tions are the more valuable since satellites generally have no atmospheres
(and hence no limb-darkening) to contend with. Since they orbit their par-
ent planets in a manner predictable by Newton's law of gravity, their posi-
tions can form the basis for determining the parent planet positions. This
is complicated considerably, however, by the difficulty in constructing
highly accurate theories of satellite motions, caused by the complex inter-
actions of the satellites with each other, with the planets, and with the non-
spherical parent planet whose mass distribution we don't always know as
well as we'd like. The modern era has seen the advent of other types of
observations, including ground-based radar, lunar laser ranging, spacecraft
telemetry, and space-based astrometry. The European HIPPARCOS
mission
6
is a successful example of a space astrometry mission. We hope
other missions, such as
FAME
(
USNO)
7
, and
SIM
(
JPL)
8
or
GAIA
(
ESA)
9
,
will follow.
The second step in generating an ephemeris is to develop a comprehen-
sive solar system model that we then integrate numerically. We must in-
clude complications, such as planetary (especially Earth) rotation dynam-
ics and lunar motion, as well as more subtle effects, including general rela-
tivity, tidal interactions between Earth and Moon, and planetary topogra-
phy models (for better resolution of radar data). The state of the art has
advanced to the point that it is becoming necessary to include the masses
of individual asteroids
10
as well as a mass model for the asteroid belt.
Both of these kinds of masses are in general very poorly known, yet aster-
oidal mass uncertainties are now the largest source of error in high-
precision ephemerides of the inner planets. Currently, the
JPL
ephemeri-
des (specifically, DE405) include mass estimates for 300 asteroids. These
masses are based on
IRAS
magnitudes, albedo estimates, and mean density
estimates.
The solar system model contains many adjustable parameters, such as
masses, orbital elements, initial positions and velocities, gravity model pa-
rameters, and so on. The third step in generating an ephemeris is to simul-
taneously fit all of these model parameters to the available observations.
MURISON: MODELING PLANETARY MOTIONS
6 of 20
10
James Hilton of USNO is the world's foremost expert in determination of asteroid
masses. See
http://aa.usno.navy.mil/hilton/asteroid_masses.htm
9
http://astro.estec.esa.nl/SA-general/Projects/GAIA/gaia.html
8
http://sim.jpl.nasa.gov/
7
http://aa.usno.navy.mil/FAME/
6
http://astro.estec.esa.nl/Hipparcos/hipparcos.html
