I'm currently studying how to calculate planetary orbits and I'm stuck. I have calculated the polar coordinates of the planet, with the at the origin and the x-axis as the striped line in this picture: Now I have to transform the polar coordinates into heliocentric ecliptic coordinates. To do so, I first have to convert them into cartesian coordinates (simple enough) and then I have to switch the plane of reference so that the x-axis will point towards [tex]\Upsilon[/tex]. How do I do this? The answer is found below, but could anyone tell me the actual process of getting this answer?