1988/11/21 by W X Wang · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · Mathematics · #Geophysics and Gravity Measurements #Historical Astronomy and Related Studies #Relativity and Gravitational Theory #Coordinate system #Equipotential surface #Spherical coordinate system #Elliptic coordinate system #Prolate spheroidal coordinates #Ellipsoidal coordinates #Spheroid #Legendre function #Equipotential #Physics #Homogeneous #Point (geometry) #Polar coordinate system #Legendre polynomials #Cylindrical coordinate system #Cartesian coordinate system #Bipolar coordinates #Classical mechanics #Mathematical analysis #Coordinate space #Geometry #Mathematics #Prolate spheroid #Generalized coordinates #Quantum mechanics #Statistical physics
paper · doi:10.1088/0305-4470/21/22/026
openalex publication_date 1988/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The explicit expressions of the external potential for a homogeneous spheroid in a rectangular coordinate system have been studied previously by several researchers. The author presents the simplest forms of the potential in existing expressions, as derived from the reciprocal of the distance between two points expanded with the Legendre functions of the first and second kind in a spheroidal coordinate system. The numerical comparison of the potentials in spheroidal and rectangular coordinate systems shows exactly their identity. It is now feasible to calculate the gravitational potential for an astronomical body have spheroidal shape in its spheroidal coordinate system and to determine directly the equipotential surfaces by setting the corresponding spheroidal coordinate to a constant.