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Relativity: The Special and General Theory

The Galileian System of Co-ordinates
As is well known, the fundamental law of the mechanics of Galilei-Newton, which is
known as the law of inertia, can be stated thus: A body removed sufficiently far from
other bodies continues in a state of rest or of uniform motion in a straight line. This law
not only says something about the motion of the bodies, but it also indicates the
reference-bodies or systems of coordinates, permissible in mechanics, which can be used
in mechanical description. The visible fixed stars are bodies for which the law of inertia
certainly holds to a high degree of approximation. Now if we use a system of co-
ordinates which is rigidly attached to the earth, then, relative to this system, every fixed
star describes a circle of immense radius in the course of an astronomical day, a result
which is opposed to the statement of the law of inertia. So that if we adhere to this law we
must refer these motions only to systems of coordinates relative to which the fixed stars
do not move in a circle. A system of co-ordinates of which the state of motion is such that
the law of inertia holds relative to it is called a " Galileian system of co-ordinates." The
laws of the mechanics of Galflei-Newton can be regarded as valid only for a Galileian
system of co-ordinates.
 
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