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. 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) ----Introduction to Solar System Dynamics----

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

4. 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>10 4 Small object studies have statistical significance

6. ----Introduction to Solar System Dynamics---- 2.a2.a a: semimajor axis e: eccentricity v: true anomaly (0…360 deg) rprp rara Basic orbital elements (ellipse) r p : Radius of periapsis (perihelion) r a : Radius of apoapsis (aphelion) e=0: circle e<1: ellipse e=1: parabola e>1: hyperbola v r

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. ----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 Ascending node ω Ω

9. ----Introduction to Solar System Dynamics---- Useful orbital parameters (elliptical orbit) 1)Velocity: 2)Period: 3)Energy: 4)Angular momentum: M: mass of central body m: mass of orbiting body r: distance of m from M (M>>m) (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 m i : mass of disturbing body “i” r i : distance of m i from M R i : 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-gravitational forces Non-spherical masses Long term effects Sources: Solar radiation Outgassing Heating Precession: change in the orientation of the orbit (Ω,ω) Size, shape and orbital plane: change in (a,e,i) of the orbit

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 1.Collisions Important in the early solar system Not only the result of perturbations 2.Capture to orbit Important for giant planets 3.Scattering of solar system objects Escape orbits Distant populations of small bodies 4.Chaotic orbits 5.Stable or unstable configurations: resonances

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

15. ----Introduction to Solar System Dynamics---- Mean-motion resonance Simple, small integer relation between orbital periods (Kepler’s 3 rd law) Favored mean motion resonance in solar system: T 1 :T 2 =N/(N+1), N: small integer

16. ----Introduction to Solar System Dynamics---- Example 2:1 mean motion resonance t=0 t=T 1 t=2T 1 =T 2 t T1T1 2T 1 4T 1 6T 1 8T 1 … R 1 2 0

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 1.Jupiters moons (Laplace) Io in 2:1 resonance with Europa, Europa in 2:1 resonance with Ganymede 2.Saturn’s moons & rings Mimas & Tethys, Enceladus & Dione (2:1), Gravity waves in Saturn’s rings 3.Kirkwood gaps in asteroid belt Resonances can lead to eccentric orbits  collisions Empty regions of asteroids 4.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 r p ~ 5 AU, e~0.999  r a ~10000 AU

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

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

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 Scattered belt Plutinos Other resonances Classical belt 3:2 with Neptune Out of resonances Low eccentricity a<50 AU High eccentricities Origin unknown

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