Modelling of Perturbations For Precise Orbit Determination
An orbit determination and propagation package is developed in Python to predict satellite trajectories accurately
with position differences of within 1 km after one orbit when compared to simulated satellite true position. The effect of
Earth’s non-uniform gravitational fields, caused by equatorial bulge and non-sphericity, is modelled using zonal spherical
harmonics from J2 to J6 and the orbit is propagated numerically via Runge-Kutta-4 (RK4) method. The full J2-6
gravitational coefficients model yields improvement in position accuracy over the J2-only model. Furthermore, the use of
additional state vector observations via differential correction allow for refinement of initial orbital parameters, hence
achieving good agreement with simulated satellite positions. The orbit determination and propagation software package is
tested using two real-life applications: satellite collision avoidance and Earth observation. The first application is a
simulation of the orbital hypervelocity collision between Iridium 33 and Cosmos 2251 using publicly available NORAD
Two Line Elements (TLE) data. The two satellites’ simulated time of closest approach is 16:55:40 UTC, 10 February 2009,
accurate to within one minute. The second application is a geo-registration of the International Space Station (ISS) using
photographs taken by ISS Expedition 35 crew and corresponding ISS TLEs, calculatingits position over a rotating Earth
coordinate frame and generating a ground-track. The location of ISS over an “unknown” longitude and latitude location on
15:01:42 UTC 27 March 2013 was interpolated to be 1.00 N, 103.43 E, matching actual ISS position to within 0.1 degrees.
Key words- Orbit Propagation, Orbit Determination, Differential Correction, Conjunction Analysis, Geo-registration.