# Homework Help: Height of an ellipse above the plane in three dimensions (z parameter)

1. Sep 26, 2011

### jmm5872

1. The problem statement, all variables and given/known data
What is the expression for z (the height above the xy-plane) in terms of r,f,w,i.

r = the distance
f = the angle between the semi-major axis and the r vector
w = the angle that the semi-major axis makes with the y-axis
i = the angle that the plane of the ellipse makes with the xy-plane

This is actually an Astronomy problem, where the ellipse is the orbit of an asteroid and the xy-plane is the plane of the solar system (planetary orbital plane).

2. Relevant equations

3. The attempt at a solution

I started by parametrizing the ellipse with respect to one of the foci:

x = c+r*cos(f)
y = r*sin(f)
z = (c+r*cos(f))tan(i)

This doesn't seem correct, or complete I guess. I'm not sure how w comes into play? w rotates the ellipse relative to the y-axis but I can't picture where it should go?