What is the true anomaly of the molniya spacecraft when it is at the descending node? as a reminder, the molniya orbit is shown in the figure to the right. clearly explain your answer (no credit for an answer without explanation).
2. what is(are) the arguments(s) of the perigee for an orbit whose line of nodes is orthogonal to its line of apsis? clearly explain your answer (no credit for an answer without explanation).
3. a spacecraft is on an elliptical orbit with an eccentricity e and semi-major axis a. when the spacecraft is at r = a, determine the sine of the flight direction angle (as a function of a single parameter).
4. using the expression of the (massless) angular momentum, determine the angular speed of the spacecraft on orbit at the perigee, at the apogee, and at r = a (there’s an easy way of doing this and a more complicated think carefully).
5. the international space station (iss) has a mass of roughly 420,000 kg. the specific impulse of the rocket engines used is about 270 s. we saw in class that to raise the iss orbit from 350km in altitude to 400 km, we needed two δv, each for about 14 m/s.
a. calculate the mass of propellant used for each maneuver (be careful with what to use for the second mi).
b. assume these maneuvers are done twice a year (in reality, more maneuvers are done but for smaller altitude boost), calculate the total mass of propellant needed per year to maintain the orbit of iss.
c. assume a cost to orbit of $10,000/kg, how much does iss orbit maintenance costs per year? comment on the result.