Trajectory Calculator

Initial distance between positions =
Initial velocity of the first position =
Velocity of the second position =
Maximum possible velocity =
Acceleration =



Notes:

This calculator finds the quickest trajectory that concludes coincident to the target trajectory, that is, concluding on the target with the target's speed. The target trajectory is assumed to move at constant speed. The chase trajectory is a trapezoidal trajectory with constant acceleration, deceleration and a maximum speed.

In the 1990s I wanted to add satellite tracking to my computerized telescope. It is not easy to slew across the sky to precisely center a fast moving satellite in the eyepiece. I found a paper on radio telescopes that had math on trajectory matching but was clearly wrong. Deriving the correct math was a modest but interesting exercise. Details on the derivation and the Javascript functions can be found at http://www.bbastrodesigns.com/lib/trajLib.js. Corresponding unit tests can be found at http://www.bbastrodesigns.com/lib/trajLib%20unitTests.htm.

Mel Bartels