The rotational speeds of stars in the disc of a spiral galaxy are virtually independent of the distances of the stars from the centre of the galaxy. In common parlance, the stellar speed versus distance plot known as a galactic rotation curve is by observation typically nearly flat. This observation provides strong evidence that most galactic…

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…

Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced…

The precession rate of the Earth-Moon system by the gravitational influence of the Sun is derived. Attention is focussed on a physically transparent but complete presentation accessible to first- or second-year physics students. Both a shortcut and a full analysis are given, which allows the inclusion of this material as an example of the physics…

The recently observed acceleration of the expansion of the universe is a topic of intense interest. The favoured causes are the "cosmological constant" or "dark energy". The former, which appears in the Einstein equations as the term [lambda]g[subscript [mu]v], provides an extremely simple, well-defined mechanism for the acceleration. However,…

We examine the equant model for the motion of planets, which was the starting point of Kepler's investigations before he modified it because of Mars observations. We show that, up to first order in eccentricity, this model implies for each orbit a velocity, which satisfies Kepler's second law and Hamilton's hodograph, and a centripetal…

According to Poincare, a geometry cannot be an object of experience since any geometrical experiment must be realized with physical objects, such as rulers and light rays, and it is only their properties that can be tested. This position was apparently refuted by general relativity and the successful confirmation of its predictions by astronomical…