Transcript Solar System Dynamics

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
----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)
----Introduction to Solar System Dynamics----
The Solar System
----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----
Basic orbital elements (ellipse)
rp
ra
v
r
a(1  e )
1  e cos v
e<1: ellipse
e=1: parabola
r
2
e=0: circle
e>1: hyperbola
2.a
a: semimajor axis
e: eccentricity
v: true anomaly (0…360 deg)
rp: Radius of periapsis
(perihelion)
rp  a (1  e)
ra: Radius of apoapsis
(aphelion)
ra  a (1  e)
----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)
ω
Ω
(always towards a reference
direction)
ω: Argument of periapsis
Ascending
node
----Introduction to Solar System Dynamics----
Useful orbital parameters (elliptical orbit)
1) Velocity:
2 1
u  GM   
r a
3
2) Period:
a
T  2
GM
3) Energy:
E
4) Angular
momentum:
GMm
2a
M: mass of central body
m: mass of orbiting body
r: distance of m from M
(M>>m)
(Constant!)
 
L  m  r  u,
L  m G  M  a  (1  e 2 )
(Constant!)
----Introduction to Solar System Dynamics----
Orbital perturbations
GM
U total  
  Ri
r
i

Ri  Gmi 

 
ri  r 
1
  3 
ri  r
ri 
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-spherical
masses
Non-gravitational
forces
• Long term effects
Sources:
• Solar radiation
Size, shape and
orbital plane:
change in (a,e,i)
of the orbit
Precession:
change in the
orientation of the
orbit (Ω,ω)
• Outgassing
• Heating
----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
Secular
(usually
(Precession periods) amplification of e)
Mean motion
(orbital periods)
Spin-orbit
(e.g. Earth-Moon)
----Introduction to Solar System Dynamics----
Mean-motion resonance
• Simple, small integer relation between orbital periods
3

a1 
T1  2

GM  T12 a13

 2 3


3

a2  T2 a2
T2  2 GM 


(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
2
1
t=T1
t=2T1=T2
R
0
T1 2T1 4T1 6T1 8T1…
t
----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)
----Introduction to Solar System Dynamics----
Resonance in the solar system: a few examples
1.
Jupiters moons (Laplace)
•
2.
3.
4.
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)
----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.:
rp  a(1  e)
1 e

  ra  rp
1 e
ra  a(1  e) 
For rp~ 5 AU, e~0.999 ra~10000 AU
----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)
a>10000 AU
New
a<10000 AU
Returning
Short
Period (SP)
T<20 y
T>20 y
Jupiter
family
Halley
type
Orbital Distribution: the Oort cloud
Most comets are LP and come
from a distant source
Orbital energy per
unit mass
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-Neptunian
Objects
(Kuiper Belt)
Resonant
Classical
belt
• Out of resonances
• Low eccentricity
• a<50 AU
Plutinos
3:2 with
Neptune
Other
resonances
Scattered
belt
• 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