Notice that the satellite’s speed doesn’t depend on its mass; even if it were a
baseball, if its orbit radius were R, then its orbit speed would still be.
- A communications satellite of mass m is orbiting the earth at
constant speed in a circular orbit of radius R. If R is increased by a
factor of 4, what happens to T, the satellite’s orbit period (the time it
takes to complete one orbit)?
Here’s How to Crack It
From question 7, we know that
Now, since v = 2πR/T, we have
This tells us that T is proportional to R , so if R increases by a factor of 4, then
T will increase by a factor of 4 = 8.