“Instant” is not a concept that makes sense with relativity. One observer’s “instant” is another observer’s “back in time.” I’m not totally sure why this doesn

“Instant” is not a concept that makes sense with relativity. One observer’s “instant” is another observer’s “back in time.” I’m not totally sure why this doesn’t result in spiraling into the sun as you describe, but I think it’s because the sun’s gravitational field is basically constant, and it’s changes which propagate at the speed of light.