<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>One of the aspects of geopotential models is orbit integration of satellites. The geopotential acceleration has the largest influence on a satellite with respect to the other perturbing forces. The equation of motion of satellites is a second-order vector differential equation. These equations are further simplified and developed in this study based on the geopotential force. This new expression is much simpler than the traditional one as it does not derivatives of the associated Legendre functions and the transformations are included in the equations. The maximum degree and order of the geopotential harmonic expansion must be selected prior to the orbit integration purposes. The values of the maximum degree and order of these coefficients depend directly on the satellite's altitude. In this article, behaviour of orbital elements of recent geopotential satellites, such as CHAMP, GRACE and GOCE is considered with respect to the different degree and order of geopotential coefficients. In this case, the maximum degree 116, 109 and 175 were derived for the Earth gravitational field in short arc orbit integration of the CHAMP, GRACE and GOCE, respectively considering millimeter level in perturbations.</p></abstract>

One of the aspects of geopotential models is orbit integration of satellites. The geopotential acceleration has the largest influence on a satellite with respect to the other perturbing forces. The equation of motion of satellites is a second-order vector differential equation. These equations are further simplified and developed in this study based on the geopotential force. This new expression is much simpler than the traditional one as it does not derivatives of the associated Legendre functions and the transformations are included in the equations. The maximum degree and order of the geopotential harmonic expansion must be selected prior to the orbit integration purposes. The values of the maximum degree and order of these coefficients depend directly on the satellite's altitude. In this article, behaviour of orbital elements of recent geopotential satellites, such as CHAMP, GRACE and GOCE is considered with respect to the different degree and order of geopotential coefficients. In this case, the maximum degree 116, 109 and 175 were derived for the Earth gravitational field in short arc orbit integration of the CHAMP, GRACE and GOCE, respectively considering millimeter level in perturbations.

Simplification of Geopotential Perturbing Force Acting on A Satellite

Division of Geodesy, Royal Institute of Technology, Stockholm, Sweden

Dept. of Geodesy and Geomatics, K.N. Toosi University of Technology, Tehran, Iran

Artificial Satellites

{"article-title":"Simplification of Geopotential Perturbing Force Acting on A Satellite"}

One of the aspects of geopotential models is orbit integration of satellites. The geopotential acceleration has the largest influence on a satellite with...

Simplification of Geopotential Perturbing Force Acting on A Satellite

Published Online: May 29, 2009

Page range: 45 - 64

DOI: https://doi.org/10.2478/v10018-009-0006-7

Keywords
Geopotential, orbit integration, average power acceleration, orbital elements

This content is open access.

Simplification of Geopotential Perturbing Force Acting on A Satellite

Published Online: May 29, 2009

Page range: 45 - 64

DOI: https://doi.org/10.2478/v10018-009-0006-7

KeywordsGeopotential, orbit integration, average power acceleration, orbital elements

This content is open access.

Keywords
Geopotential, orbit integration, average power acceleration, orbital elements