Investigating the suitability of Analytical and Semi-analytical Satellite theories for Space Object Catalogue maintenance in Geosynchronous regime

Kurzfassung

Currently, the number of space debris particles is about 33,500, out of which approximately 1100 are in geosynchronous orbits, which are tracked and whose orbital data are provided from US Space surveillance network, with instances of colliding and increasing the number of space debris. To further not exacerbate this situation, it is important to track and maintain a catalogue of these objects. To determine orbits of tracked objects and to propagate them in time, to correlate for not having duplicates in a catalogue, and to predict the close encounters of the satellites with tracked objects, it is important to have computationally efficient ephemeris propagators. For the purpose the well-known flavors of Simplified General perturbation theories for deep space(SDP4/SDP8), Kamel’s theory – a dedicated geosynchronous satellite perturbation theory formulated in equinoctial elements, and draper semi-analytical satellite theory – which makes use of generalized method for averaging, are examined for their best possible fit with numerically generated orbits and also for their computational loads. These propagators are selected in order to gain the understanding of behavior of different analytical formulations and semi-analytical propagation techniques. Previous studies on analytical and semi-analytical propagator have claimed that they are computationally lean and much faster than the numerical propagators, if any of the above mentioned propagator meets the requirements specified by Space Situational Awareness demands, it will considerably reduce the computational burden on the system. If cross-track and along-track accuracies are within the limits, then they can also be used for the purpose of collision predictions, which usually require high number of function calls in determining the close encounters. Simplified General Perturbation - 4 (SGP4) theory was developed based on Brower’s theory for the purpose of propagating Low-altitude satellites, further it was extended to be used for deep space satellites (SDP4) which includes solar and lunar perturbations which constitutes to the accuracies of objects in orbits with mean motion greater than half a day. Further SGP8 was developed by Hoots then extended to SDP8 similar to SDP4. Kamel’s theory uses a set of non-singular canonical orbital elements, i.e. equinoctial elements, to express the perturbations of a geosynchronous satellite’s orbit under the action of Earth’s and third bodies’ gravity field. The Earth's triaxiality effect is represented by zonal and tesseral harmonics up to J33 coefficients. Solar motion is described by an elliptic orbit expansion and lunar motion is represented by the Hill-Brown theory with coefficients up to 10-3 rad. DSST is a mean element orbit propagator based upon the generalized method of averaging. DSST was developed by P. Cefola with his colleagues at Draper Laboratory and Computer Sciences Corporation, Maryland, with the mathematical development relying on recursive series to model conservative perturbations and numerical quadrature in modeling non-conservative effects. Geosynchronous objects are defined by European Space Agency’s DISCOS catalogue as objects which lie between the following limits • Mean motion between 0.9 to 1.1 revolution per sidereal day (0.9≤n≤1.1) • Eccentricity smaller than 0.2 (0≤e≤0.2) • Inclination smaller than 70˚ (0˚≤i≤70˚) For all the orbits within these ranges, speed and accuracies of the selected analytical and semi-analytical theories’ are determined. Analytical and semi-analytically generated orbits are fitted with SP theory orbit for the arc lengths of few days. Details of which are elaborated in the paper.