The real question should be: what is the speed of gravitational change propagation? This might be a little confusing at first, but this answer will help to make sense of the topic.
Other questions that arise
Since this question is quite a big one to ask, there are also some other questions that it uncovers alongside it. As we know, the earth is orbiting the sun, meaning that it is held in the sun’s gravity. If the sun were to disappear out of existence right this second, so would its light and gravity.
The earth would not be the same, or survive, without either of these. Our seasons and temperate conditions rely on the sun’s light, warmth and the way that we orbit around it. So, the sun has disappeared a second ago… when would we feel the difference on earth? When would we fall out of orbit?
When would the earth go dark? Which would come first?
How do we answer these?
In order to answer all of these new questions and, therefore, the main question at hand, we have to first answer how fast gravity is. As stated above, the question should be about the speed of gravitational change propagation. Or even the speed of gravitational waves.
Gravitational waves
The theory of General Relativity, coined by Einstein, suggests that gravitational waves travel at the same speed as light when in a vacuum. But this is not a surprising thing, since all particles and waves that are massless will also travel at the speed of light.
The same does not apply to objects with mass, since other factors will affect their speed. We use the phrase ‘speed of light’ as a generally accepted phrase, but it can be quite misleading since other waves and massless particles will travel at that speed too.
But what about the earth! The sun has just disappeared!
Going back to our hypothetical alternate solar system where the sun has suddenly ceased to exist… what would happen to it? Since we now know that gravitational waves travel the same speed of light, we can work out that the last light from the sun would take 8 minutes and around 19 seconds to reach earth before going dark.
This means that the last ‘wave’ of gravitational pull, or the sun’s last gravitational effects would also take that long to reach earth. So, our sky would not go dark (in the areas where it was daytime) until 8 minutes and 19 seconds after the sun disappeared.
The earth, with nothing to orbit, would likely carry on with its sideways trajectory and float away into space, away from its usual orbit path. But humans and life on earth would not last long without the warmth and light of the sun. So much of our daily life revolves around these two things.
How do we know that the speed of gravity is the same as the speed of light?
Just same way that we ‘know’ anything else in science: experimentation. Since this is a theoretical prediction, there needed to be experiments carried out for it to be believed. And the speed of gravity being the same as the speed of light has been confirmed experimentally by scientists.
Realistically, all things in science are theoretical until proven or confirmed by experimentation. But since it has been confirmed in a vacuum setting, we can confidently say that the speed of gravity is the same as the speed of light which is 299,792,458 m/s.
And that, although it is called the speed of light, all massless particles and waves (gravity included) will also travel at that speed in a vacuum.