A question about a moving satellite (Kepler)

[sapz]

Homework Statement

Hi

I have a question about a satellite moving in an elliptic motion. It begins its motion on the x axis, when x=2Re, and with a velocity: Vx=0, Vy=v0, Vz=-0.5V0.

Re is radius of the earth.

Solving this I arrived at:
r0 = 10Re/4.
e=1/4.
Rmin = 2Re.
Rmax = 10Re/3.

Given all that, How do I find the z and y coordinates of the satellite, when x=0?

Homework Equations

The Attempt at a Solution

 

[tms]

Given all that, How do I find the z and y coordinates of the satellite, when x=0?

If you mean the initial conditions, you are given them: the object starts on the x axis, so y and z start off as zero.

 

[sapz]

No, I mean I want to find, during the elliptical motion, where the satellite will meet the plane ZY.

 

[haruspex]

The origin is one focus, yes? Can you write down the equation of the ellipse?