User:Cleonis/Sandbox/Apparent motion

The expression apparent motion is used often in physics conversation. Usage of the expression apparent motion is frequently criticized, for if it is meaningful to speak of 'apparent motion' then there must also be a 'true motion', and how is that a meaningful distinction?

The expressions 'apparent motion' and its counterpart 'true motion' can be given unambiguous meaning by relating them to the primary aim of physics: to explain events taking place in terms of one or more of the fundamental interactions of nature: Gravitational interaction, Electromagnetic interaction, weak nuclear interaction, strong nuclear interaction.

Mapping motion in a coordinate system

Apparent retrograde motion of Mars

The left side of the animation shows the motion of the celestical bodies as mapped in an inertial coordinate system that is co-moving with the center of mass of the solar system. The orbits of all the objects are accounted for in terms of gravitational interaction.

The right side of the animation shows the motion of the celestial bodies as mapped in a coordinate system that is itself accelerating with respect to the center of mass of the solar system. In that case 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.

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 for motion with respect 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. There is no physical content to such a conversion.

Definition of apparent motion

This provides an unambiguous definition of 'apparent motion'. When a non-inertial coordinate system is used to map motion, then apparent motion is introduced. The apparent motion is the motion of the non-inertial coordinate system with respect to the inertial coordinate system.

Definition of inertial coordinate system

Newton's three laws of motion provide the means for an operational definition of the concept of inertial coordinate system. A coordinate system is inertial when the following conditions are met:
(1) When no force is exerted, objects move in a straight line, with constant velocity.
(2) In order to change the velocity of an object a force must be exerted. For a given mass the exerted force and resulting acceleration are always in the same proportion.
(3) When two object exert a force on each other, causing them to change theyr velocity with respect to each other, then their common center of mass will remain moving on the same straight line, with the same uniform velocity.

The above operational definition singles out the same equivalence class of coordinate systems as the following definition:
An inertial frame of reference is the frame of reference that is co-moving with the center of mass of a test mass that has been released to free motion.