# Elliptical orbit question

elliptical orbit question plz help

see attachment

## Homework Equations

2a (average distance of satellite from central body) = A (aphelium) + P (perihelium)
ME = KE + PE
ME = -GMm/24
KE = .5mv^2
PE = -GMm/r
ME orignall = ME final

## The Attempt at a Solution

I tried to put ME = KE + PE = constant.
I solved for theoretical A, and P, if the velocity was only transverse.
Then, I subtracted the theoretical P by the distance caused by the KE. I sitll did not get the answer htough

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Please list all of the formulas and steps you did. Not sure what you are defining as A and P.

anyone?

Given the components of the velocity, can you determine the angle at that point? What is the polar equation for an ellipse in terms of the eccentricity?

There is a formula for eccentricity in terms of energy and angular momentum. If you don't know it, then you will have to solve for it using the conservation of energy and the conservation of angular momentum.

I looked at the wiki page, and have no clue hwo to apply conservation of angular momentum. could someone please show me how to do it?

Calculate the angular momentum of the satellite using

$$\vec{L} = m\vec{r}\times \vec{v}$$

D H
Staff Emeritus

Don't even bother with the satellite mass. It's just going to divide out in the end. Just use specific energy and specific angular momentum.

I looked at the wiki page
Which wiki page? There are several of them.

and have no clue hwo to apply conservation of angular momentum. could someone please show me how to do it?
No, we can't show you how to do it. That would be cheating.

Can you look up the polar form of the equation for an ellipse, in terms of r, $\theta$, and the eccentricity? Can you find the angle, given the components of the velocity?

The polar form of an ellipse has two unknowns: 'a' and eccentricity. So it won't be enough to solve for the eccentricity alone.

D H
Staff Emeritus