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h1. State of Art of the Orbit Propagators

h3. The State-Of-Art

Orbit propagators are mathematical models made to estimate the satellite’s position and velocity. These models take into account the effects which move the satellite apart from its ideal orbit. These perturbations are mostly the result of the non-spherical earth mass distribution, the atmospheric resistance and the gravitation effects from the sun or the moon for high orbit satellites.

Five of these propagators exist : SGP, SGP4, SDP4, SGP8, SDP8 and HPOP. SGP means Simplified General Perturbations models and SDP means Simplified Deep Space Perturbations. Here is a short description for each of these propagators :

* SGP is the first orbit propagator. It has been developed by Hilton and Kuhlman in 1966 thanks to one of Kozai's research work made in 1959. It is made for satellites orbiting near the Earth which includes satellites with an orbital period lower than 225 minutes. This model assumes that the eccentricity is low and that the perigee's altitude is constant.

* SGP4 has been developed by Ken Cranford in 1970. It is a improvement of the previous propagator in order to track the growing number of satellites in orbit at this time. It is also used for near Earth satellites.

* SDP4, developed by Hujsak in 1979, is the SGP4 propagator adapted for deep space objects. This includes satellites with an orbital period greater than 225 minutes. For period above this value, the satellite's orbit is disturbed by the moon and the sun, but also, by some resonance effects for orbital periods of 12 and 24 hours.

* SGP8, also used for near Earth satellites, is almost like the SGP4 propagator but the calculation methods are different. However it follows the same models for the atmospheric and gravitational effects.

* SDP8 is the SGP8 propagator adapted to deep-space effects. Moreover, SGP8 and SDP8 are better to manage the orbital decay.

* HPOP propagator which stands for High Precision Orbit Propagator, is the most accurate of all the models. The error has an order of 12 meters per orbit. This propagator takes into account the following perturbations : gravitational effects of the moon and the sun, atmospheric drag and solar radiation pressure.

In this project, we chose to use the SGP4 orbit propagator. On one hand because we are dealing with low orbit satellites, and on the other hand, because this propagator is the most commonly use to develop satellite tracking software. Besides, the NORAD (North American Aerospace Defence Command) element sets are provided using SGP4 or SDP4. Thus it was more accurate to implement one of those two propagators.

h3. References

Complete description of the orbit propagators : https://celestrak.com/NORAD/documentation/spacetrk.pdf

A french link with all the formulas of each propagators : http://astropedia.free.fr/satel/satel2.html

High Precision Orbit Propagator : http://smad.com/space-systems/software/high-precision-orbit-propagator/

The SGP4 propagator has been implemented with the Matlab code provided here : 

http://www.mathworks.com/matlabcentral/fileexchange/28888-satellite-orbit-computation/content/SGP4/sgp4.m