국내 최대 기계 및 로봇 연구정보

기술보고서

기술보고서 게시판 내용
타이틀	Normalization of Gravitational Acceleration Models
저자	Eckman, Randy A.;; Brown, Aaron J.;; Adamo, Daniel R.
Keyword	ACCELERATION (PHYSICS); ALGORITHMS;; GRAVITATIONAL FIELDS;; LEGENDRE FUNCTIONS;; MATHEMATICAL MODELS;; RECURSIVE FUNCTIONS;; SENSITIVITY;; SINGULARITY (MATHEMATICS); SPACE FLIGHT;; SPHERICAL HARMONICS
URL	http://hdl.handle.net/2060/20110023121
보고서번호	JSC-CN-23097
발행년도	2011
출처	NTRS (NASA Technical Report Server)
ABSTRACT	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.