A Novel Two-Step Laser Ranging Technique for a Precision Test of the Theory of Gravity

Abstract

All powered spacecraft experience residual systematic acceleration due to anisotropy of the thermal radiation pressure and fuel leakage. The residual acceleration limits the accuracy of any test of gravity that relies on the precise determination of the spacecraft trajectory. We describe a novel two-step laser ranging technique, which largely eliminates the effects of non-gravity acceleration sources and enables celestial mechanics checks with unprecedented precision. A passive proof mass is released from the mother spacecraft on a solar system exploration mission. Retro-reflectors attached to the proof mass allow its relative position to the spacecraft to be determined using optical ranging techniques. Meanwhile, the position of the spacecraft relative to the Earth is determined by ranging with a laser transponder. The vector sum of the two is the position, relative to the Earth, of the proof mass, the measurement of which is not affected by the residual accelerations of the mother spacecraft. We also describe the mission concept of the Dark Matter Explorers (DMX), which will demonstrate this technology and will use it to test the hypothesis that dark matter congregates around the sun. This hypothesis implies a small apparent deviation from the inverse square law of gravity, which can be detected by a sensitive experiment. We expect to achieve an acceleration resolution of $\sim 10^{-14} m/s^2$. DMX will also be sensitive to acceleration towards the galactic center, which has a value of $\sim 10^{-10} m/s^2$. Since dark matter dominates the galactic acceleration, DMX can also test whether dark matter obeys the equivalence principle to a level of 100 ppm by ranging to several proof masses of different composition from the mother spacecraft.