Analytical theory of motion and new ephemeris of Triton from observations.

Modelling the motion of Triton, the main satellite of Neptune, is specific. Earlier researchers built Triton's ephemeris by numerical integration of the equations of its motion. However, these ephemeris can be accessed only by using online ephemeris server or by borrowing a special calculating program and huge data file from authors of the ephemeris. In addition, the interval of the earlier ephemeris is limited. In this paper, simple and easily programmable formulae are presented for computing Triton's ephemeris for any instant of time. The formulae are based on a new analytical theory of Triton's motion all necessary perturbing factors being taken into consideration. The parameters of the theory are fit to all published observations made from 1847 to 2012 (10 254 observations in total). After the parameters were fit to observations, the root-mean-square residuals were 0.228 arcsec, the weighted average residual being 0.036 arcsec. The new ephemeris of Triton slightly differs from those produced by other authors because of differences in the sets of used observations. The new ephemeris of Triton are put on our online ephemeris server. It is shown that the available observations do not allow to determine reliably the quadratic term in the orbital longitude of Triton. Such a term would be an additional indicator of the accuracy of the theory and observations. [ABSTRACT FROM AUTHOR]