- #1

k1point618

- 25

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## Homework Statement

Two satellites are launched at a distance R from a planet of negligible radius. (Yes, that's what the problem says...) Both satellites are launched in the tangential direction. the first satellite launches correctly at a speed [tex]v_0[/tex] and enters a circular orbit. The second satellite, however, is launched at a speed [tex]\frac{1}{2}v_0[/tex] . What is the minimum distance between the second satellite and the planet over the course of its orbit?

## Homework Equations

## The Attempt at a Solution

I thought about using energy. The two satellites both start out with the same potential energy but different kinetic energy.

So satellite one's TME: [tex]-\frac{GMm}{R} + \frac{1}{2}mv_0^2[/tex]

where as satellite two's TME:[tex]-\frac{GMm}{R} + \frac{1}{8}mv_0^2[/tex]

And the second satellite's minimum distance is when its potential is the least...

Somehow I think this problem might relate to angular momentum... L = mvr, but not exactly sure.

THANK YOU =D