Picture of the sun taken from Earth
Photo courtesy of Alora Manley
The theory of relativity puts an absolute upper limit on the speed with which any information can travel. This is the speed of light, about 186 thousand miles per second. The sun is about 93 million miles away, so light takes about 500 seconds, or a little over 8 minutes, to travel from the sun to the Earth. When you look at the sun (carefully, because it’s very bright) you are seeing it as it was eight minutes ago.
So any sudden change in the sun will not be able to affect the position of the Earth for eight minutes. After that, the amount by which the Earth’s position is affected will depend on what exactly is happening with the sun.