The article examines the effects of coordinate systems on time dilation experienced by clocks on the surfaces of the Earth and Moon. It asserts that the fractional differences in clock rates are invariant across three models: a center-of-mass locally inertial frame, a rotating system aligned with the Earth-Moon axis, and a translated rotating system with the Earth at the origin. The findings assume a Keplerian orbit and highlight the role of centrifugal forces and gravitational potentials in these calculations.
In various coordinate systems analyzing the Moon and Earth's relationship, the fractional difference in clock rates remains constant, despite differing frames of reference.
Comparing the results in both rotating and non-rotating systems reveals a consistency in the outcomes, affirming theoretical predictions and simplifying complex gravitational interactions.
The derived expressions for proper time intervals on the Moon and Earth underscore the influence of centrifugal potential and other factors on time dilation.
This study relied on a Keplerian orbit assumption for the Earth-Moon system, enabling focused calculations on the surface clock comparisons.
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