9th International Conference and Exhibition on Satellite & Space Missions
Toronto, Canada
Aravind Gundakaram
Mahindra University, India
Title: Mathematical modelling and numerical solution for high precision satellite ephemeris determination
Biography
Biography: Aravind Gundakaram
Abstract
In this paper, we develop a high precision satellite orbit determination model for satellites orbiting the Earth. Solving this model entails numerically integrating the differential equation of motion governing a two-body system, for which we employ Fehlberg’s formulation of the Runge-Kutta class of numerical integrators with adaptive stepsize control. Various perturbing forces are also accounted for in the mathematical model, such as the acceleration due to the geopotential of the Earth, third-body gravitational effects, solar radiation pressure and atmospheric drag. For applications requiring high precision modelling, we also account for Earth radiation pressure, the perturbative effects of solid-Earth tides and ocean tides, and also make adjustments to the total acceleration for relativistic effects.
We have provided explicit expressions to calculate the force exerted by each perturbation that contributes to the total acceleration of the satellite. In situations where calculating certain terms in these expressions poses practical challenges, we have provided recurrence relations to assist with implementation. The implementation of this model yields a satellite orbit propagator, which we call the Satellite Orbit Determiner (SED). We have discussed the architecture of SED and the methodology it employs, and have presented the numerical results obtained from it. These results are compared with the widely used High Precision Orbit Propagator (HPOP). Currently, SED has only been implemented for the two-body problem, but future advancements will enable it to handle the three-body problem as well.