Astronomical Applications Department, U.S. Naval Observatory NAO 150 Page 7
This requires performing a
nonlinear least squares
analysis of a comparison
between a numerical inte-
gration of the solar system
model and the observa-
tional data. This analysis
results in (hopefully minor)
adjustments to the model
parameters. We then inte-
grate the model again, us-
ing the adjusted parameter
values, then compare again
to the observations. We it-
erate this process until the
parameters stop changing
appreciably. At that point,
we have the best fit of the
solar system model to the available observations.
1.5. Observation Types
For observing planetary positions, the various observational data types
fall naturally into the two broad categories: timing (in a sense, the radial
coordinate from the observer) and positions on the sky (i.e., transverse to
the radial direction). The hierarchy of types is illustrated in Figure 5.
1.6. Example: Space-Based Asteroid and Natural Satellite Observations
Figure 6 shows space-based astrometric observations by HIPPARCOS of
the 48 asteroids and 3 natural satellites it was able to reach. For the bright-
est asteroids, the single-measurement accuracy is less than 10 milliarcsec-
onds. The accuracy of the satellites is degraded by the fact that at the reso-
lution of the HIPPARCOS telescope these objects are not point sources
but extended bodies, introducing centroiding difficulties. This figure also
shows the projected single-measurement accuracy of the
FAME
satellite
11
.
(The
USNO
is hoping to launch FAME in 2003 or 2004 as a
NASA
MIDEX
MURISON: MODELING PLANETARY MOTIONS
7 of 20
11
See the FAME homepage at
http://aa.usno.navy.mil/FAME/
Figure 5 -- Observation types.
Observation
Types
Transverse
Radial
Transit Circle
Differential
Satellite-Satellite
Satellite-Planet
Doppler
Time Delay
One-Way
Two-Way
Doppler Radar
Pulsar
Two-Way S/C
S/C Ranging
One-Way S/C
Differential Radar
LLR
Radar Ranging
Radar
Spacecraft
Global
Occultation
Spacecraft-Planet
Star-Planet
Satellite-Planet
