Spacecraft Doppler tracking as a xylophone detector of gravitational radiation

We discuss spacecraft Doppler tracking for detecting gravitational waves in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. By using the four-link radio system first proposed by Vessot and Levine, we derive a new method for removing from the combined data the frequency fluctuations due to the Earth troposphere, ionosphere, and mechanical vibrations of the antenna on the ground. This method also reduces the frequency fluctuations of the clock on board the spacecraft by several orders of magnitude at selected Fourier components. The nonzero gravitational wave signal remaining at these frequencies makes this Doppler tracking technique the equivalent of a xylophone detector of gravitational radiation. In the assumption of calibrating the frequency fluctuations induced by the interplanetary plasma, a strain sensitivity equal to 4.7×${10}^{-18\mathrm{}}$ at ${10}^{-3\mathrm{}}$ Hz is estimated. Experiments of this kind could be performed (at minimal additional cost) with future interplanetary missions by adding instrumentation to the spacecraft payload and the ground station.