yes it is possible by very few different ways.
Nothing acting solely from on or within the Earth could change its orbit or seriously alter its rotation.
One way to move an object is to throw mass in the opposite direction, the way jets or rockets do.
If we think really big and imagine blasting a chunk out of the Earth as big as North America and 100 miles thick so that its final speed, after escape, with respect to the Earth is 25,000 miles an hour, we will have expelled only 1/500 of the total mass of the Earth. The Earth would move in the opposite direction 1/500 as fast or 50 miles an hour. The speed of the Earth in its orbit is about 67,000 miles an hour. We will not change the orbit of the Earth very much--if we apply the impulse to speed up the earth in its orbit we would put the Earth into a new orbit with its most distant point about 70,000 miles further from the Sun than now--and the Earth's distance from the Sun varies now by three million miles over the course of a year! Exactly the same arguments apply to changing the orbit of the Earth through the impact of a large asteroid. The largest asteroid, Ceres, about 600 miles in diameter, is only about as massive as our hypothetical chunk of Earth above. Changing the orbit of a planet is a tall order. An impact big enough to have even a tiny effect on the Earth's orbit or rotation would almost certainly destroy all life on Earth as well.
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