skip to main content

SciTech ConnectSciTech Connect

Title: Prolate spheroidal harmonic expansion of gravitational field

As a modification of the oblate spheroidal case, a recursive method is developed to compute the point value and a few low-order derivatives of the prolate spheroidal harmonics of the second kind, Q{sub 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 low-order derivatives of P-bar {sub 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.
Authors:
 [1]
  1. National Astronomical Observatory, Ohsawa, Mitaka, Tokyo 181-8588 (Japan)
Publication Date:
OSTI Identifier:
22340223
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astronomical Journal (New York, N.Y. Online); Journal Volume: 147; Journal Issue: 6; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANTIPROTONS; ASTEROIDS; CALCULATION METHODS; COSMOLOGY; DATA; EXPANSION; GRAVITATIONAL FIELDS; HARMONICS; LEGENDRE POLYNOMIALS; MODIFICATIONS; PLANETS