A time-dependent extension to Brouwer's method for orbital elements correction

Abstract

One of the most popular methods for orbital elements correction, by means of O-C calculus, is based on Brouwer's method [2], which is very well adapted for integrating short periods of time. We propose a general method to integrate over long intervals of time, when we have good observations, based upon a time-dependent functional relation between the derivatives of all elements with respect to all variations in the initial elements. First, we verify the truth of the unrestricted hypothesis by means of the proposed analytical method and a numerical derivation. In [6], we have incorporated a correction frame model jointly with this general method and, then, we have constructed the residual function which is minimized by the least squares method. But, as we are going to see later, there are correlations between the parameters frame correction model and the initial elements involved in the adjustment. They are obtained here, as well as an expression for the equinox correction from these frame parameters. Finally, by means of a simply weighted method, with the observations from MPC's magnetic tape, in FK4 system, we obtain an estimation for these frame parameters and an equinox correction which is in great accord with the adopted value (see [3]).