Measurement of gravitational time delay using drag-free spacecraft and an optical clock

Abstract

Improved accuracy in measurement of the gravitational time delay of electromagnetic waves passing by the sun may be achieved with two drag-free spacecraft, one with a stable clock and laser transmitter and one with a high-stability transponder. We consider one spacecraft near the Earth-Sun L1 point with an advanced optical clock, and the transponder on a second satellite, which has a 2 year period orbit and eccentricity e = 0.37. Superior conjunctions will occur at aphelion 1, 3, and 5 years after launch of the second spacecraft. The measurements can be made using carrier phase comparisons on the laser beam that would be sent to the distant spacecraft and then transponded back. Recent development of clocks based on optical transitions in cooled and trapped ions or atoms indicate that a noise spectral amplitude of about 5 × 10⁻¹⁵/ at frequencies down to at least 1 microhertz can be achieved in space-borne clocks. An attractive candidate is a clock based on a single laser-cooled Yb⁺ trapped ion. Both spacecraft can be drag-free at a level of 1×10⁻¹³m/s²/ at frequencies down to at least 1 microhertz. The corresponding requirement for the LISA gravitational wave mission is 3 × 10⁻¹⁵m/s²/ at frequencies down to 10⁻⁴ Hz, and Gravitational Reference Sensors have been developed to meet this goal. They will be tested in the LISA Pathfinder mission, planned by ESA for flight in 2011. The requirements to extend the performance to longer times are mainly thermal. The achievable accuracy for determining the PPN parameter γ is about 1 × 10⁻⁸.