Doppler search for a gravitational background radiation with two spacecraft

Mathematics – Group Theory

Scientific paper

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Background Radiation, Doppler Effect, Gravitational Wave Antennas, Spacecraft Tracking, Filters, Group Theory, Interplanetary Spacecraft, Legendre Functions, Noise Spectra, Signal Detection, Spectral Energy Distribution

Scientific paper

The prospect of detecting a gravitational wave background by means of a simultaneous Doppler tracking of two spacecraft are discussed. It is found that the cross spectrum of the Doppler shifts of the two spacecraft is a filtered expression of the energy density spectrum of the background. The filter function, which is expressed as a series in terms of Legendre polynomials, is obtained by an integration over the rotation group, assuming the background to be isotropic. The main noise sources are examined, and the advantages of a measurement with two spacecraft are noted.

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