A satellite travels in a geodesic by the sun with sufficient velocity to escape the sun's orbit. The distance of closest approach is 100 light seconds when the satellite's velocity is perpendicular to the sun as observed by light. At this point in time, t = 0, the satellite will compare 2 observations: the direction from the satellite to the center of the sun's light with the direction from the satellite to the perceived force of gravity from the sun. Are they perfectly aligned or is there any difference, even if very small? Want to isolate how the sunlight might be affected by the sun's gravitational field versus how propagation of the sun's gravitational field might be affected by the field itself.
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1$\begingroup$ The Earth is attracted to the instantaneous position of the Sun located 8 minutes or 4 Sun's diameters ahead of its observed position in the sky: arxiv.org/abs/gr-qc/9909087v2 $\endgroup$– safesphereCommented May 13, 2021 at 4:21
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$\begingroup$ Safesphere: Your answer precisely addressed my question -- would have credited the answer if yours was not just a comment. It is interesting that the consensus of answers from physics.stackexchange.com/questions/633187/… seem to suggest that gravitational fields are limited by the speed of light in some cases. Reading link (thank you) provided and its references to understand better... $\endgroup$– Clay HoldsworthCommented May 17, 2021 at 2:54
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Answer from Safesphere's link: https://arxiv.org/abs/gr-qc/9909087v2, "Does eqn. (2.4) imply that gravity propagates instantaneously? ...it clearly does not...Indeed, the vector (2.5) does not point toward the “instantaneous” position of the source, but only toward its position extrapolated from this retarded data...Indeed, it can be rigorously proven that no gravitational influence in general relativity can travel faster than the speed of light"
This resolves how celestial objects are attracted to the instantaneous position of other celestial objects by gravity (i.e. not delayed by propagation at c), but also how massive objects outside our light event horizon are also outside our gravitational event horizon. (See correctly answered Can gravity from a massive object outside our cosmological event horizon have any effect on Earth?) Thank you, Safesphere, for the excellent resource.