Eccentricity of orbit. Apogee and perigee positions and distances

[shad0w0f3vil]

Homework Statement

A satellite is in an elliptical orbit about the Earth. The center of the Earth is a focus of the elliptical orbit. The perigee (C) is the point in the orbit where the satellite is closest to the Earth's center (F). The perigee distance (P) is the distance from the perigee to the Earth's center. The apogee (D) is the point furtheest from the Earth's center. The apogee distance (A) is the distance from the apogee to the Earth's center.

Show that the eccentricity of the orbit in terms of A and P is e=(A-p)/(A+P).

The Attempt at a Solution

Not sure where to begin, i know the distance from the center of the orbit to F is sqrt(a^2 - b^2), where a is the semi-major axis and b is the semi-minor axis.

 

[Kurdt]

How is the distance from a focus of an ellipse to the centre calculated?

 

[shad0w0f3vil]

How is the distance from a focus of an ellipse to the centre calculated?

I mean the center of the elipse.

Let c equal the distance between the elipse center and a focus.
a = the semi major axis
b = semi minor

c=sqrt(A^2 - b^2)

Is that what you meant?

 

[D H]

Not sure where to begin, i know the distance from the center of the orbit to F is sqrt(a^2 - b^2), where a is the semi-major axis and b is the semi-minor axis.

The center of the Earth is not at the center of the ellipse. It is at one of the two foci of the ellipse.

 

[shad0w0f3vil]

Sorry my bad, I did already understand that, just struggled to put it into words

 

[D H]

It's a bit hard to help you here because you left out a very important part of the original post:

Homework Equations

What equations are relevant to solving this problem?

 

[Kurdt]

If you look up an ellipse in a textbook or even on the internet you'll probably find what you need to do this question.

 

[shad0w0f3vil]

yeh i will just ask my teacher, i can get an answer that isn't wrong, just not sure if its the answer the teacher is looking for.

Thanks for all your help you guys!