I'm a programmer trying to model satellite orbits. What formula can I use to determine the latitude of a satellite after a quarter orbit, given the initial launch latitude and inclination? For example, given a start of [30,0] and an initial inclination of 60 degrees, what would be [x,90]?
Here's the code in action if it helps to clarify things.
The graphics library takes care of the map projection, which is why I only need to get the latitude. The crux of it are these lines here. It's a very VERY rough approx that doesn't model itself on sinusoidal motion but the mathematician in me knows that it's total bunk.
//The launch latitude
var start = 30;
//The launch direction
var degree = 60;
//The degree as a percentage from vertical
var degPerc = Math.abs(degree) / 90;
//Whether the launch is oriented North or South
var direction = (degree >= 0) ? 1 : -1;
//The latitude encountered after a quarter orbit
var mid = (start + ((90-start) * 2 * degPerc)) * degPerc * direction;