Summary

We have collected formulae relevant for the transformation between planetocentric and heliocentric coordinate systems and determined the precision of these transformations for the period 1950-2060, most relevant for space science. We give a very short but complete description of orbit determination from Keplerian orbital elements. With the simple set of formulae given in this paper (and adapted from Simon et al. (1994)) the positions of the inner planets can be determined to $160''$ though for the Earth this precision can be increased to $29''$. Adding disturbance terms from Simon et al. (1994) increases the precision to $8''$. This sets the limits for the precision to be achieved by a single set of Keplerian elements. For higher precision the installation of an integrated ephemeris is recommended.

We also determined Keplerian orbital elements for major interplanetary spacecraft within the precision limits given by the NSSDC data source. These allow quick approximate calculations of spacecraft positions and also allow to cross check existing position data sets. Formulae given in this paper can easily be implemented in software. Programs used in preparation of this paper have been written in the IDL language and are available from our website ²⁴.