Mars seasonal polar caps as a test of the equivalence principle

The seasonal polar caps of Mars can be used to test the equivalence principle in general relativity. The north and south caps, which are composed of carbon dioxide, wax and wane with the seasons. If the ratio of the inertial (passive) to gravitational (active) masses of the caps differs from the same ratio for the rest of Mars, then the equivalence principle fails, Newton’s third law fails, and the caps will pull Mars one way and then the other with a force aligned with the planet’s spin axis. This leads to a secular change in Mars’s along-track position in its orbit about the Sun, and to a secular change in the orbit’s semimajor axis. The caps are a poor Eötvös test of the equivalence principle, being 4 orders-of-magnitude weaker than laboratory tests and 7 orders-of-magnitude weaker than that found by lunar laser ranging; the reason is the small mass of the caps compared to Mars as a whole. The principal virtue of using Mars is that the caps contain carbon, an element not normally considered in such experiments. The Earth with its seasonal snow cover can also be used for a similar test.

Figure 1

Schematic of the Mars equivalence principle test. Mars orbits the Sun. Mars’s spin axis is shown as lying in the orbital plane for the purposes of illustration. The polar caps (white) wax and wane with insolation. When one cap is larger than the other, there is a self-force (thick arrows) if the equivalence principle fails. The planet self-accelerates, leading to a secular change in the size of the orbit. For the case shown above the orbit shrinks. If the thick arrows pointed the other way, the orbit would expand.