An approximate formula for the gravitational vector potential is given by Mashhoon 2008:
(Vj)≈GJJ×rrr3
where G is the gravitational constant, JJ the rotational momentum of the Earth, and rr=(x,y,z) (there's an additional c factor in Mashhoon's formula, but that's included in the c3 factor in the original question).
Using the values G≈6.67⋅1011m3/(kgs2), c=299792458m/s, J≈7⋅1033kgm2/s (0,0,1), and taking a point roughly on the equator with x=R,y=0,z=0, where R≈6.38⋅106m is Earth's radius, we obtain
1c3(Vj)≈(0, 4⋅10−16, 0)1c3(Vixj)ij≈[0−7⋅10−230−1⋅10−2200000] m−1
The formula given in Mashhoon is valid "far from the source", so not valid for a point at the equator. But the estimates above should give a rough initial idea.
This post imported from StackExchange Physics at 2025-01-21 21:50 (UTC), posted by SE-user pglpm