Speed Boost Angles 8 16 32 64 Animate

### Boost Velocity

Change of velocity during a boost.

This animation uses two speeds/velocities, not one:

• the usual β, for the speed of a boosted grid with respect to another, along the x-axis.
• the velocity of an object. The object has a velocity in both the unboosted grid (green dots), and the boosted grid (white dots).

Each velocity vector starts at the origin (in the center), and ends in a single dot. The βx-component is vertical, and the βy-component is horizontal (as shown by the axes in the center.) The center has speed=0, and the large outer circle with the degree divisions represents the speed limit (speed=1).

The β boost between grids is positive in the direction of the +βx-axis. It starts out as the classical aberration formula, and the form stays as a circle. As speeds increase, the form changes to an ellipse, contracts, and compresses against the speed limit (β=1) circle.

Note that:

• the boosted speed never exceeds the speed limit (the large outer circle).
• when the object's speed is 1 in the unboosted grid, its speed remains 1 in the boosted grid.
• when the object's speed is 1, only the direction of the velocity vector changes. This is simply the aberration of light.