From Kepler to Fine Orbit Tuning of GOCE
Klokocnik, Jaroslav¹; Floberghagen, Rune²; Bezdek, Ales¹; Kostelecky, Jan^3
1Astronomical Inst. Czech Acad. Sci., CZECH REPUBLIC; ²ESA, ITALY; ³Res. Inst. Geodesy..., CZECH REPUBLIC

Johannes Kepler, living in Prague, utilized observations carried out by Tycho Brahe also on the Czech territory to formulate the law known today as the "3rd Kepler law". We recall it in its classical form and will derive it for relationship between the mean motion and selected mean semi-major axis of orbit of an artificial Earth satellite (AES) accounting for the polar flattening of the Earth. This simple tool has amazing applications in selection of orbits of AES to fulfill given tasks "at the best". There is a close relation between density of ground tracks by satellite data, on which in turn precision and resolution of products derived from such measurements are dependent, and semi-major axis (or height of flight) of the satellite used. We tell the story of the GRACE satellites, which during their free decay in the atmosphere encountered important orbit resonances during those the density of ground tracks significantly (but temporarily) decreased. Consequently, also the quality of the monthly solutions for the variations of the gravity field has decreased. What we learned from GRACE, we applied for orbit choice of GOCE, the first satellite equipped by a gravity gradiometer. GOCE is also equipped by ultra-precise ion motor for orbit corrections so that the height of flight can be kept within very small range ±5 meters. It is feasible to choose and keep the orbit at selected high(er) order resonance and, by this way, to reach the maximum quality of products derived from gradiometric measurements. This process is called "fine orbit tuning". Now we are aware: orbit choice for remote sensing AES affects significantly the accuracy of the results derived from their measurements, thus the fine orbit tuning can be very useful tool. Our approach captured interest of ESA in the project of bistatic altimetry satellite GNSS-R. We also investigated the orbit choice for planetary orbiters of Mars, Venus and the Moon from viewpoint of possible most accurate determination of gravity field parameters of these bodies.