# Why must the speed of the aether wind be so small compared to the speed of light?

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.

• Where is the equation "changed"? – HDE 226868 Oct 4 '15 at 0:51
• Sorry, bad way to phrase it. – Isaac Liu Oct 4 '15 at 13:13