1 / 41

ASTM001/MTH724U SOLAR SYSTEM

ASTM001/MTH724U SOLAR SYSTEM. Carl Murray / Nick Cooper. Lecture 2: Structure of the Solar System. Books That Changed the World. The Almagest. Copernicus’ De Revolutionibus Orbium Celestium. Kepler’s Harmonices Mundi. The Five Convex Regular Polyhedra. cube. octahedron. tetrahedron.

eagan-gallagher
Download Presentation

ASTM001/MTH724U SOLAR SYSTEM

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ASTM001/MTH724U SOLAR SYSTEM Carl Murray / Nick Cooper Lecture 2: Structure of the Solar System

  2. Books That Changed the World

  3. The Almagest

  4. Copernicus’ De Revolutionibus Orbium Celestium

  5. Kepler’s Harmonices Mundi

  6. The Five Convex Regular Polyhedra cube octahedron tetrahedron icosahedron dodecahedron

  7. Kepler’s Model of Planetary Spacing • Each planet moves in a shell separated from next by regular polyhedron • Six planets separated by five shells • Thickness of shell is important • Ordering of polyhedra is important Orbits of Jupiter, Saturn and Mars

  8. Kepler’s Model

  9. Galileo’s Dialogue

  10. The “Retrograde” Path of Mars Apparent motion of Mars, June – November 2003

  11. Kepler’s First Law The planets move in ellipses with the Sun at one focus

  12. Kepler’s Second Law A line drawn from the Sun to a planet sweeps out equal areas in equal times

  13. Kepler’s Third Law It is most certain and most exact that the proportion between the periods of any two planets is precisely three halves the proportion of the mean distance J. Kepler, 15 May 1618 The square of the orbital period of a planet is proportional to the cube of its semi-major axis

  14. Daphnis making waves in the Keeler Gap Keeler Gap ‘Fast lane’ Arrows show direction of motion of ring particles relative to Daphnis ‘Slow lane’

  15. Newton’s Universal of Gravitation Any two bodies attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them

  16. Newton’s Laws of Motion • Bodies remain in a state of rest or uniform motion unless acted upon by a force • The force experienced by a body is equal to the rate of change of momentum • To every action there is an equal and opposite reaction

  17. Orbit Determination Choose an appropriate mathematical model for the orbit. The model is defined by a set of parameters. The numerical values of the model parameters are initially unkown. Orbit Models Fixed Ellipse 2-body Point-masses Orbital elements Precessing Ellipse 2-body Oblate primary Orbital elements Full Equations of Motion n-body Oblate primary Position/velocity Use the model to estimate the observed quantities. Iteratively solve for the set of parameter values which generates a satisfactory match between the estimated and actual observations.

  18. Titius’ 1766 Translation of Bonnet’s Contemplation de la Nature

  19. The Titius-Bode ‘Law’ of Planetary Distance The distance of a planet from the Sun obeys a geometric progression.

  20. The Titius-Bode ‘Law’ of Planetary Distance

  21. Bode’s Law for Uranian Satellites?

  22. Bode’s Law for Uranian Satellites?

  23. Uniqueness of Uranian System Actual system: Generate 100,000 sets of 5 satellites and calculate best fit for each set

  24. The Saturn System (as of 1997) 2:1 2:1 4:3

  25. The Geometry of Orbital Resonance 2:1 Resonance, Stable configuration: 2:1 Resonance, Unstable configuration:

  26. Resonance in the Saturn System • Saturn Ring Features (gaps, edge waves, density waves) • Janus : Epimetheus (co-orbital - horseshoe motion) • Dione : Helene : Polydeuces (co-orbital - tadpole motion) • Tethys : Telesto : Calypso (co-orbital - tadpole motion) • Mimas : Tethys (4:2) • Titan : Hyperion (4:3) • Enceladus : Dione (2:1) • Mimas : Anthe (10:11), Mimas : Methone (14:15), Mimas : Aegaeon (7:6) • Most regular satellites are in synchronous rotation (like The Moon). Hyperion (shown in the movie) is an exception. Hyperion

  27. Polydeuces Longitude lag (deg) Longitude lag (deg) Helene Saturn Dione Y (km) Polydeuces X (km)

  28. Resonance in Saturn’s Ring System

  29. Resonance in the Jupiter System

  30. Resonance in the Uranus System Currently no known resonances between the major satellites 5:3 near-resonance between Cordelia and Rosalind Anomalously high inclination of Miranda (4.22 deg) suggests existence of resonances in the past

  31. Resonance in Uranus’ Ring System 24:25 resonance between Cordelia and epsilon ring inner edge 14:13 resonance between Ophelia and epsilon ring outer edge

  32. Resonance in Neptune’s Ring System 42:43 resonance between Galatea and Adams ring

  33. Resonance in the Planetary System Jupiter-Saturn near 5:2 resonance Neptune-Pluto 3:2 resonance

  34. Spin-orbit Resonance in the Planetary System Mercury 3:2 spin-orbit resonance Pluto-Charon 1:1:1 spin-orbit resonance

  35. Resonance in the Asteroid Belt

  36. Trojan Asteroids

  37. Preference for Commensurability Two orbits are commensurate when For orbits in the solar system Let ratio be bounded by and Let

  38. Preference for Commensurability A: Enceladus-Dione B: Mimas-Tethys C: Titan-Hyperion D: Io-Europa E: Europa-Ganymede F: Neptune-Pluto

  39. High phase-angle Cassini image of Saturn

  40. High phase-angle Cassini image of Saturn 2006-258

  41. Websites NASA Solar System Exploration http://solarsystem.nasa.gov/index.cfm JPL Solar System Dynamics http://ssd.jpl.nasa.gov JPL Cassini http://saturn.jpl.nasa.gov/ Royal Astronomical Society http://www.ras.org.uk

More Related