Orbit correction without variational equations. The orbits of Caliban, 46P/Wirtanen and 67P/Churyumov-Gerasimenko

Abstract

Differential orbit correction is performed by computing an osculating orbit from observations from which the perturbations have been subtracted. No variational equations need to be integrated except to solve for non-gravitational forces. The perturbations in the observations are obtained by subtracting a two-body orbit from an integrated, perturbed orbit. The method is used to update the orbits of the Uranian satellite Caliban and of the comets 46P/Wirtanen and 67P/Churyumov-Gerasimenko with recent observations. The method is shown to agree very well with, but is considerably faster than, the conventional method based entirely on variational equations. Algorithms are given for both methods.