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I was doing some reading on the Michelson-Morley Experiment. One of the principle equations for the equations is this one.

$$\frac { 2w }{ c } \times \frac { 1 }{ 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } }$$

Where v is the speed aether wind, c is the speed of light, and w is the distance light travels from point A to point B. The equation is then changed to this one.

$$\frac { 2w }{ c } \left( 1+\frac { { v }^{ 2 } }{ { c }^{ 2 } } \right) $$

The two equations are nearly equal, given the fact that if x is a very small number, 1+x is the same as 1/(1-x). So the second equation is dependent on the fact that the speed of the aether wind is very small compared to the speed of light. My question is: why did Michelson think that the speed of the aether is very slow compared to the speed of light. The text I was reading mentioned something about the timing of the eclipses of Jupiter's satellites, but didn't go into detail.

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  • $\begingroup$ Where is the equation "changed"? $\endgroup$ – HDE 226868 Oct 4 '15 at 0:51
  • $\begingroup$ Sorry, bad way to phrase it. $\endgroup$ – Isaac Liu Oct 4 '15 at 13:13
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If the velocity of the aether wind is a sizeable fraction of c, the apparent velocity of c will depend strongly and obviously on the direction in which the measurement is taken. Since this is not true, the aether wind velocity must be quite small, which requires a sensitive instrument to detect the effects. It was exactly this range of possible wind speeds that the Michelson-Morley was designed to test, and the analysis required to understand the results is what you read.

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  • $\begingroup$ So if the velocity of the aether wind is large, the speed of light would be obviously slower if looked at against the aether wind? Also, do you know what the eclipses of Jupiter's satellites has to do with it? $\endgroup$ – Isaac Liu Oct 4 '15 at 13:17
  • $\begingroup$ 1) Yes. Exactly. And it doesn't happen 2)The variation in the apparent timing of the positions of the moons of Jupiter can be accounted for in terms of distance. But if there is any sort of wind, the timing of those moons will be greatly disturbed by the velocities of the Jupiter system with respect to the earth's, depending on where in the orbit you are, and therefor the orientation of the sight line with respect to the aether wind. With long distances, the effects of relative wind velocities accumulate. $\endgroup$ – WhatRoughBeast Oct 5 '15 at 20:31
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The speed of the earth in its orbit about the sun is about 30 km/s. Michelson assumed that the speed of the earth through the rest frame of the ether was of this order.

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