Gravitational potential energy of a disk-sphere pair of galaxies

Details Gravitational potential energy of a disk-sphere pair of galaxies Gravitational potential energy of a disk-sphere pair of galaxies

Dec 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975ap%26ss..38..407b&link_type=abstract

Astrophysics and Space Science, vol. 38, Dec. 1975, p. 407-418. Research supported by the University Grants Commission of New De

Mathematics

8

Galactic Clusters, Gravitational Fields, Potential Energy, Astronomical Models, Density Distribution, Functions (Mathematics), Galactic Structure, Integral Equations, Tables (Data)

Scientific paper

Expressions are obtained for the potential energy due to the mutual gravitational interaction between a disk galaxy and a spherical galaxy of arbitrary dimensions. The density distribution in the disk galaxy is represented by a polynomial in ascending powers of the distance from the disk's center; that in the spherical galaxy, by the superposition of spherical polytropes with integral indices and equal radii. It is shown that an overlapping coplanar disk-sphere pair of galaxies can be modeled as two mass points when the separation between their centers has a certain critical value. However, if the separation is less than the critical separation, the mass-point model will overestimate the values of the gravitational potential and the force of attraction: if the separation is greater than the critical one, the model will underestimate these values. For a typical disk-sphere pair with equal radii, it is found that the critical separation is about 0.55 times the radius for the potential and about 0.79 times the radius for the force of attraction.

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