Report No. 3276

Xzyqgon File

Sector: Lunar Station Alpha

Topic: Required launch velocity of LS50 quasion probe rockets for meteor interception

This report addresses the calculation of the launch velocity of the rocket fired from Lunar Station 50 at 3:00 PM on July 21, 21xy, to intercept the meteor on a collision course with Lunar Station Alpha.

Let R denote the radius of Xzyqgon (all distances will be measured in km). Let d denote the distance from Lunar Station 50 (henceforth denoted LS50) to the meteor at 3 PM. Let u denote the speed of the meteor (all speeds in km/sec), and let v denote the maximum possible speed at which the research rockets can be launched.

The situation at 3 PM is shown in Figure A. The circle is the “great circle” on Xzyqgon on which both LS50 and Lunar Station Alpha (henceforth abbreviated LSα) sit. Referring to Figure A, M is the location of the meteor, N is the North Pole where LSα is located, F is the location of LS50, and O is the center of Xzyqgon. Finally, P is the intersection of the path of the research rocket and the path of the meteor, and Q is where the great circle through LS50 and LSα meets the Equator.