test particles moving in the equatorial plane, and shows that the period of a nearly circular orbit (as observed by a distant observer) will be same as for the Schwarzschild vacuum. Third, with for timelike, null, spacelike geodesics, we find where is a kind of effective potential. In the timelike case, we see from this that there exist stable circular orbits at , which agrees perfectly with Newtonian theory (if we ignore the fact that now the angular but not the radial distance interpretation of r agrees with flat space notions). In contrast, in the Schwarzschild vacuum we have to first order in m the expression . In a sense, the extra term here results from the nonlinearity of the vacuum Einstein field equation. Static observers It makes sense to ask how much force is required to hold a test particle with a given mass over the massive object which we assume is the source of this static spherically symmetric gravitational field. To find out, we need only adopt the simple frame field Then, the acceleration of the world line of our test particle is simply Thus, the particle must maintain radially outward to maintain its position, with a magnitude given by the familiar Newtonian expression (but again we must bear in mind that the radial coordinate here cannot quite be identified with a flat space radial coordinate). Put in other words, this is the "gravitational acceleration" measured by a static observer who uses a rocket engine to maintain his position. In contrast, to second order in m, in the Schwarzschild vacuum the magnitude of the radially outward acceleration of a static observer is m r−2 + m^2 r−3; here too, the second term expresses the fact that Einstein gravity is slightly stronger "at corresponding points" than Nordström gravity. The tidal tensor measured by a static observer is where we take . The first term agrees with the corresponding solution in the Newtonian theory of gravitation and the one in general relativity. The second term shows that the tidal forces are a bit stronger in Nordström gravity than in Einstein gravity. Extra-Newtonian precession of periastria In our discussion of the geodesic equations, we showed that in the equatorial coordinate plane we have where for a timelike geodesic. Differentiating with respect to proper time s, we obtain Dividing both sides by gives We found earlier that the minimum of V occurs