14th-order harmonics in the geopotential from analysis of satellite orbits at resonance

Details 14th-order harmonics in the geopotential from analysis of satellite orbits at resonance 14th-order harmonics in the geopotential from analysis of satellite orbits at resonance

Feb 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986p%26ss...34..183k&link_type=abstract

Planetary and Space Science (ISSN 0032-0633), vol. 34, Feb. 1986, p. 183-195.

Mathematics

15

Geopotential, Orbital Resonances (Celestial Mechanics), Satellite Orbits, Satellite Perturbation, Harmonics, Mathematical Models, Resonance

Scientific paper

The earth's gravitational potential is usually expressed as a double series of tesseral harmonics of degree l and order m, and values of coefficients for l and m up to 36 or more are determined in recent models. The individual harmonic coefficients of a particular order m can most accurately be evaluated by analyzing the perturbations on satellites which experience nth-order resonance (i.e., repeat their ground track after m revolutions). Results from analyses of 15 satellite orbits at 14th-order resonance are used to evaluate seven pairs of individual coefficients of 14th order and odd degree (l = 15, 17, . . . 27), and 6 pairs of coefficients of even degree (l = 14, 16, . . . 24). The five most accurate pairs of values, for l = 14, 15, 16, 17, and 19 have a mean standard deviation corresponding to an accuracy of 0.9 cm in geoid height. These values are used as a test of the accuracy of three recent comprehensive models of the geopotential; the agreement is generally satisfactory, the differences being consistent with the expected errors (about 3 x 10 to the -9th) in the models. Values for the pair of coefficients of order 28 and degree 28 are obtained, again with standard deviation equivalent to 0.9 cm in geoid height.

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