Equations

Question 1

Newton ULG

Answer 1

F = − (GM1m2) r(hat)/r^2

Question 2

Conservation of Energy

Answer 2

E = 1/2 *mv^2 - GMm/r = GMm/2r - GMm/r

Question 3

Orbit equation

Answer 3

r = p/(1+e cos(𝜃−𝜃0)) = (h2⁄𝜇)/(1+e cos(𝜃−𝜃0)) = for ellipses = a(1−e2)/(1+e cos(𝜃−𝜃0))

Question 4

Vis viva equation

Answer 4

𝑣 = √(𝜇 [2/𝑟 − 1/𝑎])

Question 5

Rocket equation

Answer 5

∆𝑉 = 𝐶. 𝑙𝑛 [ 𝑚0/(𝑚0 −∆𝑚) ]

Question 6

Rayleigh Criterion/Angular resolution

Answer 6

𝜃 = 1.22 * λ/𝐷

Question 7

Conservation of angular momentum

Answer 7

ra*va = rp *vp