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• W1987215826 abstract "Exact analytical solutions are given for the three finite disks with surface density $Sigma_n=sigma_0 (1-R^2/alpha^2)^{n-1/2} textrm{with} n=0, 1, 2$. Closed-form solutions in cylindrical co-ordinates are given using only elementary functions for the potential and for the gravitational field of each of the disks. The n=0 disk is the flattened homeoid for which $Sigma_{hom} = sigma_0/sqrt{1-R^2/alpha^2}$. Improved results are presented for this disk. The n=1 disk is the Maclaurin disk for which $Sigma_{Mac} = sigma_0 sqrt{1-R^2/alpha^2}$. The Maclaurin disk is a limiting case of the Maclaurin spheroid. The potential of the Maclaurin disk is found here by integrating the potential of the n=0 disk over $alpha$, exploiting the linearity of Poisson's equation. The n=2 disk has the surface density $Sigma_{D2}=sigma_0 (1-R^2/alpha^2)^{3/2}$. The potential is found by integrating the potential of the n=1 disk." @default.
• W1987215826 created "2016-06-24" @default.
• W1987215826 creator A5032624165 @default.
• W1987215826 date "2009-03-09" @default.
• W1987215826 modified "2023-09-27" @default.
• W1987215826 title "POTENTIAL-DENSITY PAIRS FOR A FAMILY OF FINITE DISKS" @default.
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• W1987215826 doi "https://doi.org/10.1088/0004-637x/693/2/1310" @default.
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