Annoying ellitpical orbit problem

[superaznnerd]

Homework Statement

a planet in elliptical orbit about a star has speed of 100 m/s at its closest approach of 1X 10^10m . what is the speed at its furthest approach of 3X10^10m? What has happened to its total mechanical energy?

Homework Equations

The Attempt at a Solution

 

[ideasrule]

You have to at least give it a try before asking for help.

 

[superaznnerd]

I tried to figure out it using mGh+1/2mv^2 = mechanical energy original = mechanical energy final. However, I know there has to be an easier way to do it, using ratios. Could you please tell me the trick?