Analytical Expressions For Orbital Perturbations Due To Lorentz Force


The selection of orbit propagation models strongly affects various space situational awareness applications like future object population prediction, collision avoidance maneuvers, object detection, object tracking, and catalog maintenance. Two key considerations in the selection of orbit propagation models are accuracy and computational cost. While one can use accurate numerical orbit propagation techniques for short propagation periods, it can be computationally taxing when the propagation period is long and/or when a large number of objects are to be propagated. This can be remedied by using analytical orbit propagation techniques, which not only facilitate fast orbit propagation but also permit meaningful theoretical insight into the structure of the perturbations. Most previous analytical object propagation in the near-Earth realm has been carried out in the presence of zonal and tesseral harmonics of Earth's gravity, Sun and Moon gravities, atmospheric drag, and solar radiation pressure. However, for high-energy plasma weather and under eclipse where objects can get highly charged, Lorentz force should be included for better accuracy in orbital propagation. Lorentz force should also not be ignored for high-area-to-mass ratio objects. Among the work that has taken Lorentz force into consideration, most have made the simplifying assumption of non-tilted Earth magnetic dipole or have developed analytical formulas valid only for low Earth orbit region. In this paper, new analytical formulas for Lorentz perturbations are developed using a tilted dipole Earth magnetic field and a constant charge-to-mass ratio. The derived analytical formulas are valid for all near-Earth altitudes. Two sets of formulas are derived, one for small eccentricities and one for large eccentricities. The analytical results are validated using numerical simulations. A comparative study is also carried out using different charging levels and area-to-mass ratios for the low Earth orbit and geosynchronous Earth orbit regions.


Mechanical and Aerospace Engineering

Keywords and Phrases

Analytical orbit theory; Charging; Geosynchronous Earth orbit; High area-to-mass ratio objects; Lorentz force; Low area-to-mass ratio objects; Low Earth orbit

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Article - Journal

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Publication Date

01 May 2021