at where . Evaluating the derivative, using our earlier results, and setting , we find which is (to first order) the equation of simple harmonic motion. In other words, nearly circular orbits will exhibit a radial oscillation. However, unlike what happens in Newtonian gravitation, the period of this oscillation will not quite match the orbital period. This will result in slow precession of the periastria (points of closest approach) of our nearly circular orbit, or more vividly, in a slow rotation of the long axis of a quasi-Keplerian nearly elliptical orbit. Specifically, (where we used and removed the subscript from ), whereas The discrepancy is so the periastrion lag per orbit is and to first order in m, the long axis of the nearly elliptical orbit rotates with the rate This can be compared with the corresponding expression for the Schwarzschild vacuum solution in general relativity, which is (to first order in m) Thus, in Nordström's theory, if the nearly elliptical orbit is transversed counterclockwise, the long axis slowly rotates clockwise, whereas in general relativity, it rotates counterclockwise six times faster. In the first case we may speak of a periastrion lag and in the second case, a periastrion advance. In either theory, with more work, we can derive more general expressions, but we shall be satisfied here with treating the special case of nearly circular orbits. For example, according to Nordström's theory, the perihelia of Mercury should lag at a rate of about 7 seconds of arc per century, whereas according to general relativity, the perihelia should advance at a rate of about 43 seconds of arc per century. Light delay Null geodesics in the equatorial plane of our solution satisfy Consider two events on a null geodesic, before and after its point of closest approach to the origin. Let these distances be with . We wish to eliminate , so put (the equation of a straight line in polar coordinates) and differentiate to obtain Thus Plugging this into the line element and solving for dt, we obtain Thus the coordinate time from the first event to the event of closest approach is and likewise Here the elapsed coordinate time expected from Newtonian theory is of course so the relativistic time delay, according to Nordström's theory, is To first order in the small ratios this is just . The corresponding result in general relativity is which depends logarithmically on