Relativistic time corrections for Apollo 12 and Apollo 13

Results are presented of computer calculations on the relativistic time corrections relative to a ground-based clock of on-board clock readings for a lunar mission, using simple Newtonian gravitational potentials of earth and moon and based on actual trajectory data for Apollo 12 and Apollo 13. Although the second order Doppler effect and the gravitational red shift give rise to corrections of opposite sign, the net accumulated time corrections, namely a gain of 560 (+ or - 1.5) microseconds for Apollo 12 and gain of 326 (+ or - 1.3) microseconds for Apollo 13, are still large enough that with present day atomic frequency standards, such as the rubidium clock, they can be measured with an accuracy of about + or - 0.5 percent.