Analytical radial adaptive method for spherical harmonics gravity models

Ahmed M. Atallah, Ahmad Bani Younes, Robyn M. Woollands, John L. Junkins

Research output: Chapter in Book/Report/Conference proceedingConference contribution


High precision propagation for satellites orbiting a large body with a highly nonlinear gravity field (planets, moons, asteroids) require accurate computation of the gravitational acceleration at each integration step. This is a computationally expensive operation that depends mainly on the orbit geometry and the accuracy to which the solution is required. High accuracy solutions require a large degree and order in the spherical harmonic series which significantly increases the computation time. In order to maintain a specific accuracy solution for a satellite in a highly elliptic orbit, a high gravity degree and order are needed near perigee and a lower degree and order are required at apogee. In this paper we present an analytic method for which the degree of the spherical harmonic series is automatically selected based on the desired solution accuracy specified by the user, and the instantaneous radial distance of the satellite from the Earth. We present results for several orbit test cases that demonstrate a significant speedup when using our analytical radial adaptive model for computing spherical harmonic gravity.

Original languageEnglish (US)
Title of host publicationSpaceflight Mechanics 2019
EditorsFrancesco Topputo, Andrew J. Sinclair, Matthew P. Wilkins, Renato Zanetti
PublisherUnivelt Inc.
Number of pages12
ISBN (Print)9780877036593
StatePublished - 2019
Externally publishedYes
Event29th AAS/AIAA Space Flight Mechanics Meeting, 2019 - Maui, United States
Duration: Jan 13 2019Jan 17 2019

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


Conference29th AAS/AIAA Space Flight Mechanics Meeting, 2019
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Aerospace Engineering
  • Space and Planetary Science


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