The formula for time dilation in a circular orbit is readily available but the literature seems to indicate it would not be so simple in the case of an elliptical orbit, and no simple formula seems to be available.(adsbygoogle = window.adsbygoogle || []).push({});

Given that time dilation in a circular orbit adds the velocity effect (GM/r) to the gravitational effect (2GM/r)

t = sqrt(1 - (GM/r + 2GM/r)/c²)

t = sqrt(1 - 3GM/rc²)

And given that velocity at perihelion in an elliptical orbit is

vp = sqrt(GM((2/r) - (1/a)))

Can it be deduced that time dilation in an elliptical orbit at perihelion is

t = sqrt(1 - (GM((2/r) - (1/a)) + 2GM/r)/c²)

t = sqrt(1 - (2GM/r - GM/a + 2GM/r)/c²)

t = sqrt(1 - (4GM/r - GM/a)/c²)

t = sqrt(1 - GM((4/r) - (1/a))/c²)

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# Time dilation in an elliptical orbit

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