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Normalization of gravitational acceleration models
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Brown, Aaron J. Eckman, Randy A. |
| Copyright Year | 2011 |
| Description | Unlike the uniform density spherical shell approximations of Newton, the con- sequence of spaceflight in the real universe is that gravitational fields are sensitive to the nonsphericity of their generating central bodies. The gravitational potential of a nonspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities which must be removed in order to generalize the method and solve for any possible orbit, including polar orbits. Three unique algorithms have been developed to eliminate these singularities by Samuel Pines [1], Bill Lear [2], and Robert Gottlieb [3]. This paper documents the methodical normalization of two1 of the three known formulations for singularity-free gravitational acceleration (namely, the Lear [2] and Gottlieb [3] algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre Polynomials and ALFs for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms. |
| File Size | 453638 |
| Page Count | 43 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_20110023121 |
| Archival Resource Key | ark:/13960/t0cv9h159 |
| Language | English |
| Publisher Date | 2011-01-24 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Sensitivity Algorithms Spherical Harmonics Recursive Functions Acceleration Physics Legendre Functions Gravitational Fields Singularity Mathematics Mathematical Models Space Flight Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Article |
