Upper limit on the amplitude of gravitational waves around 0.1Hz from the Global Positioning System

Abstract

The global positioning system (GPS) is composed of thirty one satellites having atomic clocks with 10 −15 accuracy on board and enables one to calibrate the primary standard for frequency on the ground. Using the fact that oscillators on the ground have been successfully stabilized with high accuracy by receiving radio waves emitted from the GPS satellites, we set a constraint on the strain amplitude of the gravitational wave background hc. We find that the GPS has already placed a meaningful constraint, and the constraint on the continuous component of gravitational waves is given as hc < 4.8 × 10 −12 (1/f ) at 10 −2 f 10 0 Hz, for stabilized oscillators with ∆ν/ν ≃ 10 −12 . Thanks to the advantage of the Doppler tracking method, seismic oscillations do not affect the current constraint. Constraints on hc in the same frequency range from the velocity measurements by the lunar explorers in the Apollo mission are also derived.