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Io, Rømer* and the Speed of Light (c) Dirk Froebrich * plus Picard, Cassini, Huygens

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* A bit of History * The simple Experiment * A TINY bit of Astrophysics * The nitty-gritty details * How to do it yourself with a TINY bit of Maths

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A bit of Historical Context 1598 Tycho Brahe’s catalogue of stellar positions 1608 Telescope invented by Lippershey 1609 1st & 2nd of Kepler’s Laws published 1610 Moons of Jupiter discovered by Galilei 1619 3rd Law of Kepler 1676 Rømer’s Measurements of c 1687 Newton’s Law of Gravity 1727 Bradley’s Aberration of star light c 1737/65 Harrison ‘solved’ Longitude Problem 1838 Bessel’s Parallax of 61Cyg 1st distance to star 1842 Doppler Effect 1849 Fizeau’s 1st completely terrestrial c-measurement 1861 Maxwell’s Equations 1905 Einstein’s Special Relativity

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Rømer 1676 (calculations by Huygens) The simple Experiment

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The Magnitude System: Hellenistic Practice: brightest stars are 1st magnitude (m=1) faintest stars are 6th magnitude (m=6) Pogson (1856): A 1st magnitude star is 100 times brighter than a 6th magnitude star! The Eye is a negative logarithmic detector.

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Rømer 1676 (calculations by Huygens) The nitty-gritty details

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Io: Period: 1.769137786d Radius: 1821.3km Orbital radius: 421700km Distance: 5.2AU from Sun Magnitude: 5.02mag (at oposition) To measure the speed of light at 3 by predicting the Io eclipse times, one needs to know Io’s period to within 3s!

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How to measure c yourself with a tiny bit of Maths

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Measure Io‘s period when Jupiter is in Quadrature +/- 3weeks 4orbits are one week! L K: P1 = 4 * (P + P) F G: P2 = 4 * (P - P) Period: P = (P1 + P2) / 8 P = (P1 – P2) / 8 If FG = LK = x V E * P = x c * P = x c = (P / P) * V E = 10,000 * V E c = (P / P) * (2 * AU/yr) = 63,200 AU/yr = 299,792,458 m/s MorningEvening P2P1 P- P P+ P

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Io, Rømer* and the Speed of Light (c) Dirk Froebrich * plus Picard, Cassini, Huygens

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