# Binary Stars v c - v c + v v Apparent motion as seen from Earth

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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

Stellar Aberration c c c v v v v v

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

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

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