A comparison of a class of numerical methods for calculating the orbit of an asteroid
by
Dejan Timarac
University of Auckland
Coauthors: Philip W. Sharp (University of Auckland)

Since the celebrated work of Gauss in the early nineteenth century, many numerical methods have been developed to calculate the orbit of an asteroid from observations of its right ascension and declination.

One class of methods, probably the class which leads to the most accurate orbits, use N-body simulations to model the interaction between the asteroid, the Sun, the planets and possibly other asteroids. With these methods, least square techniques are used to find the initial position and velocity of the asteroid and possibly its mass so that the difference between the calculated and observed angular position is minimised.

We present a comparison of the efficiency of some methods in this class. We also illustrate the advantages and disadvantages of several techniques that potentially improve the efficiency, such as omitting relativistic effects in the model equations.

Date received: September 28, 2000