  Newtonian gravity and general relativity give exactly the same expression for
the period of an object in circular orbit around a static central mass.
However, when the effects of the curvature of spacetime and solar radiation
pressure are considered simultaneously for a solar sail propelled satellite,
there is a deviation from Kepler's third law. It is shown that solar radiation
pressure affects the period of this satellite in two ways: by effectively
decreasing the solar mass, thereby increasing the period, and by enhancing the
effects of other phenomena, rendering some of them detectable. In particular,
we consider deviations from Keplerian orbits due to spacetime curvature, frame
dragging from the rotation of the sun, the oblateness of the sun, a possible
net electric charge of the sun, and a very small positive cosmological
constant.
