  We propose a method to account for the Earth oblateness effect in preliminary
orbit determination of satellites in low orbits with radar observations. This
method is an improvement of the one described in (Gronchi et al 2015), which
uses a pure Keplerian dynamical model. Since the effect of the Earth oblateness
is strong at low altitudes, its inclusion in the model can sensibly improve the
initial orbit, giving a better starting guess for differential corrections and
increasing the chances to obtain their convergence. The input set consists of
two tracks of radar observations, each one composed of at least 4 observations
taken during the same pass of the satellite. A single observation gives the
topocentric position of the satellite, where the range is very accurate, while
the line of sight direction is poorly determined. From these data we can
compute by a polynomial fit the values of the range and range rate at the mean
epochs of the two tracks. In order to obtain a preliminary orbit we wish to
compute the angular velocities, that is the rate of change of the line of
sight. In the same spirit of (Gronchi et al 2015), we also wish to correct the
values of the angular measurements, so that they fit the selected dynamical
model if the same holds for the radial distance and velocity. The selected
model is a perturbed Keplerian dynamics, where the only perturbation included
is the secular effect of the $J_2$ term of the geopotential. The proposed
algorithm models this problem with 8 equations in 8 unknowns.
