User:Cleonis/Sandbox/Coordinate accelleration

Apparent retrograde motion of Mars

If the orbits of the planets and all the other objects in the solar system are mapped in an inertial coordinate system that is co-moving with the center of mass of the solar system, then the orbits of all the objects can be accounted for in terms of gravitational interaction.

On the other hand, if the orbits of the planets are mapped in a coordinate system that is itself accelerating with respect to the center of mass of the solar system, then the motion with respect to that coordinate system is accounted for in terms of gravitational interaction, plus the coordinate acceleration that is involved. The coordinate acceleration is the acceleration of the non-inertial coordinate system with respect to the inertial coordinate system.

In the animation the representation on the right shows the motions of Sun, Mars and Earth with respect to a coordinate system that is co-moving with the Earth.

A general property of coordinate transformation is that under coordinate tranformation from one euclidean coordinate system to another everything is preserved. All relative positions are preserved, all relative velocities are preserved, all relative accelerations are preserved.

In transforming laws of motion to a non-inertial coordinate system, the laws of motion are not changed. All that is changed in coordinate transformation is notation of the laws of motion. Transforming laws of motion to a non-inertial coordinate system is comparable to transforming notation of length from meters to centimeters. Such a transformation is a transformation of notation, there is no physical content to it.