We construct time independent configurations of two gravitating elastic bodies. These configurations either correspond to the two bodies moving in a circular orbit around their center of mass or strictly static configurations.

4 Classical perturbation theory 4 4.1 The classical theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4.2 The precession of the perihelion of Mercury . . . . . . . . . . . . . . . . . . . . 6 4.2.1 Delaunay action–angle variables . . . . . . . . . . . . . . . . . . . . . . 6 4.2.2 The restricted, planar, circular, three–body problem . . . . . . . . . . . 7 4.2.3 Expansi...

(1) irii'ii = -gradiU(ql9 ..., qn), i = 1, ..., n, where gradf denotes the gradient with respect to q(. Thoughout this paper we use a single dot over a variable to represent its derivative with respect to time t and a double dot to represent its second derivative with respect to t. The potential energy U has a singularity whenever q(=q^ We write this singular set ^v = {€€(«?: *, = *,}, A = U Au...

Einstein’s general theory of relativity establishes equality between matter–energy density and the curvature of spacetime. As a result, light and matter follow natural paths in the inherent spacetime and may experience bending and trapping in a specific region of space. So far, the interaction of light and matter with curved spacetime has been predominantly studied theoretically and through ast...