Citation
Abstract
An approximate analytic formulation of Earth-based ranging measurements to a radio beacon on the surface of another planet is presented. Simple mathematical models that describe lander/beacon ranging measurements are derived. Also included in this article are the partial derivatives of the range observable with respect to body-fixed coordinates of a radio beacon on the surface of a target planet. Additionally, partial derivatives are derived for target planet orientation, rotation, and for the ephemeris. View period calculations are presented for the three Deep Space Network (DSN) complexes at Goldstone, California, Canberra, Australia, and Madrid, Spain. The calculations indicate that for the case of Mars itself, total hours of visibility vary from ~280 to ~460 hours per month over a single martian synodic period (about 26 months in length), while total hours of visibility for three hypothetical beacons located along the martian prime meridian vary from ~90 to ~280 hours per month over the same period of time. Variations of the partial derivatives over time suggest that the information content of the range data is void of any singular geometries that would lead to an “ill-conditioned” information array. The only parameter that may be poorly determined, as confirmed by Viking lander range data, is the body-fixed z-height component of the surface radio beacon. The ranging model and its partial derivatives provide a sufficient framework with which to perform analytic and numerical error covariance studies of beacon location and planetary pole ortentation/ephemeris determination.
Details
- Volume
- 42-103
- Published
- November 15, 1990
- Pages
- 7–86
- File Size
- 738.1 KB