Celestial Mechanics

Question 1

Newton’s law of gravity

given in exam

Answer 1

Gm1m2
F = ———- . ( r_ / r )
r^2

where r is magnitude of vector r_

Question 2

Kepler’s first law

Answer 2

Planets move in elliptical orbits with the sun at one focus of the ellipse

Question 3

Kepler’s second law

Answer 3

The line joining the sun to a planet sweeps out equal area in equal times
(gets faster closer to the focus(sun))

Question 4

Kepler’s third law

Answer 4

The square of the orbit period t, is proportional to the third power of the semi-major axis of the orbit

t^2 ∝ a^3

Question 5

General equation for a ellipse

Answer 5

P
r = ——————–
1 + eCosθ

e = 0 is a circle
0

Question 6

Equation for Kepler’s third law

given in exam

Answer 6

4π^2
t^2 = ———— . a^3
Gm1

Question 7

What is the Hohmann transfer

Answer 7

when a spacecraft transfers between and LEO to a GEO

Question 8

What happens during the Hohmann transfer

Answer 8

Two impulse velocities are used. First to take spacecraft out of circular orbit r1, and second to put it into circular orbit r2

Question 9

What is the equation to find the semi-major axis in a Hohmann transfer

Answer 9

a = (r1 + r2) / 2