TITLE:
Certain Aspects of the Gravitational Field of a Disk
AUTHORS:
Jonathan D. Weiss
KEYWORDS:
Disk-Shaped Mass, Gravitational Effects of a Disk-Shaped Mass, Calculational Techniques of Such Gravitational Effects
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.12,
December
27,
2018
ABSTRACT:
There are at least two reasons why one would study the gravitational field of a
disk. The first is that many astronomical objects, such as spiral galaxies like
the Milky Way, are disk-like. The second is that the field of a disk is interesting,
particularly when compared to that of a spherical, or near-spherical, object,
which is much easier to analyze because of its high degree of symmetry.
It is hoped that this study will augment previous work on this subject. The
aspects presented in this paper are as follows: 1) both the radial and vertical
gravitational fields of a thin disk within the plane of the disk and above it; 2) a
comparison of some of the field results obtained by Lass and Blitzer (1983)
involving elliptic integrals to those obtained by a standard numerical integration,
now available online, and separately through the use of Legendre polynomials;
3) the logarithmic divergence of the radial field at the edge of a thin
disk; 4) the fields in the plane of a disk containing a central hole, particularly
within the hole, such as the rings of Saturn; 5) circular orbits within the plane
of a single disk and half way between two disks, and their stability; 6) the escape
velocity at a point within the Milky Way, particularly at the position of
the solar system and without any added, or subtracted, orbital effects around
the galactic center; and 7) the radial field at the circular edge of a disk of finite
thickness.