Space Lecture 2

Question 1

conservation of energy per mass

Answer 1

1/2*v^2-mu/r=const

Question 2

second law of Kepler

Answer 2

1/2r^2d/dt(phi)=H/2=const (constant area per time)

Question 3

Equation for acceleration of a body

Answer 3

d^2/dt^2(r)=r^2*d/dt(phi)-mu/r

Question 4

Equation of a conical section

Answer 4

r = p / (1+ecos(theta)) where p = (H^2/mu) = a(1-e^2)

Question 5

Position of foci

Answer 5

r_f = a*e

Question 6

distance to pericenter

Answer 6

r_p = a*(1-e)

Question 7

distance to apocenter

Answer 7

r_a = a*(1+e)

Question 8

semi-major axis

Answer 8

a=(r_a+r_p)/2

Question 9

eccenticity

Answer 9

e=(r_a-r_p)/(r_a+r_p)

Question 10

Another conical eq representation

Answer 10

a(1-e^2)/(1+ecos(theta)) comes from 2a=r_p+r_a