Secular Acceleration of Io Derived from Mutual Satellite Events

Timings and light curves of the mutual phenomena of the Galilean satellites in 1908, 1914, and 1973–1997 have been used first to improve the values of the most important parameters in Sampson's satellite theory (published in 1921) and second to reduce the considerable remaining discrepancies in the observations by solving for constant changes, Δ n i , and rates, i , in the mean motions of the four satellites. Earlier determinations of the values—primarily 1 —have been based mainly on observations of ordinary eclipses that are much less precise than the mutual event observations and also suffer from uncertainty in the UT-ET correction prior to 1900. Because of strong correlations, it is not possible to obtain meaningful least-squares solutions for both Δ n i and i , except for Io for which we obtain Δ n 1 = (0.4 ± 1.1) × 10 -6 deg day -1 and 1 / n 1 = 3.6 ± 1.0 in units of 10 -10 yr -1 . This Δ n 1 value is comparable to the values determined for Δ n 2 , Δ n 3 , and Δ n 4 . Although the data can be satisfied nearly as well by correcting only the mean motions, this leads to a 10 times larger Δ n 1 value, which seems unacceptably large. Furthermore, 1 = 0 would require an unphysically large tidal torque from Jupiter to overcome Io's orbital decay because of the observed energy dissipation in Io. Our determination of 1 / n 1 is in reasonable agreement with the values 3.3 ± 0.5 (from de Sitter, published in 1928) and 4.54 ± 0.95 (from Goldstein & Jacobs, published in 1995), both of which were derived from analyses of eclipses of the satellites by Jupiter and some photographic observations. However, it conflicts with the value -0.074 ± 0.087 found by Lieske (published in 1987) from Jovian eclipse timings. Our results imply that Io is now spiraling slowly inward, losing more orbital energy from internal dissipation than it gains from Jupiter's tidal torque. These results suggest that Q , the specific dissipation function of Jupiter, is around 200,000 for an Io heat flux of 1.3 × 10 14 W.