Question

Two satellites are launched at a distance R from a planet of negligible radius. Both satellites are
launched in the tangential direction. The first satellite launches correctly at a speed v0 and enters
a circular orbit. The second satellite, however, is launched at a speed
1
2
v0. What is the minimum
distance between the second satellite and the planet over the course of its orbit?

Answer 1

Where you wrote:
1
2
v0,
is that supposed to be (v0/2) ?

If so, the second satellite does not have sufficient kinetic energy to maintain a circular orbit at distance R.

Answer 2

@drwls it doesn’t matter that the second satellite can’t maintain a circular orbit, you want to find when the second satellite is closest to the planet in its (elliptical) orbit.