ASTEROID ORBIT FITTING WITH RADAR AND ANGULAR OBSERVATIONS
The asteroid orbit fitting problem using their radar and angular observations has been considered. The problem was solved in a standard way by means of minimization of weighted sum of squares of residuals. In the orbit fitting both kinds of radar observations have been used: the observations of time delays and of Doppler frequency shifts. The weight for angular observations has been set single for all of them and it has been determined as inverse mean-square residual obtained in the orbit fitting using just angular observations. The weights of radar observations have been set as inverse squared errors of these observations published together with them in the Minor Planet Center electronical circulars (MPECs). For the orbit fitting some five asteroids have been taken from these circulars. The asteroids have been chosen fulfilling the requirement of more than six radar observations of them to be available. The asteroids are 1950 DA, 1999 RQ36, 2002 NY40, 2004 DC and 2005 EU2. Several orbit fittings for these asteroids have been done: with just angular observations; with just radar observations; with both angular and radar observations. The obtained results are quite acceptable because in the last case the mean-square angular residuals are approximately equal to the same ones obtained in the fitting with just angular observations. As to radar observations mean-square residuals, the time delay residuals for three asteroids do not exceed 1 qs, for two others - 10 μs and the Doppler shift residuals for three asteroids do not exceed 1 Hz, for two others - 10 Hz. The motion equations included perturbations from 9 planets and the Moon using their ephemerides DE422. The numerical integration has been performed with Everhart 27-order method with variable step. All calculations have been executed to a 34-digit decimal precision (i.e. using 128-bit floating-point numbers). Further, the sizes of confidence ellipsoids of improved orbit parameters have been compared. It has been accepted that an indicator of ellipsoid size is a geometric mean of its six semi-axes. A comparison of sizes has shown that confidence ellipsoids obtained in orbit fitting with both angular and radar observations are several times less than ellipsoids obtained with just angular observations.