A question about a moving satellite (Kepler)

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SUMMARY

The discussion centers on calculating the z and y coordinates of a satellite in elliptical motion when its x coordinate equals zero. The satellite begins its motion on the x-axis at coordinates (2Re, 0, -0.5V0), where Re is the Earth's radius. Key parameters derived include the semi-major axis (r0 = 10Re/4), eccentricity (e = 1/4), minimum radius (Rmin = 2Re), and maximum radius (Rmax = 10Re/3). The user seeks to determine the coordinates at the intersection of the satellite's path with 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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