5 research outputs found
On detecting the gravitomagnetic field of the earth by means of orbiting clocks
Based on the recent finding that the difference in proper time of two clocks
in prograde and retrograde equatorial orbits about the Earth is of the order
10^{-7}s per revolution, the possibility of detecting the terrestrial
gravitomagnetic field by means of clocks carried by satellites is discussed. A
mission taking advantage of this influence of the rotating Earth on the proper
time is outlined and the conceptual difficulties are briefly examined.Comment: Talk given at the 32nd COSPAR Scientific Assembly, held at Nagoya,
Japan, 12-19 July 1998, 4 pages LATE
An alternative derivation of the gravitomagnetic clock effect
The possibility of detecting the gravitomagnetic clock effect using
artificial Earth satellites provides the incentive to develop a more intuitive
approach to its derivation. We first consider two test electric charges moving
on the same circular orbit but in opposite directions in orthogonal electric
and magnetic fields and show that the particles take different times in
describing a full orbit. The expression for the time difference is completely
analogous to that of the general relativistic gravitomagnetic clock effect in
the weak-field and slow-motion approximation. The latter is obtained by
considering the gravitomagnetic force as a small classical non-central
perturbation of the main central Newtonian monopole force. A general expression
for the clock effect is given for a spherical orbit with an arbitrary
inclination angle. This formula differs from the result of the general
relativistic calculations by terms of order c^{-4}.Comment: LaTex2e, 11 pages, 1 figure, IOP macros. Submitted to Classical and
Quantum Gravit
On the Possibility of Measuring the Gravitomagnetic Clock Effect in an Earth Space-Based Experiment
In this paper the effect of the post-Newtonian gravitomagnetic force on the
mean longitudes of a pair of counter-rotating Earth artificial satellites
following almost identical circular equatorial orbits is investigated. The
possibility of measuring it is examined. The observable is the difference of
the times required to in passing from 0 to 2 for both senses of
motion. Such gravitomagnetic time shift, which is independent of the orbital
parameters of the satellites, amounts to 5 s for Earth; it is
cumulative and should be measured after a sufficiently high number of
revolutions. The major limiting factors are the unavoidable imperfect
cancellation of the Keplerian periods, which yields a constraint of 10
cm in knowing the difference between the semimajor axes of the satellites,
and the difference of the inclinations of the orbital planes which, for
, should be less than . A pair of spacecrafts
endowed with a sophisticated intersatellite tracking apparatus and drag-free
control down to 10 cm s Hz level might allow to meet
the stringent requirements posed by such a mission.Comment: LaTex2e, 22 pages, no tables, 1 figure, 38 references. Final version
accepted for publication in Classical and Quantum Gravit
Spinning test particles and clock effect in Schwarzschild spacetime
We study the behaviour of spinning test particles in the Schwarzschild
spacetime. Using Mathisson-Papapetrou equations of motion we confine our
attention to spatially circular orbits and search for observable effects which
could eventually discriminate among the standard supplementary conditions
namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the
world line chosen for the multipole reduction and whose unit tangent we denote
as is a circular orbit then also the generalized momentum of the
spinning test particle is tangent to a circular orbit even though and
are not parallel four-vectors. These orbits are shown to exist because the spin
induced tidal forces provide the required acceleration no matter what
supplementary condition we select. Of course, in the limit of a small spin the
particle's orbit is close of being a circular geodesic and the (small)
deviation of the angular velocities from the geodesic values can be of an
arbitrary sign, corresponding to the possible spin-up and spin-down alignment
to the z-axis. When two spinning particles orbit around a gravitating source in
opposite directions, they make one loop with respect to a given static observer
with different arrival times. This difference is termed clock effect. We find
that a nonzero gravitomagnetic clock effect appears for oppositely orbiting
both spin-up or spin-down particles even in the Schwarzschild spacetime. This
allows us to establish a formal analogy with the case of (spin-less) geodesics
on the equatorial plane of the Kerr spacetime. This result can be verified
experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum
gravity, 200