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### Boosted Rel-Velocity

Change of rel-velocity during a boost.
This animation uses *two* rel-speeds/velocities, not one:

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

Each rel-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 rel-speed=0, and the large outer circle with the degree divisions represents the speed limit (rel-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 rel-speed never exceeds the speed limit (the large outer circle).
- when the object's rel-speed is 1 in the unboosted grid, its rel-speed remains 1 in the boosted grid.
- when the object's rel-speed is 1, only the direction of the velocity vector changes.
The circle of dots remains a circle.
This is simply the aberration of light.