Deviation Analysis of the De-Boost Impulse in De-Orbit Maneuver of a Spacecraft

Deviation Analysis of the De-Boost Impulse in De-Orbit Maneuver of a Spacecraft

This paper investigates the effect of de-boost impulse deviation on extra-atmospheric trajectory of a spacecraft in de-orbit maneuver. The mentioned deviation can be divided on three main components such as error of de-boost impulse orientation, error of de-boost impulse value and error of de-boost impulse execution time. Since the Cowell’s formulation is not a proper form for deviation analysis and designing control law for orbital maneuver, so a part of this paper is devoted to extracting a proper mathematical model. After definition of an appropriate set of orbital elements, using a combination of the Cowell’s formulation and the method of variation of parameters, a mathematical model is derived, to that end, the concept of osculating orbit and matrices algebra play main roles. Finally, the model is developed as six coupled nonlinear first order ODEs in terms of orbital elements. This equation can be expressed in affine form that it is a suitable form for designing control law in order to orbital correction. Using simulation of derived mathematical model in MATLAB_SIMULINK software, the effect of de-boost impulse deviation on re-entry angle and re-entry velocity is analyzed and finally the obtained results are validated by STK software. The results show that de-orbit trajectory of a spacecraft from de-orbit point to re-entry point should be continuously under control to guarantee that it will not escape from the atmosphere, not exceed the heating and landing point limits.