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Astrophysics, Earth and Planetary Astrophysics, astro-ph.EP,General Relativity and Quantum Cosmology, gr-qc, Physics, Atomic Physics, physics.atom-ph, Physics, Geophysics, physics.geo-ph
Abstract:
The successful miniaturization of extremely accurate atomic clocks invites
prospects for satellite missions to perform precise timing experiments. This
will allow effects predicted by general relativity to be detected in Earth's
gravitational field. In this paper we introduce a convenient formalism for
studying these effects, and compute the fractional timing differences generated
by them for the orbit of a satellite capable of accurate time transfer to a
terrestrial receiving station on Earth, as proposed by planned missions. We
find that (1) Schwarzschild perturbations would be measurable through their
effects both on the orbit and on the signal propagation, (2) frame-dragging of
the orbit would be readily measurable, and (3) in optimistic scenarios, the
spin-squared metric effects may be measurable for the first time ever. Our
estimates suggest that a clock with a fractional timing inaccuracy of
$10^{-16}$ on a highly eccentric Earth orbit will measure all these effects,
while for a low Earth circular orbit like that of the Atomic Clock Ensemble in
Space Mission, detection will be more challenging.
