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

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Presentation transcript:

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

* 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

A bit of Historical Context 1598 Tycho Brahe’s catalogue of stellar positions 1608 Telescope invented by Lippershey st & 2nd of Kepler’s Laws published 1610 Moons of Jupiter discovered by Galilei rd 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

Rømer 1676 (calculations by Huygens) The simple Experiment

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.

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

Io: Period: d Radius: km Orbital radius: km 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!

How to measure c yourself with a tiny bit of Maths

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

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