Question $2[15$ points$]$ The team from GoThrusters underestimated the fuel required for a mission to Mars, and now Valentina is stuck orbiting Mars, without enough fuel to get out of orbit. Arkstar is safe in a circular orbit with an altitude of $340$ km above the Martian surface. Your team plans to rendezvous with the spacecraft in orbit, and subsequently deorbit the two spacecraft together.

A$.$ Valentina is in an elliptical orbit with an apoapsis of $450$ km above the Martian surface, and an eccentricity of $0\mathrm{.}055.[4$ points$]$

i$.$ The semimajor axis

ii$.$ The periapsis radius

iii. The velocity of satellite at periapsis iv$.$ The velocity of the satellite at apoapsis

B$.$ While waiting for your team to rescue them, since Valentina and Arkstar still have radio communication between them, they decide to race around Mars.

i$.$ At their fastest, who is faster? $[3$ points$]$

ii$.$ Who takes the shortest amount of time to go around Mars? $[3$ points$]$

iii. At what distance from the Martian surface would Valentina orbit at the same speed as Arkstar? What value would true anomaly take at this location?