Documentation |
Implement spherical harmonic representation of planetary gravity
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/r^{2}). 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.
Specifies the parameter and output units:
Units | Height |
---|---|
Metric (MKS) | Meters |
English | Feet |
Specify the degree of harmonic model. Recommended degrees are:
Planet Model | Degree |
---|---|
EGM2008 | 120 |
EGM96 | 70 |
LP100K | 60 |
LP165P | 60 |
GMM2B | 60 |
EIGENGL04C | 70 |
Specify if out-of-range input invokes a warning, error, or no action.
Specify the planetary model. From the list, select:
Planet Model | Notes |
---|---|
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. |
EGM96 | Earth |
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.
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:
Variable | Description |
---|---|
Re | Scalar of planet equatorial radius in meters (m). |
GM | Scalar of planetary gravitational parameter in meters cubed per second squared (m^{3}/s^{2}) |
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.
[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.