Some day you might think about doing this in 3D with some animation sequence, but postpone that. Do not worry about perspective, either - just project (x, y, z) to (x, z). Try adding color and improve the text layout. You might also draw several images with different emphasis.

Hints. There are two different wasy to proceed. One is to use the fact that the projection of a circle is an ellipse. THe other is to draw the projection of a great circle as a bunch of small line segments. How do you draw ellipses in general? How do you find the great circle through two points on the unit sphere? How find its projection? How draw a spherical triangle ABC?