Find Speed Changes for Spacecraft Orbit Transfer: Mplanet/MEarth = 0.75

[Faraz]

Question
A spacecraft starts in elliptical orbit JK (red solid curve) around some planet and transfers to elliptical orbit MN (blue solid curve). To do so, it changes its speed at Kand inserts into the circular orbit KL (dashed green curve). At L, it changes speed again to insert into elliptical orbit LM (dashed magenta curve). Finally, at M, it changes speed to insert into the final orbit MN. Find all the changes in speed. Mass of planet compared to mass of Earth: Mplanet /MEarth = 0.75 Radius of planet: Rplanet = 3000 mi a = 400 mi b = 1200 mi c = 300 mi d = 1000 mi

Homework Equations

I just want to make sure I did it correctly before submitting my answer (ATTACHED)

The Attempt at a Solution

 

[SteamKing]

Question
A spacecraft starts in elliptical orbit JK (red solid curve) around some planet and transfers to elliptical orbit MN (blue solid curve). To do so, it changes its speed at Kand inserts into the circular orbit KL (dashed green curve). At L, it changes speed again to insert into elliptical orbit LM (dashed magenta curve). Finally, at M, it changes speed to insert into the final orbit MN. Find all the changes in speed. Mass of planet compared to mass of Earth: Mplanet /MEarth = 0.75 Radius of planet: Rplanet = 3000 mi a = 400 mi b = 1200 mi c = 300 mi d = 1000 mi

Homework Equations

I just want to make sure I did it correctly before submitting my answer (ATTACHED)

The Attempt at a Solution

Your calculations need total revision.

You've mixed miles and the metric system in you calculations and produced some really strange results.

 

[gneill]

...Also note that in your formula for velocity, the r variable is the value of the orbit radius at the point of interest, not the radius of the planet.