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 AM  Vol.9 No.12 , December 2018
Certain Aspects of the Gravitational Field of a Disk
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.
Cite this paper: Weiss, J. (2018) Certain Aspects of the Gravitational Field of a Disk. Applied Mathematics, 9, 1360-1377. doi: 10.4236/am.2018.912089.
References

[1]   https://en.wikipedia.org/wiki/Protoplanetary_disk

[2]   Lass, H. and Blitzer, L. (1983) The Gravitational Potential Due to Uniform Disks and Rings. Celestial Mechanics, 30, 225-228.
http://adsbit.harvard.edu//full/1983CeMec..30..225L/0000225.000.html
https://doi.org/10.1007/BF01232189


[3]   Krough, F.T., Ng, E.W. and Snyder, W.V. (1982) The Gravitational Field of a Disk. Celestial Mechanics, 26, 395-405.
http://adsbit.harvard.edu//full/1982CeMec..26..395K/0000395.000.html
https://doi.org/10.1007/BF01230419


[4]   “Elliptic Integral” in Wikipedia.
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[7]   Mathematics Stack Exchange.
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[8]   Mathematics Stack Exchange.
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[9]   “Milky Way” in Wikipedia.
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[10]   “Measuring the Milky Way: One Massive Problem, One New Solution”.
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[11]   “List of Nearest Galaxies” in Wikipedia.
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[12]   Dzierba, A.R. Circular Orbits and Their Stability: A Physics Lecture.
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