Geodesic deviation on a sphere

What you are seeing: two parallel geodesics on a sphere starting at the equator with a small longitudinal offset. They both head north and meet at the pole, even though they started "parallel". This convergence is the geodesic deviation produced by positive curvature.

Figure 1. Two nearby geodesics and their separation on a selectable surface: converging on the sphere, parallel on the plane, diverging on the saddle.

Surface

Δφ (init)0.30

WHAT TO TRY

Switch between the sphere, plane, and saddle and watch whether the separation shrinks, holds, or grows.
Drag the canvas to rotate; vary the initial separation and compare against the diagnostic plot.