916) 2001 CP44, (1627) Ivar, (1036) Ganymed, (1866) Sisyphus, and (450894) 2008 BT18 were observed in March, April and May 2018. Observations were carried out with the 77 cm Schmidt Camera at Tonantzintla, Puebla, Mexico. This telescope was recently equipped with a new image acquisi- tion system—a SBIG STF-8300 CCD and a five filter wheel—, and an updated Control System. Whenever weather conditions allowed the observation or the tar- get object had sufficient brightness, observations always were performed correctly which proved that the modernization of the Schmidt Camera was successful for the purpose of the present work. The goal of the second part was to obtain a minimum of one lightcurve of the observed objects, and consequently the period of rotation, amplitude of the lightcurve, and the relation between the maximum and minimum cross sections of every asteroid. This process—lightcurve photometry—was performed using the software MPO Canopus. The rotational period and amplitude of (25916) 2001 CP44, (1627) Ivar, (1036) Ganymed, and (1866) Sisyphus are consistent with previously published results. However, the results of asteroid (450894) 2008 BT 18 are not conclusive. Due to the binary nature of (450894) 2008 BT 18, it was crucial to observe the object the largest number of nights possible, this in

77 78 CHAPTER 6. CONCLUSION AND FUTURE WORK order to cover not only the period of the main body but also the one from the satellite—which is believed to be several times longer than period of the asteroid itself. Unfortunately, weather conditions, the low brightness and large apparent motion against the sky of the asteroid made the task impossible. Even so, the period found for (450894) 2008 BT 18 is a close approach to a true period. The last part of this work concerns the Lightcurve Inversion Method. The results from the lightcurve analysis of the observed asteroids together with the data from ALCDEF served as input to the execution of the inversion process implemented in the software MPO LCInvert. The outputs of the mentioned method are the orientation of the pole and the shape of the asteroid. Asteroids (1627) Ivar and (1036) Ganymed show results that are consistent to the reported in the DAMIT database. The pole and shape of (25916) 2001 CP44 obtained are very close to a true solution, nevertheless, to improve the result, 3 or 4 lightcurvess at a different phase angle are needed; pole or shape solutions for this asteroid have not been reported. In the case of asteroids (1866) Sisyphus and (450894) 2008 BT18, the best solution with the current data available was shown; more lightcurves at different phase angles are needed, but from different apparitions as well so lightcurves can reflect the most of the asteroids’ geometry. Statistics of asteroid discovering are promising, without a doubt within the fol- lowing years the objective to find most of NEAs will be achieved, nonetheless it is the asteroid characterization what is falling well behind. Not a significant fraction of the near 20,000 NEAs so-far discovered has its main characteristics determined, at best, the period or the spectral type has been calculated, but an even small fraction has its pole direction or shape determined. The results of this thesis indicate three things, first, the capability of the Schmidt Camera to perform high quality asteroid photometry, second, the utility of the public lightcuve databases like ALCDEF and third, the usefulness of the software MPO LCInvert. On account of the former, future work will be driven to continue the observation and characterization of the highest possible number NEAS to reduce this bottleneck in science. Bibliography

[1] Benner, L. A. M. et al. (2008). 2008BT18. Central Bureau Electronic Telegrams, No. 1450, 1 (2008). Edited by Green, D. W. E. [2] Boehnhardt, H. (2009). Earth and Solar System: Asteroids and Kuiper Belt Objects. In Roth G. D. (Ed.), Handbook of Practical Astronomy(pp. 483-497). Berlin Heidelberg: Springer-Verlag. [3] Brownlee, D.E. (2001). The origin and properties of dust impacting the earth. In Peucker-Ehrenbrink, B., Schmitz, B. (Eds.), Accretion of Ex- traterrestrial Matter Throughout Earth’s History(pp. 1–12). New York, NY: Springer. [4] Busch, M. W. (2010). Shapes and Spins of Near-Earth Asteroids. Doctoral Thesis, California Institute of Technology, Pasadena, California. [5] Cardona, O. et al (2009). Nuevo Sistema de Control Camara Schmidt. Reporte Tecnico, INAOE, Tonantzintla, Puebla, Mexico. [6] Cardona, O. et al (2011). Nuevo sistema de adquisicion de imagenes atro- nomicas de la Camara Schmidt usando un CCD enfriado. Reporte Tecnico, INAOE, Tonantzintla, Puebla, Mexico. [7] Carry, B. et al. (2016). Spectral properties of near-Earth and Mars- crossing asteroids using Sloan photometry. Icarus, 268, 340-354. [8] DeMeo, F. E., et al. (2009). An extension of the Bus asteroid taxonomy into the near-infrared. Icarus, 202(1), 160-180. [9] Dimock, R. (2010). Asteroids and Dwarf Planets and How to Observe Them. New York, NY: Springer-Verlag New York. [10] Dˇurech, J. (2016). Physical Models of Asteroids. Habilitation Thesis, Charles University, Prague, Czech Republic. [11] Elkins-Tanton, L. T. (2010). Asteroids, Meteorites and Comets: The Solar System. New York, NY: Facts On File, Inc. [12] Elvis, M. et al. (2013). Precision Rotation Periods and Shapes of Near-Earth Asteroids. Alternate Science Investigations for the Kepler

79 80 BIBLIOGRAPHY

Spacecraft. Advanced online publication. https://arxiv.org/ftp/arxiv/ papers/1309/1309.2333.pdf

[13] Encyclopedia of the Solar System (2nd Ed.). (2007). San Diego, CA: Aca- demic Press.

[14] Gallaway, M. (2016). An Introduction to Observational Astrophysics. Berlin: Springer International Publishing.

[15] Glikson, A. Y. (2013). The Asteroid Impact Connection of Planetary Evo- lution: With Special Reference to Large Precambrian and Australian impacts. Dordrecht, The Netherlands: Springer.

[16] Hanusˇ, J. et al. (2015). Thermophysical modeling of asteroids from WISE thermal infrared data: Significance of the shape model and the pole orienta- tion uncertainties. Icarus, 256, 101-116.

[17] Harris, A. W. & Harris, A. W. (1997). On the Revision of Radiometric Albedos and Diameters of Asteroids. Icarus, 126(2), 450-454.

[18] Harris, A. W., et al. (2014). On the maximum amplitude of harmonics of an asteroid lightcurve. Icarus, 235, 55-59.

[19] Hirayama, K. (1928). Groups of asteroids probably of common origin. ApJ., 31(743), 185-188.

[20] International Astronomical Union (2006). RESOLUTION B5: Def- inition of a Planet in the Solar System and RESOLUTION B6: Pluto. Retrieved from https://www.iau.org/static/resolutions/Resolution_ GA26-5-6.pdf

[21] Ivanov, B. (2008). Geologic Effect of Long Terrestrial Impact Crater For- mation. In Adushkin, V. & Nemchinov I. (Eds.), Catastrophic Events Caused by Cosmic Objects(pp. 163-205). Dordrecht, The Netherlands: Springer Netherlands.

[22] Jauregui-Garcia, J. M. et al (2014). Sistema de Control para la Camara Schmidt de Tonantzintla. Reporte Tecnico, INAOE, Tonantzintla, Puebla, Mexico.

[23] Kaasalainen, M. & Torppa, J. (2001). Optimization Methods for As- teroid Lightcurve Inversion: I. Shape Determination. Icarus, 153(1), 24-36.

[24] Kaasalainen, M. et al. (2001). Optimization Methods for Asteroid Lightcurve Inversion: II. The Complete Inverse Problem. Icarus, 153(1), 37- 51.

[25] Kaasalainen, M. et al. (2004). Photometry and models of eight near- Earth asteroids. Icarus, 167(1), 178-196. BIBLIOGRAPHY 81

[26] Kaasalainen, M. & Durech, J. (2007). Inverse Problems of NEO Pho- tometry: Imaging the NEO Population. Proceeding IAU Symposium, 236, in press.

[27] Koeberl, C. (2013). Asteroid Impact. In Bobrowsky, P. T. (Ed.), Encyclo- pedia of Natural Hazards(pp. 18-28). Dordrecht, The Netherlands: Springer Netherlands.

[28] Kuntner, M. L. (2003). Astronomy: A Physical Perspective. Cambridge, United Kingdom: Cambridge University Press.

[29] Lin, C. et al. (2018). Photometric survey and taxonomic identifications of 92 near-Earth asteroids. Planetary and Space Science, 152, 116-135.

[30] Liou, K. N. (2002). An Introduction to Atmospheric Radiation. San Diego, Ca.: Academic Press.

[31] Lissauer, J. J. and de Pater, I. (2013). Fundamental Planetary Science: Physics, Chemistry and Habitability. New York, NY: Cambridge University Press.

[32] Mainzer, A. et al. (2011). NEOWISE Observations of Near-Earth Ob- jects: Preliminary Results. ApJ., 743(2), 157-172.

[33] Mainzer, A. K. et al. (2016).NEOWISE Diameters and Albedos V1.0 NASA Planetary Data System.

[34] Minor Planet Observer (2009). LCInvert: Installation and Operating Instructions. Colorado Springs, CO: Bdw Publishing.

[35] Moltenbrey, M. (2016). Dawn of Small Worlds: Dwarf Planets, Aster- oids, Comets. Cham: Springer International Publishing.

[36] National Research Council of the National Academies. (2010). Defending Planet Earth: Near-Earth Object Surveys and Hazard Mitigation Strategies. Washington, DC: National Academies Press.

[37] Nesvorny,´ D. et al. (2015). Identification and dynamical properties of asteroid families. In Michel, P. et al. (Eds.), Asteroids IV(297-321). Tucson: The University of Arizona Press.

[38] Reddy, V. et al. (2008). Compositional Investigation of Binary Potentially-Hazardous Asteroid 2008 BT18: A Basaltic Achondrite. Ameri- can Astronomical Society, DPS meeting 40, id.25.07; Bulletin of the Ameri- can Astronomical Society, 40, 433.

[39] Romanishin, W. (2006). Introduction to Astronomical Photometry Using CCDs. Retrieved from http://www.physics.csbsju.edu/370/ photometry/manuals/OU.edu_CCD_photometry_wrccd06.pdf 82 BIBLIOGRAPHY

[40] Thomas, C. A. et al. (2014). Physical Characterization of Warm Spitzer- observed Near-Earth Objects. Icarus, 228, 217-246. [41] Trigo-Rodr´ıguez, J. M. et al.(Eds.). (2016). Assessment and Mitiga- tion of Asteroid Impact Hazards Proceedings of the 2015 Barcelona Asteroid Day. Cham, Switzerland: Springer. [42] Valdes, J. R. et al (2016). Pruebas para determinar las propiedades op- ticas de la Camara Schmidt de Tonantzintla.. Reporte Tecnico, INAOE, To- nantzintla, Puebla, Mexico. [43] Viikinkoski, M. et al. (2017). Adaptive optics and lightcurve data of asteroids: twenty shape models and information content analysis. Astronomy & Astrophysics, 607(A117), pp. 14. [44] Warner, B. D. (2003). A Practical Guide to Lightcurve Photometry and Analysis. New York, NY: Springer-Verlag New York. [45] Warner, B. D., et al. (2009). The asteroid lightcurve database. Icarus, 202(1), 134-146. [46] Zappala,´ V. et al. (1990). Asteroid Families: I. Identification by Hier- archical Clustering and Reliability Assessment. The Astronomical Journal, 100(6), 2030-2046. [47] Zappala,´ V. et al. (1994). Asteroid Families: II. Extension to Unnum- bered Multiopposition Asteroids. The Astronomical Journal, 107(2), 772-801.