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**Session 116 - The Solar System.**

*Oral session, Thursday, January 18*

*Salon del Rey Central, Hilton*

## [116.04] On the Evolution of the Galilean Satellites of Jupiter

*S. J. Goldstein Jr., K. C. Jacobs (Univ.Virginia and Hollins Col.)*

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 commen-
surate 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.

**Program
listing for Thursday**