Precise estimates of the general term of the Laplace series for gravitational potentials

Details Precise estimates of the general term of the Laplace series for gravitational potentials Precise estimates of the general term of the Laplace series for gravitational potentials

Jan 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012phsp.conf..186k&link_type=abstract

Physics of Space: the 41st Annual Student Scientific Conference, Edited by P.E. Zakharova, E.D. Kuznetsov, A.B. Ostrovskii, S.V.

Physics

Scientific paper

The main type of representation of the gravitational potential of celestial bodies is the Laplace series in spherical harmonics V_n. It is well known that the sequence V_n on the enveloping sphere is majorized by the sequence Cn^{-σ} with σ=5/2 for bodies of irregular structure. Simple examples show that the estimate is attainable for bodies having a common piece of a surface (hemisphere, spherical sector) or having a common piece of a curve (cylinder) with the enveloping sphere. Here we establish that this estimate admits an extension for bodies having a finite set of points lying on the enveloping sphere, and σ=3 in this case. We suggest that the value of the exponent σ is close to 3 for the Earth, the Moon, terrestrial planets, regular satellites, and asteroids.

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