Abstract
A standard topic in an advanced undergraduate classical mechanics course is the determination of the orbits in a gravitational field. In the present paper we report on the calculation of bound orbits in the gravitational field of a spiral galaxy. Calculations such as these could serve to focus attention on an area of cutting edge astrophysics and could serve as an instructive exercise for advanced undergraduates. In the computations given in this paper, use is made of real data on the flat rotation curve of NGC 3198 obtained by Begeman et al (van Albada et al 1985 Astrophys. J. 295 305–13; Begeman 1989 Astron. Astrophys. 223 47–60; Begeman 1987 PhD Thesis University of Groningen http://irs.ub.rug.nl/ppn/291578543), and a fitting of that data to a theoretical model outlined in a previous paper (Bacon and Sharrar 2010 Am. J. Phys. at press). The galaxy is modelled as a thin exponential disc of baryonic matter combined with a spherically symmetric dark matter halo. The bound orbits in the plane of the galaxy are investigated. The computations are carried out using an icon-driven systems-modelling program that avoids the need for extensive programming expertise. The range of orbits investigated includes bound circular orbits and bound closed and open orbits that precess. The bound closed and open orbits are bounded by circles generated by the loci of the apsides of the orbit.
Published Version
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