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

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