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.
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0.001 Negligible Negligible 12 and Apollo Apollo 13 atomic frequency standards calculations center of mass cesium standard clock on Apollo clock readings CM from center CM standard versus coordinate Corrections for Apollo Covered National Aeronautics Distance of CM Doppler effect Earth model ellipsoid error estimates errors in equation final time corrections Goddard Space Flight gravitational potential gravitational red shift ground-based clock inertial frame jus for Apollo large ranging errors Lavery metric tensor Name and Address namely a gain Number Period Covered National reentry relativistic blue shift relativistic time corrections Report Date Relativistic respect to clock rubidium clock rubidium standard Security Classif shift of clock simple Newtonian gravitational Space Flight Center spacecraft standard speed of clock Splashdown standard is bounded standard versus Earth Sun Earth Moon Table Theory of Relativity tinuously differentiable tracking and ephemeris trapezoidal rule versus an Earth versus Earth clock versus Earth standard versus the Earth