Io, Rømer* and theSpeed 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 yourselfwith a TINY bit of Maths

A bit of Historical Context

1598 Tycho Brahe’s catalogue of stellar positions1608 Telescope invented by Lippershey1609 1st & 2nd of Kepler’s Laws published1610 Moons of Jupiter discovered by Galilei1619 3rd Law of Kepler

1676 Rømer’s Measurements of c1687 Newton’s Law of Gravity

1727 Bradley’s Aberration of star light c1737/65 Harrison ‘solved’ Longitude Problem

1838 Bessel’s Parallax of 61Cyg 1st distance to star1842 Doppler Effect1849 Fizeau’s 1st completely terrestrial c-measurement1861 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: 1.769137786dRadius: 1821.3kmOrbital radius: 421700kmDistance: 5.2AU from SunMagnitude: 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 = xVE * P = xc * P = x

c = (P / P) * VE = 10,000 * VE

c = (P / P) * (2 * AU/yr) = 63,200 AU/yr = 299,792,458 m/s

MorningEvening

P2P1

P-PP+P

Io, Rømer* and theSpeed of Light (c)

Dirk Froebrich

* plus Picard, Cassini, Huygens