Identifying Solar System Patterns
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Astrodynamics
Politecnico di Torino SEEDS SpacE Exploration and Development Systems Astrodynamics II Edition 2006 - 07 - Ver. 2.0.1 Author: Guido Colasurdo Dipartimento di Energetica Teacher: Giulio Avanzini Dipartimento di Ingegneria Aeronautica e Spaziale e-mail: [email protected] Contents 1 Two–Body Orbital Mechanics 1 1.1 BirthofAstrodynamics: Kepler’sLaws. ......... 1 1.2 Newton’sLawsofMotion ............................ ... 2 1.3 Newton’s Law of Universal Gravitation . ......... 3 1.4 The n–BodyProblem ................................. 4 1.5 Equation of Motion in the Two-Body Problem . ....... 5 1.6 PotentialEnergy ................................. ... 6 1.7 ConstantsoftheMotion . .. .. .. .. .. .. .. .. .... 7 1.8 TrajectoryEquation .............................. .... 8 1.9 ConicSections ................................... 8 1.10 Relating Energy and Semi-major Axis . ........ 9 2 Two-Dimensional Analysis of Motion 11 2.1 ReferenceFrames................................. 11 2.2 Velocity and acceleration components . ......... 12 2.3 First-Order Scalar Equations of Motion . ......... 12 2.4 PerifocalReferenceFrame . ...... 13 2.5 FlightPathAngle ................................. 14 2.6 EllipticalOrbits................................ ..... 15 2.6.1 Geometry of an Elliptical Orbit . ..... 15 2.6.2 Period of an Elliptical Orbit . ..... 16 2.7 Time–of–Flight on the Elliptical Orbit . .......... 16 2.8 Extensiontohyperbolaandparabola. ........ 18 2.9 Circular and Escape Velocity, Hyperbolic Excess Speed . .............. 18 2.10 CosmicVelocities -
Geological Timeline
Geological Timeline In this pack you will find information and activities to help your class grasp the concept of geological time, just how old our planet is, and just how young we, as a species, are. Planet Earth is 4,600 million years old. We all know this is very old indeed, but big numbers like this are always difficult to get your head around. The activities in this pack will help your class to make visual representations of the age of the Earth to help them get to grips with the timescales involved. Important EvEnts In thE Earth’s hIstory 4600 mya (million years ago) – Planet Earth formed. Dust left over from the birth of the sun clumped together to form planet Earth. The other planets in our solar system were also formed in this way at about the same time. 4500 mya – Earth’s core and crust formed. Dense metals sank to the centre of the Earth and formed the core, while the outside layer cooled and solidified to form the Earth’s crust. 4400 mya – The Earth’s first oceans formed. Water vapour was released into the Earth’s atmosphere by volcanism. It then cooled, fell back down as rain, and formed the Earth’s first oceans. Some water may also have been brought to Earth by comets and asteroids. 3850 mya – The first life appeared on Earth. It was very simple single-celled organisms. Exactly how life first arose is a mystery. 1500 mya – Oxygen began to accumulate in the Earth’s atmosphere. Oxygen is made by cyanobacteria (blue-green algae) as a product of photosynthesis. -
Mars Express Orbiter Radio Science
MaRS: Mars Express Orbiter Radio Science M. Pätzold1, F.M. Neubauer1, L. Carone1, A. Hagermann1, C. Stanzel1, B. Häusler2, S. Remus2, J. Selle2, D. Hagl2, D.P. Hinson3, R.A. Simpson3, G.L. Tyler3, S.W. Asmar4, W.I. Axford5, T. Hagfors5, J.-P. Barriot6, J.-C. Cerisier7, T. Imamura8, K.-I. Oyama8, P. Janle9, G. Kirchengast10 & V. Dehant11 1Institut für Geophysik und Meteorologie, Universität zu Köln, D-50923 Köln, Germany Email: [email protected] 2Institut für Raumfahrttechnik, Universität der Bundeswehr München, D-85577 Neubiberg, Germany 3Space, Telecommunication and Radio Science Laboratory, Dept. of Electrical Engineering, Stanford University, Stanford, CA 95305, USA 4Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91009, USA 5Max-Planck-Instuitut für Aeronomie, D-37189 Katlenburg-Lindau, Germany 6Observatoire Midi Pyrenees, F-31401 Toulouse, France 7Centre d’etude des Environnements Terrestre et Planetaires (CETP), F-94107 Saint-Maur, France 8Institute of Space & Astronautical Science (ISAS), Sagamihara, Japan 9Institut für Geowissenschaften, Abteilung Geophysik, Universität zu Kiel, D-24118 Kiel, Germany 10Institut für Meteorologie und Geophysik, Karl-Franzens-Universität Graz, A-8010 Graz, Austria 11Observatoire Royal de Belgique, B-1180 Bruxelles, Belgium The Mars Express Orbiter Radio Science (MaRS) experiment will employ radio occultation to (i) sound the neutral martian atmosphere to derive vertical density, pressure and temperature profiles as functions of height to resolutions better than 100 m, (ii) sound -
Flight and Orbital Mechanics
Flight and Orbital Mechanics Lecture slides Challenge the future 1 Flight and Orbital Mechanics AE2-104, lecture hours 21-24: Interplanetary flight Ron Noomen October 25, 2012 AE2104 Flight and Orbital Mechanics 1 | Example: Galileo VEEGA trajectory Questions: • what is the purpose of this mission? • what propulsion technique(s) are used? • why this Venus- Earth-Earth sequence? • …. [NASA, 2010] AE2104 Flight and Orbital Mechanics 2 | Overview • Solar System • Hohmann transfer orbits • Synodic period • Launch, arrival dates • Fast transfer orbits • Round trip travel times • Gravity Assists AE2104 Flight and Orbital Mechanics 3 | Learning goals The student should be able to: • describe and explain the concept of an interplanetary transfer, including that of patched conics; • compute the main parameters of a Hohmann transfer between arbitrary planets (including the required ΔV); • compute the main parameters of a fast transfer between arbitrary planets (including the required ΔV); • derive the equation for the synodic period of an arbitrary pair of planets, and compute its numerical value; • derive the equations for launch and arrival epochs, for a Hohmann transfer between arbitrary planets; • derive the equations for the length of the main mission phases of a round trip mission, using Hohmann transfers; and • describe the mechanics of a Gravity Assist, and compute the changes in velocity and energy. Lecture material: • these slides (incl. footnotes) AE2104 Flight and Orbital Mechanics 4 | Introduction The Solar System (not to scale): [Aerospace -
Planetarian Index
Planetarian Cumulative Index 1972 – 2008 Vol. 1, #1 through Vol. 37, #3 John Mosley [email protected] The PLANETARIAN (ISSN 0090-3213) is published quarterly by the International Planetarium Society under the auspices of the Publications Committee. ©International Planetarium Society, Inc. From the Compiler I compiled the first edition of this index 25 years ago after a frustrating search to find an article that I knew existed and that I really needed. It was a long search without even annual indices to help. By the time I found it, I had run across a dozen other articles that I’d forgotten about but was glad to see again. It was clear that there are a lot of good articles buried in back issues, but that without some sort of index they’d stay lost. I had recently bought an Apple II computer and was receptive to projects that would let me become more familiar with its word processing program. A cumulative index seemed a reasonable project that would be instructive while not consuming too much time. Hah! I did learn some useful solutions to word-processing problems I hadn’t previously known exist, but it certainly did consume more time than I’d imagined by a factor of a dozen or so. You too have probably reached the point where you’ve invested so much time in a project that it’s psychologically easier to finish it than admit defeat. That’s how the first index came to be, and that’s why I’ve kept it up to date. -
Outer Planets: the Ice Giants
Outer Planets: The Ice Giants A. P. Ingersoll, H. B. Hammel, T. R. Spilker, R. E. Young Exploring Uranus and Neptune satisfies NASA’s objectives, “investigation of the Earth, Moon, Mars and beyond with emphasis on understanding the history of the solar system” and “conduct robotic exploration across the solar system for scientific purposes.” The giant planet story is the story of the solar system (*). Earth and the other small objects are leftovers from the feast of giant planet formation. As they formed, the giant planets may have migrated inward or outward, ejecting some objects from the solar system and swallowing others. The giant planets most likely delivered water and other volatiles, in the form of icy planetesimals, to the inner solar system from the region around Neptune. The “gas giants” Jupiter and Saturn are mostly hydrogen and helium. These planets must have swallowed a portion of the solar nebula intact. The “ice giants” Uranus and Neptune are made primarily of heavier stuff, probably the next most abundant elements in the Sun – oxygen, carbon, nitrogen, and sulfur. For each giant planet the core is the “seed” around which it accreted nebular gas. The ice giants may be more seed than gas. Giant planets are laboratories in which to test our theories about geophysics, plasma physics, meteorology, and even oceanography in a larger context. Their bottomless atmospheres, with 1000 mph winds and 100 year-old storms, teach us about weather on Earth. The giant planets’ enormous magnetic fields and intense radiation belts test our theories of terrestrial and solar electromagnetic phenomena. -
The Terraforming Timeline. A. J. Berliner1 and C. P. Mckay2
Planetary Science Vision 2050 Workshop 2017 (LPI Contrib. No. 1989) 8031.pdf The Terraforming Timeline. A. J. Berliner1 and C. P. McKay2, 1University of California Berkeley, Berkeley, CA 94704, [email protected], 2Space Sciences Division, NASA Ames Research Center, Mountain View, CA 94075. Introduction: Terraforming, the transformation of particularly the winter South Polar Cap, and any CO2 a planet so as to resemble the earth so that it can sup- that is absorbed into the cold ground in the polar re- port widespread life, has been described as a grand gions. Once the warming starts all this releasable CO2 challenge of both space sciences and synthetic biology will go into the atmosphere. Thus, it is important to [1,2]. We propose the following abstract on a Martian know the total before warming starts. Current esti- Terraforming timeline as a guide to shaping planetary mates of the releasable CO2 on Mars today range from science research over the coming century. a little more than the present thin atmosphere to values Terraforming Mars can be divided into two phases. sufficient to create a pressure on Mars equal to the sea The first phase is warming the planet from the present level pressure on Earth. Nitrogen is a fundamental re- average surface temperature of -60ºC to a value close quirement for life and necessary constituent of a to Earth’s average temperature to +15ºC, and re- breathable atmosphere. The recent discovery by the creating a thick CO2 atmosphere [3,4,5,6] This warm- Curiosity Rover of nitrate in the soil on Mars (~0.03% ing phase is relatively easy and quick, and could take by mass) is therefore encouraging for terraforming [7]. -
The Solar System Cause Impact Craters
ASTRONOMY 161 Introduction to Solar System Astronomy Class 12 Solar System Survey Monday, February 5 Key Concepts (1) The terrestrial planets are made primarily of rock and metal. (2) The Jovian planets are made primarily of hydrogen and helium. (3) Moons (a.k.a. satellites) orbit the planets; some moons are large. (4) Asteroids, meteoroids, comets, and Kuiper Belt objects orbit the Sun. (5) Collision between objects in the Solar System cause impact craters. Family portrait of the Solar System: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, (Eris, Ceres, Pluto): My Very Excellent Mother Just Served Us Nine (Extra Cheese Pizzas). The Solar System: List of Ingredients Ingredient Percent of total mass Sun 99.8% Jupiter 0.1% other planets 0.05% everything else 0.05% The Sun dominates the Solar System Jupiter dominates the planets Object Mass Object Mass 1) Sun 330,000 2) Jupiter 320 10) Ganymede 0.025 3) Saturn 95 11) Titan 0.023 4) Neptune 17 12) Callisto 0.018 5) Uranus 15 13) Io 0.015 6) Earth 1.0 14) Moon 0.012 7) Venus 0.82 15) Europa 0.008 8) Mars 0.11 16) Triton 0.004 9) Mercury 0.055 17) Pluto 0.002 A few words about the Sun. The Sun is a large sphere of gas (mostly H, He – hydrogen and helium). The Sun shines because it is hot (T = 5,800 K). The Sun remains hot because it is powered by fusion of hydrogen to helium (H-bomb). (1) The terrestrial planets are made primarily of rock and metal. -
Organic Matter and Water from Asteroid Itokawa Q
www.nature.com/scientificreports OPEN Organic matter and water from asteroid Itokawa Q. H. S. Chan1,2*, A. Stephant2, I. A. Franchi2, X. Zhao2, R. Brunetto3, Y. Kebukawa4, T. Noguchi5, D. Johnson2,6, M. C. Price7, K. H. Harriss7, M. E. Zolensky8 & M. M. Grady2,9 Understanding the true nature of extra-terrestrial water and organic matter that were present at the birth of our solar system, and their subsequent evolution, necessitates the study of pristine astromaterials. In this study, we have studied both the water and organic contents from a dust particle recovered from the surface of near-Earth asteroid 25143 Itokawa by the Hayabusa mission, which was the frst mission that brought pristine asteroidal materials to Earth’s astromaterial collection. The organic matter is presented as both nanocrystalline graphite and disordered polyaromatic carbon with high D/H and 15N/14N ratios (δD = + 4868 ± 2288‰; δ15N = + 344 ± 20‰) signifying an explicit extra-terrestrial origin. The contrasting organic feature (graphitic and disordered) substantiates the rubble-pile asteroid model of Itokawa, and ofers support for material mixing in the asteroid belt that occurred in scales from small dust infall to catastrophic impacts of large asteroidal parent bodies. Our analysis of Itokawa water indicates that the asteroid has incorporated D-poor water ice at the abundance on par with inner solar system bodies. The asteroid was metamorphosed and dehydrated on the formerly large asteroid, and was subsequently evolved via late-stage hydration, modifed by D-enriched exogenous organics and water derived from a carbonaceous parent body. Understanding the earliest chemical reactions involving liquid water provides crucial insights to how simple building blocks of organic compounds evolved into increasingly complex macromolecules via actions of water. -
Habitability of Planets on Eccentric Orbits: Limits of the Mean Flux Approximation
A&A 591, A106 (2016) Astronomy DOI: 10.1051/0004-6361/201628073 & c ESO 2016 Astrophysics Habitability of planets on eccentric orbits: Limits of the mean flux approximation Emeline Bolmont1, Anne-Sophie Libert1, Jeremy Leconte2; 3; 4, and Franck Selsis5; 6 1 NaXys, Department of Mathematics, University of Namur, 8 Rempart de la Vierge, 5000 Namur, Belgium e-mail: [email protected] 2 Canadian Institute for Theoretical Astrophysics, 60st St George Street, University of Toronto, Toronto, ON, M5S3H8, Canada 3 Banting Fellow 4 Center for Planetary Sciences, Department of Physical & Environmental Sciences, University of Toronto Scarborough, Toronto, ON, M1C 1A4, Canada 5 Univ. Bordeaux, LAB, UMR 5804, 33270 Floirac, France 6 CNRS, LAB, UMR 5804, 33270 Floirac, France Received 4 January 2016 / Accepted 28 April 2016 ABSTRACT Unlike the Earth, which has a small orbital eccentricity, some exoplanets discovered in the insolation habitable zone (HZ) have high orbital eccentricities (e.g., up to an eccentricity of ∼0.97 for HD 20782 b). This raises the question of whether these planets have surface conditions favorable to liquid water. In order to assess the habitability of an eccentric planet, the mean flux approximation is often used. It states that a planet on an eccentric orbit is called habitable if it receives on average a flux compatible with the presence of surface liquid water. However, because the planets experience important insolation variations over one orbit and even spend some time outside the HZ for high eccentricities, the question of their habitability might not be as straightforward. We performed a set of simulations using the global climate model LMDZ to explore the limits of the mean flux approximation when varying the luminosity of the host star and the eccentricity of the planet. -
Moons, Planets, Solar System, Stars, Galaxies, in Our Universe - an Introduction by Rick Kang Education/Public Outreach Coord
Moons, Planets, Solar System, Stars, Galaxies, in our Universe - An introduction by Rick Kang Education/Public Outreach Coord. Oregon Astrophysics Outreach HIERARCHY: one within another n Moons ORBIT Planets n Planets ORBIT Stars (Suns) n Stars orbited by Planets are Solar Systems (all Stars?) n Solar Systems form from Nebulas and recyle back into Nebulas (dust & gas) n Nebulas and Solar Systems ORBIT within Galaxies (huge Star Cities) n Many Galaxies fill our Universe Moons Our Solar System’s Planets Our Star (the Sun) Our Galaxy (Milky Way) edge-on from within the pancake (STAR CITY) Stars: distant Suns – Birth, Life, Death (Nebulas, Clusters) Solar System Formation Recycling Stars Heavy Duty Recycling: SUPERNOVA – elements galore DRAWING of our Milky Way Galaxy Looking toward Cygnus and toward galactic center Reality Check: n Visualize SOLAR SYSTEM vs. GALAXY Reality Check: n Visualize SOLAR SYSTEM vs. GALAXY n A Solar System is a VERY TINY DOT within a GALAXY…microscopic! n A ¼” paper punchout vs. a huge disk about 150 MILES WIDE (Coast to Bend or Portland to Roseburg!) Our Sister Galaxy, Andromeda, M31 Other Galaxies in Deep Space The HUBBLE ULTRA-DEEP FIELD a tiny swatch of sky-galaxies galore Hundreds of Billions of GALAXIES in our UNIVERSE n We don’t have enough data to figure out where we are within the UNIVERSE nor how big our Universe might be…evidence is it’s expanding! n We are a member of a cluster and a supercluster of galaxies. How do we know that? n If you leave from a place, how far could you travel in a given amount of time? How old is our Universe, how would that relate to its size? . -
A Review on Substellar Objects Below the Deuterium Burning Mass Limit: Planets, Brown Dwarfs Or What?
geosciences Review A Review on Substellar Objects below the Deuterium Burning Mass Limit: Planets, Brown Dwarfs or What? José A. Caballero Centro de Astrobiología (CSIC-INTA), ESAC, Camino Bajo del Castillo s/n, E-28692 Villanueva de la Cañada, Madrid, Spain; [email protected] Received: 23 August 2018; Accepted: 10 September 2018; Published: 28 September 2018 Abstract: “Free-floating, non-deuterium-burning, substellar objects” are isolated bodies of a few Jupiter masses found in very young open clusters and associations, nearby young moving groups, and in the immediate vicinity of the Sun. They are neither brown dwarfs nor planets. In this paper, their nomenclature, history of discovery, sites of detection, formation mechanisms, and future directions of research are reviewed. Most free-floating, non-deuterium-burning, substellar objects share the same formation mechanism as low-mass stars and brown dwarfs, but there are still a few caveats, such as the value of the opacity mass limit, the minimum mass at which an isolated body can form via turbulent fragmentation from a cloud. The least massive free-floating substellar objects found to date have masses of about 0.004 Msol, but current and future surveys should aim at breaking this record. For that, we may need LSST, Euclid and WFIRST. Keywords: planetary systems; stars: brown dwarfs; stars: low mass; galaxy: solar neighborhood; galaxy: open clusters and associations 1. Introduction I can’t answer why (I’m not a gangstar) But I can tell you how (I’m not a flam star) We were born upside-down (I’m a star’s star) Born the wrong way ’round (I’m not a white star) I’m a blackstar, I’m not a gangstar I’m a blackstar, I’m a blackstar I’m not a pornstar, I’m not a wandering star I’m a blackstar, I’m a blackstar Blackstar, F (2016), David Bowie The tenth star of George van Biesbroeck’s catalogue of high, common, proper motion companions, vB 10, was from the end of the Second World War to the early 1980s, and had an entry on the least massive star known [1–3].