Curved space
The sphere
Move in the current velocity direction.
All tangent directions are principal on a sphere.
The map
Arrows show local east/north direction, independent of the map's stretching.
Close a loop to compare its area with the vector's deflection.
Latitude span from the starting point
Longitude span along the equator
Angular radius on the sphere
A circle on the sphere stretches on the map.
Adjust the outline, then run the loop. Completed loops update as you resize.
0° east 90° northUpdates without clearing your path
One loop. Equal area and angle.
Perpendicular to the initial velocities
0° east · 90° north
Playback rate · same geodesics
Distance along each geodesic
Equal speeds · initially parallel velocities
Drag to set the start · remains paused
Tangent step = arrow length · smaller is more accurate
Pace of movement and projection
600 small test masses per shell
Drag to inspect a moment · playback pauses
Slower or faster playback of the same fall
Observer falls with the shell's center