Prolate Spheroidal Harmonic Expansion of Gravitational Field
Abstract
As a modification of the oblate spheroidal case, a recursive method is developed to compute the point value and a few loworder derivatives of the prolate spheroidal harmonics of the second kind, Q_{nm} (y), namely the unnormalized associated Legendre function (ALF) of the second kind with its argument in the domain, 1 < y < ∞. They are required in evaluating the prolate spheroidal harmonic expansion of the gravitational field in addition to the point value and the loworder derivatives of \overline{P}_{nm}(t), the 4π fully normalized ALF of the first kind with its argument in the domain, t <= 1. The new method will be useful in the gravitational field computation of elongated celestial objects.
 Publication:

The Astronomical Journal
 Pub Date:
 June 2014
 DOI:
 10.1088/00046256/147/6/152
 Bibcode:
 2014AJ....147..152F
 Keywords:

 celestial mechanics;
 minor planets;
 asteroids: general