Authors: Brian Coleman
Eastward and westward orbiting plane time dilation formulae envisaged for Hafele&Keating’s 1971 equatorial clocks experiment were incorrectly derived in the 2004 textbook Relativity in Rotating Frames although exact analytic expressions actually result directly from velocity composition—provided gravitational effects are disregarded. Nevertheless the same idealised equations together yield the classic formula for Sagnac’s analogous 1913 experiment where interference fringe patterns from monochromatic light waves emitted in opposite directions around a rotating wheel, shifted in accordance with rotation rate—an observation misinterpreted by some as challenging special relativity theory. Although only approximately correct for the 1971 experiment, the resulting formulae also yield—independently of general relativity theory—a notable exact formula for a rotating satellite’s clock dilation. The factor’s inverse equals the versed sine of the angle whose sine equals the satellite’s peripheral speed scaled for unit limit speed—the cubic root of the product of the Earth’s mass, the universal gravitational constant and the orbit’s rate of rotation.
Comments: 8 Pages. Equation (9) typo remedying
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