Five linear equations allow the calculation of the time derivatives of the mean motion for Io, Europa, Ganymede, and Callisto, and of the torque on Io from Jupiter. Conservation of energy, conservation of angular momentum, and the Laplace law for the mean motions give rise to three of the equations. The original theory of Sampson and the E2 ephemeris of Lieske give, by longitude comparison at Lieske's epoch,1976.6, the relative acceleration for pairs of satellites and provide two more equations. The infrared heat flow from Io measured by Veeder et al. (1994) plus the tidal power transfer is taken as the sum of the differentiated energy terms of the first equation. Solving the linear equations for various pairs of the satellites gives the following fractional derivatives in units of E-10 1/years: for Io 7.0 +/-.6, for Europa 5.0 +/-.1, for Ganymede 2.8 +/-.8, for Callisto -4.9 +/-.9. Corresponding to these accelerations are the following derivatives in the semi-major axes in cm/year: -20., -25., -20., +62. The torque that Jupiter exerts on Io is -3.9 +/-.6 in units of E+25 dyne cm, that is it opposes Io's motion. Callisto will be in 3/7 commensurate motion with Ganymede 330 thousand years in the future. All of the errors cited here are lower limits, for they neglect the errors in the mean motions of Sampson's theory.
American Astronomical Society Meeting Abstracts
- Pub Date:
- December 1995