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?