Orbital eccentricity in a logarithmic potential
Abstract
The eccentricity of particles moving in a logarithmic potential, as compared to the eccentricity in a Keplerian potential, was investigated in order to explain the nearly flat rotation curves of galaxies. To produce such a rotation curve, the mass of the galaxy must grow linearly with distance R from the galactic center. The gravitational potential must then be a logarithmic function of R. Numerical computations agree with analytic predictions to values of particle velocity (at right angles to the radius vector) = 1.4, after which the radially increasing mass of the logarithmic potential causes the two curves of eccentricity to converge.
 Publication:

16th Finnish Astronomers' Days
 Pub Date:
 1982
 Bibcode:
 1982fnad.proc...36I
 Keywords:

 Eccentricity;
 Galactic Rotation;
 Galaxies;
 Logarithms;
 Orbital Mechanics;
 Eccentric Orbits;
 Gravitational Fields;
 Radial Velocity;
 Astrophysics