comets, kuiper belt and solar system dynamics silvia protopapa & elias roussos lectures on...

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

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)

----Introduction to Solar System Dynamics----

The Solar System



• 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?


• Known asteroids+comets+trans-Neptunian objects>104

• Small object studies have statistical significance


2.a

a: semimajor axis

e: eccentricity

v: true anomaly (0…360 deg)

rp ra

Basic orbital elements (ellipse)

rp: Radius of periapsis (perihelion)

ra: Radius of apoapsis (aphelion)

)1(

)1(

ear

ear

a

p

e=0: circle

e<1: ellipse

e=1: parabola

e>1: hyperbola

ve

ear

cos1

)1( 2

v

r


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


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


Useful orbital parameters (elliptical orbit)

1) Velocity:

2) Period:

3) Energy:

4) Angular momentum:

arGMu

12

GM

aT

3

2

a

GMmE

2

)1(

,

2eaMGmL

urmL

M: mass of central body

m: mass of orbiting body

r: distance of m from M

(M>>m)

(Constant!)

(Constant!)


Orbital perturbations

3

1

i

i

iii

ii

total

r

rr

rrGmR

Rr

GMU

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


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


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


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


What is a resonance?• Integer relation between periods

• Periodic structure of the disturbing function Ri

Resonances

Orbit-orbit Spin-orbit

Mean motion(orbital periods)

Secular(Precession periods)

(usually amplification of e)

(e.g. Earth-Moon)


Mean-motion resonance• Simple, small integer relation between orbital periods

32

31

22

21

32

2

31

1

2

2

a

a

T

T

GM

aT

GM

aT

(Kepler’s 3rd law)

Favored mean motion resonance in solar system: T1:T2=N/(N+1),

N: small integer


Example 2:1 mean motion resonance

t=0 t=T1

t=2T1=T2

tT1 2T1 4T1 6T1 8T1…

R

1

2

0


Example 2:1 resonanceSatellite 1: 2:1 resonant orbit with Earth’s moon (green)

Satellite 2: not in a resonant orbit (yellow)


Resonance in the solar system: a few examples1. 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)


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

e

err

ear

earpa

a

p

1

1

)1(

)1(


Comets: classification (according to orbit size)

Comets(>1500 with well

known orbits)

Long Period (LP)

ShortPeriod (SP)

New ReturningJupiterfamily

Halleytype

T>200 y T<200 y

T<20 y T>20 ya>10000 AU a<10000 AU

Orbital Distribution: the Oort cloud

Orbital energy per unit mass

Most comets are LP and come from a distant source

From the Oort cloud to the Kuiper belt

First (after Pluto…) trans-Neptunian belt object discovery

1992QB1

Additional slides


Trans-Neptunian objects: classification

Trans-NeptunianObjects

(Kuiper Belt)

Resonant

Scatteredbelt

Plutinos Other resonances

Classicalbelt

3:2 with Neptune

• Out of resonances

• Low eccentricity

• a<50 AU• High eccentricities

• Origin unknown


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

comets, kuiper belt and solar system dynamics silvia protopapa & elias roussos lectures on...

Documents

solar system dynamics

solar system orbits

early solar system

solar system silvia

solar system objects

orbit slide

disturbing body slide

origins of solar systems