King-Hele orbit theory for periodic orbit and attitude variations

TL;DR

This paper enhances the King-Hele orbit theory by incorporating Fourier series models of the variable drag-coefficient, improving the accuracy of satellite orbit predictions in atmospheric conditions.

Contribution

The work introduces a novel modification to King-Hele theory by modeling the drag-coefficient as a Fourier series, capturing its time variations for better orbit approximation.

Findings

Improved agreement with numerical simulations.

Enhanced modeling of atmospheric drag effects.

Validated accuracy improvements over original theory.

Abstract

The analytical theory of satellite orbits in an atmosphere developed by King-Hele remains widely in use for satellite mission design because of its accurate approximation to numerical integration under simplifying assumptions. Over the course of six decades, modifications to the theory have addressed many of its weaknesses. However, in all subsequent modifications of the original theory, the assumption of a constant drag-coefficient has been retained. The drag-coefficient is a dynamic parameter that governs the physical interaction between the atmosphere and the satellite and depends on ambient as well as satellite specific factors. In this work, Fourier series expansion models of the drag-coefficient are incorporated in the original King-Hele theory to capture time-variations of the drag-coefficient in averaging integrals. The modified theory is validated through simulations that demonstrate the attained improvements in approximating numerical results over the original King-Hele formulation.