How to plot an orbit with an inclination?

Question

How do I plot an orbit with an inclination?

I've managed to plot an orbit with zero inclination:

let a = the semi-major axis of ellipse.
let e = the eccentricity of ellipse.
let ep = the polar angle of the eccentricity vector.
while theta <= 2PI
{
  r = a * (1 - e^2) / (1 + e * cos(theta)).
  coordinate = sphericalCoordinate(r, theta + ep, ?).
  plot(coordinate).
  theta += PI / 180.
}

The question mark in the algorithm is where I would place the elevation angle to plot the inclination. The actual orbit simulation is simulated with a 3rd party physics engine, so I know the velocity and mass of the two bodies. The plotting is just to show a visual trajectory of the orbit.

Answer 1

Plotting 3D things on 2D paper is problematic. Orbits are nice because they are 2D (in the right coordinate system, and over short periods-the orbit plane changes). It depends on what you want to show. You can:

plot in the orbit plane. A nice representation of the orbit. Probably the most useful single plot.

plot projected on the equatorial plane. Easy to do. Just ignore the $z$ coordinate. Can be useful if the inclination is low.

plot two of the three axes on one plot, make three plots. This is projection on one coordinate plane. I have seen this, but have never learned anything from it.

I would start by thinking about what I am trying to demonstrate with the plot, then decide what plot(s) to make.