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Gravity doesn't travel so it can't be compared to light in that way. It is an interesting thought though.
Gravity depends on weight of the object and distance not on size.
Gravity is a reciprocal attraction between 2 weights. If one of the weight suddently disappear the gravity force between the 2 weight will do the same. It's not like the sun is sending us the force and it take a certain time to reach us, the sun and the heart are both there so there is an attraction force between each other. There's no time of reaction or speed.
Okay, well the only relativity course I have taken was in special relativity, and in the course we always used Einstein's postulate that the speed of light is constant in all reference frames.
How can the force of something be compared to speed? If the sun dissapeared, all the planets would would continue in a line tangent to their orbit at the same speed they were moving at the time the sun went bye bye. They would continue at this speed until something interacted with them, either slowing them down or launching them faster.
You also have to consider that space isn't flat, and if you took the sun away instantly, it wouldn't go back to being flat instantly, kind of like a drop of water in a pond. Maybe if the earth was moving at the perfect speed, it could gain speed using the ripples in space just like constructive waves do to out run the force of gravitation.
Another idea: If nothing can go faster than light, and it takes 8 minutes for light to reach earth, if the sun dissappeared, would it take 8 minutes for it's gravity to reach earth?