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A moving clock runs more slowly than an equivalent clock at rest. Notice that at everyday speeds, in which V/c is typically less than 10-6, (and therefore (V/c)2 is less than 10-12, an unimaginably small number), ∆t and ∆t′ are essentially the same. Einstein’s result then reduces to the classical result of Newton. However, in Modern Physics, involving microscopic particles that have measured speeds approaching that of light, values of γ > 1000 are often encountered. The equations of Newtonian Physics, and the philosophical basis of the equations, are then fundamentally wrong.
All inertial observers, in an infinite number of frames of reference, would come to the same conclusion. We see, therefore, that Aristotle's conjecture is not consistent with this fundamental Principle. 2 Newton’s laws of motion During his early twenties, Newton postulated three laws of motion that form the basis of Classical Dynamics. He used them to solve a wide variety 32 of problems, including the motion of the planets. They play a fundamental part in his famous Theory of Gravitation. The laws of motion were first published in the Prlncipia in l687; they are: 1.
This means that v0 ≥ √(2GM/R). 52 Escape is possible only when the initial velocity is greater than (2GM/R)1/2 . On the Earth, v0 ≥ 25,000 miles/hour. For a star of given mass M, the escape velocity increases as its radius decreases. Michell considered the case in which the escape velocity v0 reaches a value c, the speed of light. In this limit, the radius becomes RLIMIT = 2GM/c2 He argued that light would not be able to escape from a compact star of mass M with a radius less than RLIMIT ; the star would become invisible.