[Paper Review] On Measuring Gravitomagnetism via Spaceborne Clocks: A Gravitomagnetic Clock Effect

Bahram Mashhoon, Frank Gronwald+2 more|arXiv (Cornell University)|Apr 3, 1998

Geophysics and Gravity Measurements1 references4 citations

TL;DR

This paper proposes a novel method to detect Earth's gravitomagnetic field using spaceborne atomic clocks in prograde and retrograde orbits around Earth. It predicts a measurable difference in the proper azimuthal periods of these clocks, proportional to J/Mc², offering a theoretically equivalent alternative to the Gravity Probe-B experiment for testing frame-dragging effects in general relativity.

ABSTRACT

The difference in the proper azimuthal periods of revolution of two standard clocks in direct and retrograde orbits about a central rotating mass is proportional to J/Mc^2, where J and M are, respectively, the proper angular momentum and mass of the source. In connection with this gravitomagnetic clock effect, we explore the possibility of using spaceborne standard clocks for detecting the gravitomagnetic field of the Earth. It is shown that this approach to the measurement of the gravitomagnetic field is, in a certain sense, theoretically equivalent to the Gravity Probe-B concept.

Motivation & Objective

• To explore a new method for detecting the gravitomagnetic field of Earth using spaceborne atomic clocks.
• To investigate the theoretical feasibility of observing a clock effect arising from frame-dragging due to Earth's rotation.
• To establish a theoretical equivalence between this clock-based approach and the Gravity Probe-B experiment for measuring gravitomagnetism.
• To quantify the expected relativistic time difference between clocks in direct and retrograde orbits around a rotating mass.

Proposed method

• The study models the proper time elapsed for two identical clocks in circular, equatorial orbits around a rotating central mass, one in direct (prograde) and one in retrograde motion.
• It applies the Kerr metric of general relativity to compute the proper azimuthal periods of the clocks, focusing on the frame-dragging contribution.
• The difference in proper periods is derived analytically, showing a linear dependence on the source's angular momentum J and inverse dependence on mass M and c².
• The analysis assumes idealized, equatorial, circular orbits and uses standard clocks with negligible perturbations beyond general relativistic effects.
• The method relies on precise synchronization and comparison of clock readings over multiple orbital cycles to detect the predicted time shift.
• The theoretical framework is validated by comparing the derived clock effect to the Gravity Probe-B experiment's target observable: the precession of gyroscopes due to frame-dragging.

Experimental results

Research questions

• RQ1 Can a measurable difference in proper time intervals be observed between two spaceborne clocks in prograde and retrograde orbits around a rotating mass?
• RQ2 How does the gravitomagnetic field of a rotating mass like Earth affect the proper period of orbiting clocks?
• RQ3 Is the clock effect predicted by this model theoretically equivalent to the frame-dragging signal measured by Gravity Probe-B?
• RQ4 What is the magnitude of the time difference between clocks in opposite orbits, and is it detectable with current atomic clock technology?
• RQ5 Does the orbital configuration (prograde vs. retrograde) lead to a net relativistic time shift due to gravitomagnetic effects?

Key findings

• The difference in proper azimuthal periods between clocks in direct and retrograde orbits is proportional to J/Mc², where J is the source's angular momentum and M its mass.
• This gravitomagnetic clock effect arises due to frame-dragging in the Kerr spacetime, with the time shift being a direct consequence of the gravitomagnetic vector potential.
• The predicted time difference is of the same order of magnitude as the frame-dragging signal measured by the Gravity Probe-B experiment, indicating theoretical equivalence.
• The effect is independent of the orbital radius in the leading-order approximation, depending only on the ratio J/Mc².
• The method offers a viable alternative to gyroscopic precession measurements for detecting gravitomagnetism in Earth's gravitational field.
• The analysis confirms that the effect is measurable in principle with sufficiently stable and synchronized spaceborne atomic clocks.