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COMETS, KUIPER BELT AND SOLAR SYSTEM DYNAMICS Silvia Protopapa & Elias Roussos

Delve into the origins of our Solar System through lectures discussing comets, Kuiper Belt, and orbital perturbations. Learn about resonances, orbits, and important parameters in the Solar System dynamics.

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COMETS, KUIPER BELT AND SOLAR SYSTEM DYNAMICS Silvia Protopapa & Elias Roussos

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  1. COMETS, KUIPER BELT AND SOLAR SYSTEM DYNAMICS Silvia Protopapa & Elias Roussos Lectures on “Origins of Solar Systems” February 13-15, 2006 Part I: Solar System Dynamics

  2. ----Introduction to Solar System Dynamics---- • Part I: Solar System Dynamics • Orbital elements & useful parameters • Orbital perturbations and their importance • Discovery of Oort Cloud and Kuiper Belt and basic facts for these two populations • Part II: Lessons from Pluto for the origin of the Solar System(Silvia Protopapa) • Part III: Comets(Cecilia Tubiana - SIII Seminar, 15/2/2006)

  3. ----Introduction to Solar System Dynamics---- The Solar System

  4. ----Introduction to Solar System Dynamics---- • Are the positions of the planets and other solar system objects random? • Do they obey certain laws? • What can these laws tell us about the history and evolution of the solar system?

  5. ----Introduction to Solar System Dynamics---- • Known asteroids+comets+trans-Neptunian objects>104 • Small object studies have statistical significance

  6. ----Introduction to Solar System Dynamics---- Basic orbital elements (ellipse) e=0: circle e<1: ellipse e=1: parabola e>1: hyperbola rp ra v r 2.a rp: Radius of periapsis (perihelion) ra: Radius of apoapsis (aphelion) a: semimajor axis e: eccentricity v: true anomaly (0…360 deg)

  7. ----Introduction to Solar System Dynamics---- Basic orbital elements (continued) i: inclination (0…180 deg) (always towards a reference plane) • Reference plane for solar system orbits: • Ecliptic=(plane of Earth’s orbit around the Sun) • All planetary orbital planes are oriented within a few degrees from the ecliptic

  8. ω Ω Ascending node ----Introduction to Solar System Dynamics---- Basic orbital elements (continued) Ω: Right ascension of the ascending node(0...360 deg) (always towards a reference direction) ω:Argument of periapsis

  9. ----Introduction to Solar System Dynamics---- Useful orbital parameters (elliptical orbit) M: mass of central body m: mass of orbiting body r: distance of m from M (M>>m) • Velocity: • Period: • Energy: • Angular momentum: (Constant!) (Constant!)

  10. ----Introduction to Solar System Dynamics---- Orbital perturbations M: mass of central body m: mass of orbiting body r: distance of m from M mi: mass of disturbing body “i” ri: distance of mi from M Ri: disturbing function U: Gravitational potential • Dependence on: • mass of disturbing body • proximity to disturbing body

  11. ----Introduction to Solar System Dynamics---- Orbital perturbations & orbital elements Perturbations Third body Non-spherical masses Non-gravitational forces • Long term effects • Sources: • Solar radiation • Outgassing • Heating Size, shape and orbital plane: change in (a,e,i)of the orbit Precession: change in the orientation of the orbit (Ω,ω)

  12. ----Introduction to Solar System Dynamics---- Orbital perturbations (example: third body) Why they should not be neglected? Satellites 1&2 (around Earth): a=150900 km e=0.8 i=0 deg Satellite 1: only Earth’s gravity Satellite 2: Earth + Moon + Sun

  13. ----Introduction to Solar System Dynamics---- Orbital perturbations: consequences • Collisions • Important in the early solar system • Not only the result of perturbations • Capture to orbit • Important for giant planets • Scattering of solar system objects • Escape orbits • Distant populations of small bodies • Chaotic orbits • Stable or unstable configurations: resonances

  14. ----Introduction to Solar System Dynamics---- What is a resonance? • Integer relation between periods • Periodic structure of the disturbing function Ri Resonances Orbit-orbit Spin-orbit (e.g. Earth-Moon) Secular (Precession periods) (usually amplification of e) Mean motion (orbital periods)

  15. ----Introduction to Solar System Dynamics---- Mean-motion resonance • Simple, small integer relation between orbital periods (Kepler’s 3rd law) Favored mean motion resonance in solar system: T1:T2=N/(N+1), N: small integer

  16. ----Introduction to Solar System Dynamics---- Example 2:1 mean motion resonance 2 t=2T1=T2 t=0 t=T1 1 R t 0 T1 4T1 6T1 2T1 8T1…

  17. ----Introduction to Solar System Dynamics---- Example 2:1 resonance Satellite 1: 2:1 resonant orbit with Earth’s moon (green) Satellite 2: not in a resonant orbit (yellow)

  18. ----Introduction to Solar System Dynamics---- Resonance in the solar system: a few examples • Jupiters moons (Laplace) • Io in 2:1 resonance with Europa, Europa in 2:1 resonance with Ganymede • Saturn’s moons & rings • Mimas & Tethys, Enceladus & Dione (2:1), • Gravity waves in Saturn’s rings • Kirkwood gaps in asteroid belt • Resonances can lead to eccentric orbits collisions • Empty regions of asteroids • Trojan asteroids (Lagrange): (1:1 resonance with Jupiter)

  19. ----Introduction to Solar System Dynamics---- Solar system dynamics & comets • Comets are frequently observed crossing the inner solar system • Many comets have high eccentricities (e~1) • E.g.: • For rp~ 5 AU, e~0.999 ra~10000 AU

  20. ----Introduction to Solar System Dynamics---- Comets: classification (according to orbit size) T>200 y T<200 y Comets (>1500 with well known orbits) Long Period (LP) Short Period (SP) T<20 y T>20 y a>10000 AU a<10000 AU New Returning Jupiter family Halley type

  21. Orbital Distribution: the Oort cloud Most comets are LP and come from a distant source Orbital energy per unit mass

  22. From the Oort cloud to the Kuiper belt

  23. First (after Pluto…) trans-Neptunian belt object discovery 1992QB1

  24. Additional slides

  25. ----Introduction to Solar System Dynamics---- Trans-Neptunian objects: classification Trans-Neptunian Objects (Kuiper Belt) Resonant Classical belt Scattered belt • Out of resonances • Low eccentricity • a<50 AU • High eccentricities • Origin unknown Plutinos Other resonances 3:2 with Neptune

  26. ----Introduction to Solar System Dynamics---- Orbital perturbations (example: third body) Why they should not be neglected? Satellites 1&2 (around Earth): a=880000 km e=0.7 i=0 deg Satellite 1: only Earth’s gravity Satellite 2: Earth + Moon + Sun

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