1. Binary Stars v c - v c + v v Apparent motion as seen from Earth
Observed  speed of light independent of emitter
Expected if speed of light depends on emitter

2. Stellar Aberration c c c v v v v v

3. Michelson-Morley Experiment
Mirror 1
(M1)
P1 (BS – M1 – BS):
(perpendicular motion) L
c1' =  c² – Ve²
Mirror 2
(M2)
t1 = 2L / (c² – Ve²)1/2 = 2L/c /(1 – Ve²/c²)1/2
P2 (BS – M2 – BS):
Beam
splitter
(BS)
Light source
(LS)
c2' = c – Ve; c2,r' = c + Ve
(paralle motion) L
t2 = L/(c + Ve) + L/(c – Ve) = 2Lc / (c² – Ve²)
= 2L/c / (1 – Ve²/c²)
Telescope
(T)
Approximation: S
Ether frame V S'
Earth frame
1/(1 – x²) = (1 – x²)/(1 – x²) + x²/(1 – x²) = 1 + x² + x4 + …
 1 + x² (for x << 1)
1/(1 – x²)1/2 = (1/(1 – x²))1/2 = (1 + x² + x4/4 + 3x4/4 + …)1/2
 1 + x²/2 (for x << 1)
Time difference: Dt = t2 – t1 = 2L/c (1 + Ve²/c² – (1 + Ve²/c²/2)) = LVe²/c³
Corresponding path length: Dd = c Dt
Turn setup by 90° changes role of P1 and P2, doubling the effective difference in path length
Experimental parameters: L =11 m,V= 3×104 m/s, l = 500 nm = 5×10-7 m, c = 3×108 m/s  2Dd = 0.4l
Sensitivity of M&M (1887): 2 Dd = 0.01l

4. Binary Stars Michelson/Morley Stellar Aberration v c - v
 Speed of light independent of emitter
c + v
Stellar Aberration
Michelson/Morley
 No relative motion between Earth and ether
 Earth not at rest with respect to ether