Question 1: Consider the circular, restricted, three-body problem for Neptune and its moon Triton. With Triton making up 99.5% of all mass in orbit around Triton, we can assume Triton is the only moon for that planet

a. Provide a qualitative sketch of the co-rotating coordinate system of Neptune/Triton

b. Calculate the location of the origin of this coordinate system.

c. Calculate the location of the five equilibrium points in this coordinate system.

d. Calculate the potential U(x, y, z) for each of the five equilibrium points.

e. Calculate the acceleration ??=???? for the five equilibrium points.

Question 2: A satellite is orbiting Earth in the following orbit:

??=12000 ???? ??=0.42 ??=127.8° Ω=24° ??=62°

a. When it comes to orbital perturbations, what kind of special orbit is this orbit?

b. Calculate the change rates in orbital elements due to the oblateness of the Earth (??2 term)

c. What would you have to do to change this orbit into a Frozen Orbit of Type I?

d. What would you have to do to change this orbit into a Frozen Orbit of Type II?

Question 3: A satellite in a circular Earth orbit with inclination 23° is in a 5:2 commensurate orbit.

a. How often does its ground track repeat per day?

b. What is its orbit radius?

Question 4: The ISS has solar arrays with a surface area of 2500 m2 and an estimated surface reflectivity of 1.6.

a. Neglecting the station modules, calculate the ballistic radiation coefficient for the ISS

b. Calculate the maximum possible acceleration due to solar radiation pressure in multiples of g.