Expansion of functions describing planetary surface and gravity field

Details Expansion of functions describing planetary surface and gravity field Expansion of functions describing planetary surface and gravity field

Feb 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985rpspr...3...33v&link_type=abstract

In its USSR Rept.: Space (JPRS-USP-85-001) p 33 (SEE N85-22403 13-12) Transl. into ENGLISH from Astronomicheskiy Vestnik (USS

Other

Error Analysis, Mathematical Models, Planetary Gravitation, Planetary Surfaces, Regression Analysis, Relief Maps, Lunar Gravitation, Spherical Coordinates, Spherical Harmonics

Scientific paper

The problem of description of the surface and gravity field of planets is examined using an expansion in spherical and other functions with particular consideration of the problem of expansion of lunar relief in spherical functions. The factors exerting an influence on approximating expressions can be divided into two groups. The first group includes errors generated by observational errors. Errors in the second group, generated by the mathematical description itself are stressed here. The approach used in solving the problem is statistical (regression) modeling. This approach is applied in an expansion of a function describing averaged surface relief by a number of spherical harmonics. The numerical example presented shows that the use of regression modeling makes it possible to obtain expansions with a number of terms approximately half as great as in the ordinary approach with the same or a higher descriptive accuracy. Also examined are the problems caused by the great dimensionality of the problems and the diversity of variants of initial data. The described approach gives adequate but economical models of relief and the gravity field.

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