Speaker
Dr
Martin Lara
(Space Dynamics Group, Polytechnic University of Madrid, and GRUCACI, University of La Rioja)
Description
Usual onboard orbit propagators are provided as navigation maintenance aids for earth orbiting satellites. These programs should be able to forecast satellite ephemeris within a reasonable accuracy for short time periods, which may range from minutes, as in the case of momentary lack of GPS signal, to several satellite orbits. In these brief intervals the accumulation of second order effects of the Geopotential is barely apparent, and, therefore, the propagation model can be very simple. Hence, common onboard orbit propagators are based in the fixed-step numerical integration of the J2 model, a truncation of the Geopotential limited to the zonal harmonic coefficient of the second degree.
On the other hand, the use of analytical, intermediary solutions of the J2 problem has been recently proposed as an efficient alternative to the numerical integration. The accuracy of common intermediary orbits of the J2 problem is limited to first order effects, thus providing less precise solutions than the numerical integration. However, because of the inherent uncertainty of the initial conditions to be propagated onboard, it can be shown that both alternatives, the numerical integration and the intermediary approach, enjoy the same statistics. Other benefits of using analytical solutions is that they may improve both memory allocation and computation time, a fact that may be crucial to Cubesats ore other small satellite missions, in which the computational abilities may be restricted.
Note, however, that neglecting the long-period effects associated to the odd zonal harmonics introduces small errors in the propagation, which are clearly observable even in the short-term. These errors can exceed 1 km in the along-track direction at the end of one day. Hence, taking into account the disturbing effects of some higher order harmonics may notably improve the propagation model.
Here, we propose a new intermediary solution that takes into account the first three zonal harmonics of the Geopotential (J2, J3 and J4). Since the solution is analytical, the evaluation is very fast and is not constrained to a step-by-step evaluation. In spite of the forces model of the new intermediary is much heavier than the simple J2 model, its evaluation can be fastened using some simplifications that alleviate the computational burden, in this way making the new intermediary definitely competitive when compared to the numerical integration of the J2 problem.
| Applicant type | First author |
|---|
Primary author
Dr
Martin Lara
(Space Dynamics Group, Polytechnic University of Madrid, and GRUCACI, University of La Rioja)
Co-author
Mr
Denis Hautesserres
(CNES)
