A question about a moving satellite (Kepler)

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To find the z and y coordinates of the satellite when x=0, it is essential to establish the equation of the ellipse based on the given parameters. The satellite's initial conditions indicate it starts on the x-axis with y and z at zero. The focus of the ellipse is at the origin, which is crucial for determining the trajectory. The discussion emphasizes the need to derive the elliptical equation to pinpoint the coordinates at the specified x value. Understanding these relationships will lead to the solution for the satellite's position in the ZY plane.
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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

 
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sapz said:
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.
 
No, I mean I want to find, during the elliptical motion, where the satellite will meet the plane ZY.
 
The origin is one focus, yes? Can you write down the equation of the ellipse?
 

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