Question

Satellite X moves around Earth in a circular orbit radius R. Satellite Y is also in a circular orbit around earth, and it completes one orbit for every eight orbits completed by satellite X. What is the orbital radius of satellite Y?

Answer 1

First of all, we know the difference in the period of the orbits:\[T _{Y}=8T _{X}\]We also know that the velocity of each satellite is determined by the equation which treated gives out:\[v =\frac{ 2 \pi R }{ T }\rightarrow R=\frac{ vT }{ 2\pi } \rightarrow R _{Y}=\frac{ v _{Y}T _{Y} }{ 2\pi }=\frac{ v _{Y}4T _{X} }{ \pi }\]The problem is that we don't know the velocity of satellite Y which is absolutely necessary since for what we know the radius of Y may be a 100 time bigger than the radius of X if satellite Y has a velocity 25 times bigger than tha of satellite X. There maybe a orbit equation that I am not aware about? Maybe one that includes masses that cancel of since we can assume that the satellites have the same mass.