- #1

DJSedna

- 7

- 0

## Homework Statement

Using the polar formula for an ellipse, and Kepler's second law, find the time-weighted average distance in an elliptical orbit.

## Homework Equations

The polar formula for an ellipse:

$$r = \frac { a(1-e^2)} {1 \pm e cos \theta},$$

Area of an ellipse:

$$ A = \pi a b $$

$$ b = \sqrt{a(1 - e^2)} $$

## The Attempt at a Solution

I don't know if you'd call this much of an attempt, but I understand I need to be taking some sort of integral with respect to time. I have genuinely been staring at this for hours with no idea where to start, though, and I need some idea of how to get going.

I've messed with just about every algebraic combination of the three equations above, but I haven't found anything that pops out at me and says "oh, that's it."

Sorry if this is too vague, this is the first time I've ever really needed to post here. Let me know if I can add any more information.

Thanks!