### Re: If motion is relative, why is solar system considered heliocentric?

Date: Thu Jan 5 15:39:02 2006
Posted By: Bryan Dunne, Instructor, Astronomy, University of Illinois
Area of science: Astronomy
ID: 1134098816.As
Message:

The idea that "all motion is relative" is a slight misunderstanding of Einstein's Special Theory of Relativity. Special relativity tells us that observers in uniform motion relative to one another (i.e., no changes of speed or direction of motion), cannot perform any experiment to determine which one of them is "really moving." So, if your car were traveling at a constant speed in a constant direction relative to a tree, neither you nor a person in the tree could do an experiment that would definitely say who is moving.

However, this rule doesn't apply when the direction or speed of relative motion is changing. If the speed and/or direction of motion of an object is changing, it is said to be accelerating. This is different than the common usage of acceleration which only implies an upward change in speed.

Acceleration is not relative, becuase acceleration implies the presence of a force. Newton's Second Law tells us that the acceleration of an object is equal to the force applied divided by the mass of the object (a=F/m). In the case of driving past a tree, lets say you want to stop to look at the tree. You press the brake pedal; then a friction force is applied by your brakes, causing a negative acceleration to your car, stopping it. It would be ludricrous to consider the brakes of your car changing the motion of the entire Earth, the force applied by the brakes would only cause a undetectably miniscule acceleration on something as massive as the Earth. The acceleration is applied to your car; it is not relative.

Now, lets consider how this applies to the planets. The planets travel around the Sun on roughly (but not perfectly) circular orbits. That means they are always changing their direction of motion, so they are always accelerating! So, we can't simply assign the Earth a stationary role in the center of the solar system, because its motion is undergoing accelerations, and accelerations are not relative. The Sun is placed at the center of the solar system because it holds 99.85% of the solar system's mass and the motions of the planets are due to the accelerations they experience from the force of the Sun's gravity.

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