Generalization of a method by Mossotti for initial orbit determination

TL;DR

This paper revisits and extends Mossotti's initial orbit determination method, adapting it for topocentric observations and comparing its performance with Gauss's method using synthetic asteroid data.

Contribution

The paper generalizes Mossotti's method to topocentric observations and compares its effectiveness with Gauss's method through numerical simulations.

Findings

Mossotti's method performs well with synthetic data.

The extended method provides a quadratic equation for angular momentum.

Comparison shows the method's viability for asteroid orbit determination.

Abstract

Here we revisit an initial orbit determination method introduced by O. F. Mossotti employing four geocentric sky-plane observations and a linear equation to compute the angular momentum of the observed body. We then extend the method to topocentric observations, yielding a quadratic equation for the angular momentum. The performance of the two versions are compared through numerical tests with synthetic asteroid data using different time intervals between consecutive observations and different astrometric errors. We also show a comparison test with Gauss's method using simulated observations with the expected cadence of the VRO-LSST telescope.