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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
----Introduction to Solar System Dynamics----
----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?
----Introduction to Solar System Dynamics----
• Known asteroids+comets+trans-Neptunian objects>104
• Small object studies have statistical significance
----Introduction to Solar System Dynamics----
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
----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
----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
----Introduction to Solar System Dynamics----
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!)
----Introduction to Solar System Dynamics----
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
----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
----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
----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
----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
Mean motion(orbital periods)
Secular(Precession periods)
(usually amplification of e)
(e.g. Earth-Moon)
----Introduction to Solar System Dynamics----
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
----Introduction to Solar System Dynamics----
Example 2:1 mean motion resonance
t=0 t=T1
t=2T1=T2
tT1 2T1 4T1 6T1 8T1…
R
1
2
0
----Introduction to Solar System Dynamics----
Example 2:1 resonanceSatellite 1: 2:1 resonant orbit with Earth’s moon (green)
Satellite 2: not in a resonant orbit (yellow)
----Introduction to Solar System Dynamics----
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)
----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
e
err
ear
earpa
a
p
1
1
)1(
)1(
----Introduction to Solar System Dynamics----
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
----Introduction to Solar System Dynamics----
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
----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