Spherical Harmonic Gravity Model

Implement spherical harmonic representation of planetary gravity

Library

Environment/Gravity

Description

The Spherical Harmonic Gravity Model block implements the mathematical representation of spherical harmonic planetary gravity based on planetary gravitational potential. It provides a convenient way to describe a planet gravitational field outside of its surface in spherical harmonic expansion.

You can use spherical harmonics to modify the magnitude and direction of spherical gravity (-GM/r2). The most significant or largest spherical harmonic term is the second degree zonal harmonic, J2, which accounts for oblateness of a planet.

Use this block if you want more accurate gravity values than spherical gravity models. For example, nonatmospheric flight applications might require higher accuracy.

Dialog Box

Units

Specifies the parameter and output units:

Units

Height

Metric (MKS)

Meters

English

Feet

Degree

Specify the degree of harmonic model. Recommended degrees are:

Planet ModelDegree

EGM2008

120

EGM96

70

LP100K

60

LP165P

60

GMM2B

60

EIGENGL04C

70

Action for out of range input

Specify if out-of-range input invokes a warning, error, or no action.

Planet model

Specify the planetary model. From the list, select:

Planet ModelNotes
EGM2008

Earth — Is the latest Earth spherical harmonic gravitational model from National Geospatial-Intelligence Agency (NGA). This block provides the WGS-84 version of this gravitational model. You can use the EGM96 planetary model if you need to use the older standard for Earth.

EGM96Earth
LP100K

Moon — Is best for lunar orbit determination based upon computational time required to compute orbits. This planet model was created in approximately the same year as LP165P with similar data.

LP165P

Moon — Is best for extended lunar mission orbit accuracy. This planet model was created in approximately the same year as LP165P with similar data.

GMM2B

Mars

Custom

Enables you to specify your own planetary model. This option enables the Planet mat-file parameter.

EIGENGL04C

Earth — Supports the gravity field model, EIGEN-GL04C (http://icgem.gfz-potsdam.de/ICGEM/). This model is an upgrade to EIGEN-CG03C.

When defining your own planetary model, the Degree parameter is limited to the maximum value for int16. When inputting a large degree, you might receive an out-of-memory error. For more information about avoiding out-of-memory errors in the MATLAB® environment, see Memory Usage.

Planet mat-file

Specify a MAT-file that contains definitions for a custom planetary model. The aerogmm2b.mat file in the Aerospace Toolbox is the default MAT-file for a custom planetary model.

This file must contain:

VariableDescription
Re

Scalar of planet equatorial radius in meters (m).

GM

Scalar of planetary gravitational parameter in meters cubed per second squared (m3/s2)

degree

Scalar of maximum degree.

C

(degree+1)-by-(degree+1) matrix containing normalized spherical harmonic coefficients matrix, C.

S

(degree+1)-by-(degree+1) matrix containing normalized spherical harmonic coefficients matrix, S.

When using a large value for Degree, you might receive an out-of-memory error. For more information about avoiding out-of-memory errors in the MATLAB environment, see Memory Usage.

References

[1] Gottlieb, R. G., "Fast Gravity, Gravity Partials, Normalized Gravity, Gravity Gradient Torque and Magnetic Field: Derivation, Code and Data," Technical Report NASA Contractor Report 188243, NASA Lyndon B. Johnson Space Center, Houston, Texas, February 1993.

[2] Vallado, D. A., Fundamentals of Astrodynamics and Applications, McGraw-Hill, New York, 1997.

[3] "NIMA TR8350.2: Department of Defense World Geodetic System 1984, Its Definition and Relationship with Local Geodetic Systems".

[4] Konopliv, A. S., S. W. Asmar, E. Carranza, W. L. Sjogen, D. N. Yuan., "Recent Gravity Models as a Result of the Lunar Prospector Mission, Icarus", Vol. 150, no. 1, pp 1–18, 2001.

[5] Lemoine, F. G., D. E. Smith, D.D. Rowlands, M.T. Zuber, G. A. Neumann, and D. S. Chinn, "An improved solution of the gravity field of Mars (GMM-2B) from Mars Global Surveyor", Journal Of Geophysical Research, Vol. 106, No. E10, pp 23359-23376, October 25, 2001.

[6] Kenyon S., J. Factor, N. Pavlis, and S. Holmes, "Towards the Next Earth Gravitational Model", Society of Exploration Geophysicists 77th Annual Meeting, San Antonio, Texas, September 23–28, 2007.

[7] Pavlis, N.K., S.A. Holmes, S.C. Kenyon, and J.K. Factor, "An Earth Gravitational Model to Degree 2160: EGM2008", presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13–18, 2008.

[8] Grueber, T., and A. Köhl, "Validation of the EGM2008 Gravity Field with GPS-Leveling and Oceanographic Analyses", presented at the IAG International Symposium on Gravity, Geoid & Earth Observation 2008, Chania, Greece, June 23–27, 2008.

[9] Förste, C., Flechtner, F., Schmidt, R., König, R., Meyer, U., Stubenvoll, R., Rothacher, M., Barthelmes, F., Neumayer, H., Biancale, R., Bruinsma, S., Lemoine, J.M., Loyer, S., "A Mean Global Gravity Field Model From the Combination of Satellite Mission and Altimetry/Gravmetry Surface Data - EIGEN-GL04C", Geophysical Research Abstracts, Vol. 8, 03462, 2006.

[10] Hill, K. A. (2007). Autonomous Navigation in Libration Point Orbits. Doctoral dissertation, University of Colorado, Boulder. http://ccar.colorado.edu/geryon/papers/Misc/Hill_thesis.pdf.

[11] Colombo, Oscar L., "Numerical Methods for Harmonic Analysis on the Sphere", Reports of the department of Geodetic Science, Report No. 310, The Ohio State University, Columbus, OH., March 1981.

[12] Colombo, Oscar L., "The Global Mapping of Gravity with Two Satellites", Nederlands Geodetic Commission, vol. 7 No. 3, Delft, The Nederlands, 1984., Reports of the department of Geodetic Science, Report No. 310, The Ohio State University, Columbus, OH., March 1981.

[13] Jones, Brandon A. (2010). Efficient Models for the Evaluation and Estimation of the Gravity Field. Doctoral dissertation, University of Colorado, Boulder. http://ccar.colorado.edu/geryon/papers/Misc/bajones_phd.pdf.

Was this topic helpful?