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No best answer has yet been selected by Brugel. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.Not really with an object as massive as the sun the effect the Earth has is negligable. It does cause a "wobble" however and it's one of the ways that planet spotters detect planets around other stars.
Ok imagine you are in the garden and you swing a small child around. Now the child does cause you to wobble a bit but you wouldn't say you are orbiting the child now repace the child with say a ping pong ball. Although the ball is exerting a tiny force on you it's not noticable. The sun and the earth are in similar proportion mass wise to you and the ping pong ball ie no noticable effect so to answer you question, no.
It makes a difference if you try to calculate the planet's movements.
Most of the time, you will want to be in an inertial frame of reference to make your calculations.
Neither earth nor sun 's frames of reference are strictly inertial, but the sun's frame of reference is a better approximation because it doesnt wobble as much as earth's. So it will give more accurate results.