
Rømer
and the Doppler Principle. The
velocity of light.
Erling Poulsen
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While Rømer lived
in Paris, he was timing the eclipse of Io, the innermost big
moon of Jupiter, by the shadow of the planet.
He discovered that the period between eclipses was changing,
it was a Doppler shift.
For wave functions, which propagates
with a velocity c, we have the following equations :
λ * ν=c and ν=1/T
where λ is the wavelength, ν the frequency and T the
period From these equations follows:
λ =T*c The well known
Doppler equation :
R/c=Δλ / λ Can be transformed
to :
R/c=ΔT/T Here, R is the radial velocity
between the Earth and Jupiter, T is the period between
eclipses, and ΔT is the increase or decrease in T.
If we use this version of the Doppler equation and insert the
maximum radial velocity between the Earth and Jupiter, we get
:
ΔT = 15 sec. If we integrate ΔT from one
conjunction between the Earth and Jupiter to the following
opposition, we get an accumulated Doppler shift in the period
of 16.7 minutes, near the value found by Rømer in 1676 (published
in Journal des Sçavans 1676)
COMPUTATION OF THE SPEED OF
LIGHT Rømer never did compute the speed of light,
maybe because he felt that the distance between the Earth and
the Sun was not known too well. However, there is a value in
"Adversaria" (his notebook, Royal library,
Copenhagen, fol. α^{b}, he writes: 1091 earthdiameter per minute).
1676 (september). He announces his explanation of the Io
eclipses in a lecture in Academie des Sciences. He was first
supported but later criticized by Casini, who found
difficulties in observing the same effect with the other 3
moons of Jupiter.
He announces that a eclipse on nov. 9.
will be delayed 10 minutes^{*)}. 1676 nov.
9. The eclipse is delayed. 1676 nov.
21. He reads a paper for the Academie des Sciences
about the confirmation of the theory. 1676 (december). Rømer's explanation
is published in
Journal des Sçavans
in an article not written by himself and with some
misunderstandings
(See
"Ole Rømer og den bevægede Jord  en dansk førsteplads" by
Jan Teuber in the book "Ole Rømer  videnskabsmand og samfundstjener", Gads Forlag 2004,
Copenhagen, p. 213). 1677 july 25. London, in
Philosophical
Transactions, vol XII,no. 136, Rømer's discovery is
mentioned. In the 7 months between Sçavans and Philosophical,
there was nearly nothing about the discovery.
1677 sept. 16. Huygens in Holland
reads Rømer's paper in Philosophical, and he immediately
sends a letter to Rømer asking for more information. From the
article he understands that light travells one
earthorbitdiameter in 22 minutes. 1678. Huygens presents his "Traite
de lumiere" for Academie des Scienses. In that, he uses
the diameter of earth's orbit and Rømer's value for the
light's delay in travelling over the orbits diameter to
calculate the speed of light (he was the first to present the
velosity with terrestrial units, 16^{2}/_{3}
earthdiam./sec.).
1679. Rømer mentions a eclipse
of the moon in the letter above.
1680. In London, Hooke criticizes Rømer,
as he maintains that light travels instantaneously. His
argument goes as follows:
'tis so exceeding swift that 'tis
beyond Imagination; for so far he thinks indubitable, that
it moves a Space equal to the Diameter of the Earth, or near
8000 miles, in less than one single Second of the time,
which is in as short time as one can well pronounce 1, 2, 3,
4: And if so, why not be as well instantaneous I know no
reason....
1686. In the first edition of Newtons
"Principia", he uses the 22 min. 1690. "Traite de Lumiere"
by Huygens is printed in Paris.
1692. In his papers, "Adversaria"
fol. 17, Rømer makes use of the light to determine the
distance to the stars (founded on Tychos starpositions, he
found the parallax to be less than 3,5'). He sets the distance
to more than eight lightdays.
1704. "Optics" by Newton is
published. Here he says that it takes only 8 minutes for the
light to pass from the Sun to the Earth. Maybe
Newton himself has computed the 8 minutes from "Sçavans"
instead of using the 22 minutes he used earlier. 1706. Rømer writes in a remark in
"Adversaria" (his notebook, Royal library,
Copenhagen, fol. y^{a}) that Newton uses 8 min.
for the EarthSun distance, as if he had not seen it before.
1713. In the second edition of
"Principia", Newton again uses the 8 minutes.
1842. Doppler explains the Doppler
effect.
1849. The French scientists Fizeau og
Foucault measure the velocity of light with an instrument
placed on the Earth. Fizeau informs the French Academy July
23'th, 1849.
^{*)} From observations in
august 1676 he calculates that a mooneclipse november 9th
must be delayed 10 minutes. From august we know of three
observations the 7^{th}, 14^{th} and 23^{rd}.
It was possible to calculate the relative distances in the
solar system by help of the Kepler Laws. If we use the
software WinStars 2 to find the EarthJupiter distances on
the relevant dates we get:
nov. 9^{th}  5,526 AU
aug. 7^{th}  4,254 AU, difference to
9/11 1,272 AU
aug. 14^{th}  4,316 AU, difference to 9/11 1,210 AU
aug. 23^{rd}  4,408 AU, difference to 9/11 1,118 AU
and if these differences should give a 10 minutes delay he
must have used a value of the time for light to travel one
AU of:
7,9 min/AU if the calculation was founded on the observation
of aug. 7^{th}
8,3 min/AU if the calculation was founded on the observation
of aug. 14^{th}
8,9 min/AU if the calculation was founded on the observation
of aug. 23^{rd}
values much closer to what is accepted to day compared with
the 11 minutes (22 min. for 2 AU) which should appear in the
atticle in "Sçavans", but does not.
The part of the article where you find the 22 could be
interpreted in the following way:
He tells that for a couple of revolutions of Io the effect
is very small, but if you compare 40 revolutions from one
side with 40 from the other side the effect is considerable
and that in proportion to 22.
This could be understood as the Earth moves just as long in the time of the 80 revolutions of Io
as light moves in 22 minutes. The time for the 80
revolutions are 42,5 hours x 80 = 141,67 days, in that
period earth moves 2*¶*141,67/365.25 AU = 2,436 AU, and if
it takes
light 22 minutes to travel that distance the velosity must
be 9 min./AU, close to the value above.
