The accuracy to which Phoebe's orbit can be determined is limited primarily
by the errors in the observations and by the errors in the ephemeris of Saturn
as it affects the modelling of the observations. The DE403 Saturn position
error is about 0
2; the accuracy of computed absolute positions of Phoebe
is limited to that value. The majority of the observations are absolute
positions obtained from reductions involving a variety of star catalogues and
are subject to relatively large systematic errors due to errors in those
catalogues (e.g. zone biases, proper motion). Fundamentally, the errors make
it difficult to tie the reference frame of the observation to the IERS/J2000
reference frame of the orbit. Characterizing the uncertainty in the frame-tie
is extremely difficult, especially for the older observations. Examination of
the residuals suggests an overall accuracy of the observed absolute positions
in the range from about 04 to 40.
Relative to the observation related errors, those in the dynamical modelling are small. The most important dynamical parameters, the GM's of Saturn and Titan, are well known from the Voyager encounters. Inaccuracies in the ephemerides of the perturbing bodies lead to integration errors of at most a few tens of kilometers.
The effects of any systematic observation errors are alleviated somewhat by the orbit model. The only free dynamical parameters in the orbit determination process are the components of the epoch state vector of Phoebe. Consequently, there exist implicit dynamical constraints on the size, shape, and orientation of possible orbits. It is unlikely, assuming the observations are weighted properly, that the orbit has been distorted in an attempt to accommodate a systematic error unique to a particular observation set.
To arrive at a probable accuracy for the orbit, we first examined the formal
covariance from the fit. In the development of that covariance we
included ephemeris parameters for Saturn as consider parameters (parameters
not estimated but whose uncertainties affect the statistics of the estimated
parameters). The uncertainties in the Saturn ephemeris parameters were set to
reflect the 02 error in Saturn's position. The orbit accuracy predicted
by the covariance is a lower bound because it only accounts for
observation errors as represented by the data weights and for the Saturn
ephemeris error. We next made comparisons with fits to various subsets of the
data and with fits using differing weighting strategies. Finally, we examined
sensitivities to several of the dynamical model parameter values. Based on
this analysis, our estimate of the 1
orbit uncertainties at the time
of the planned Cassini flyby (June 12, 2004) are:
| In-orbit | Radial | Out-of-plane | Period |
| 3000 km | 1000 km | 1000 km | 36 s |
|
|