Orbital mechanics of free-falling bodies for testing the weak equivalence principle in space

Abstract

Various proposed space experiments to test the weak equivalence principle (EP) use ultra-precise differential accelerometers in Earth orbit. A common feature of these accelerometers is that their test masses are physically constrained in some manner, thus imposing a limit on the achievable sensitivity. An alternative approach, analogous to the familiar drop-tower experiments, would be to release the masses inside an orbiting protective cavity, and infer the EP violation from observations of their relative trajectory. This paper addresses the errors inherent to such a scheme, focusing on the orbital mechanics aspects. Quantitative results are presented for a candidate sensing system. It is concluded that the technique is limited by initial condition errors, and will not reach the expected sensitivity of the spaceborne accelerometers.