In inversive geometry, as a point x within a unit circle approaches the center of the unit circle, its inversion point y outside the circle approaches infinity. The distance of the two points to the center of the circle, if I'm not mistaken, can be expressed as follows:
(r being the radius of the unit circle)
Without further preamble, my question is as follows:
How can we express the acceleration of point y, outside of the circle, with respect to point x?
In other words, if points x and y are spaceships, what is the acceleration of spaceship y with respect to spaceship x? AND, is this a constant acceleration, or an accerating acceleration (second or higher derivative)?