Section 3. Planetary motion Flashcards
(21 cards)
What is geocentric?
Centred around the Earth
How is the retrograde motion explained?
Epiccyles
What is an epicycle?
Circular motion around an average circular motion
What was Kepler’s first law?
A planet orbits the sun in an ellipse, with the sun at the focus of the ellipse
What was Kepler’s second law?
b2=a2(1-e2)
What was Kepler’s third law?
P(yr)2=ka(Au)3
P is the period
a is the semi major axis
k is a constant of proportionality
What is the acceleration for circular motion?
a=v2/r
What is Newton’s law of gravitation?
F=GMm/r2
What is the constant for Kepler’s third law?
k=4π2/GM
What is the virial theorem?
2< K.E >=< U >
What is the equation of motion for the one body problem?
d2r/dt2=-GMstar/|r|2
What is the equation of motion for the two body problem?
d2r/dt2=-G(m1+m2)/|r|2
What is the general version of Kepler’s third law?
P2=(a1+a2)3 4π2/G(m1_m2)
What is the Hill sphere?
The approximate sphere of influence around the second body where orbits can be long term stable
What is the equation for the radius of the Hill sphere?
RH ~ (m2/3m1)1/3 a
How was Neptune discovered?
Via perturbations of the orbit of Uranus
What do perturbations cause?
Secular resonances in e and i(inclination) of planet orbits
What is the result of periods having integer ratios?
Perturbations grow in mean motions resonances
What is the cause of tidal itneractions?
Differential gravity across an object
How do tidal bulges affect orbits?
Gravitational force on them acts to synchronise rotation with the orbit
What is the Roche limit?
The limit at which tidal forces overcome the self gravity of an object
