Download Römer and the speed of light

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
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
The simple Experiment
Rømer 1676
(calculations by Huygens)
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.
The nitty-gritty details
Rømer 1676
(calculations by Huygens)
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 3s 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 + DP)
F  G: P2 = 4 * (P - DP)
Period: P = (P1 + P2) / 8
DP = (P1 – P2) / 8
Evening
Morning
P1
P2
If FG = LK = Dx
VE * P = Dx
c * DP = Dx
c = (P / DP) * VE = 10,000 * VE
c = (P / DP) * (2p * AU/yr)
= 63,200 AU/yr
= 299,792,458 m/s
P+DP
P-DP
Io, Rømer* and the
Speed of Light (c)
Dirk Froebrich
* plus Picard, Cassini, Huygens