The Secular Accelerations of Satellites

Maximum effects of tidal friction are calculated for the principal satellites. Corrections for elasticity and for imperfection of elasticity are made for satellites of the Earth and Mars, based on results for the Earth. Bodily tidal friction accounts for about 1 per cent of the secular acceleration of the Moon, and for about 10 –4 of that of Phobos, and 10 –5 of that of Deimos. Since the secular accelerations of JV and Mimas have the wrong sign to be due to tidal friction, it appears that bodily tidal friction is not the explanation of any observed secular acceleration. Other things being equal, the greatest effect of tidal friction on a satellite orbit should be for JI. The fact that no secular effect on it has been detected indicates that the tidal lag in Jupiter is very small. The result is enough to indicate that tidal friction may have had a considerable effect on the orbit of JI, and secondary ones on Mimas, Tethys, and Triton, but the effects on all other satellites are of negligible importance in cosmogony.