The history of a velocity

By Erling Poulsen

In Einstein’s article from 1905 ”Annalen der Physik” where he publish the special theory of relativity, the velocity of light was given an important role in nature never before seen. Today this number is an important natural constant, and even in our daily life we use it, it defines the meter.

Ole Rømer has often been accredited to have found this number as the first, but that is not quite right, he never published a number, he rather found that light is retarded, it is not coming with indefinite velocity.

In the late 1600 most scientists believed in Descartes’ theory for light where the velocity is indefinite. In Paris where Rømer arrived in 1672 he was involved in many experiments and investigations, what is important here is his measuring of the velocity of sound. He cooperated with Cassini and there he learned about his examinations of the eclipses of the moons of Jupiter.  Earlier he and Picard had used such eclipses to find the difference in longitude between Paris and Tycho Brahes’ Uraniborg (1671). Some irregularities in the time and the eclipses caught his attention and he started his own observations of the planet.
The irregularities were explained in different ways but the big breakthrough came in 1676 where he found that the irregularities only depended on the changing distance between Jupiter and Earth. Cassini gave that explanation to the French academy in august. In the beginning of September Rømer told the academy, that founded on his observation of an eclipse in August a coming eclipse November 9. would be 10 minutes late compared with Cassini’s ephemerides. Observations of the November 9. eclipse confirmed Rømers prediction and on the 21. He had a lecture in the academy about it. That lecture was published in "Journal des Sçavans" December 7. in an article which was written by someone who had not understood much of the lecture (See "Ole Rømer og den bevægede Jord - en dansk førsteplads" of Jan Teuber in the book "Ole Rømer - videnskabsmand og samfundstjener", Gads Forlag 2004, p. 213).

Interesting in the article is his prediction of the 10 minutes, in those days it was possible to calculate the distance between the planets using Kepler’s laws, it means that the distances could be calculated in astronomical units (AU, the mean distance between the Earth and the Sun), but the length of one AU was not known precisely. In the lecture he mentions that his calculation is founded on observations in august from that month we know of three on the 7th, 14th & the 23rd. We do not know what observation he used to predict the eclipse on November 9. (5:35:45 pm calculated not regarding the light retardation). From Rømer’s notes we know that it was seen 5:45:35 pm close to the 10 minutes late he had predicted. If we use the program WinStars 2 to find the relevant distances between Jupiter and Earth we get:

November 9 - 5,526 AU
August 7 - 4,254 AU difference compared to November 9 1,272 AU
August 14 - 4,316 AU difference compared to November 9 1,210 AU
August 23 - 4,408 AU difference compared to November 9 1,118 AU

And if these differences were used to predict the 10 minutes delay he must have used a value of the time it would take light to travel 1 AU of

7,9 min/AU if the observation August 7. was used
8,3 min/AU if the observation August 14. was used
8,9 min/AU if the observation August 23. was used

Values much closer to the accepted 8.3 minutes we use today. Rømer is often said to have announced 22 minutes for 2 AU (Earth orbit diameter) in his lecture, but he was not. The section in "Journal des Sçavans" where you find the number 22 can be interpreted in the following way: He remarks that for a couple of orbital periods of Jupiter’s innermost big moon Io the difference is very small but if you consider many orbital periods the effect is greater. If you look on 40 revolutions from one side of the Earth orbit (F) and compare with 40 revolutions from the other side (K) then you get a great difference which compares to the number 22. This could be understood as the earth moves as far during 80 revolutions of Io as light does in 22 minutes. An orbit of Io takes 42,5 hour, that gives 141,67 days for 80 revolutions, in that period the Earth moves 2*¶*141,67/365,25 AU = 2,436 AU, and if that distance should take light 22 minutes to travel he must have used 9,0 min./AU, a result close to that above.

Now 7 month went on with discussions between Rømer and Cassini who could not accept his explanation. July 25. 1677 Rømer’s explanation is published in "Philosophical Transactions". In Holland is Huygen’s working on his theory of light and in that he needs a velocity for light therefore he writes to Rømer asking for more information but Rømer writes back that he have no time to explain.

Then in 1678 Huygen’s presents his "Traité de Lumière" for the French academy and he uses the 22 minutes for 2 AU.

In 1686 Newton publish “Principia” where he uses 22 minutes.

1690 Huygen’s publish "Traité de Lumière"

1704 Newton publish “Optics” where he uses 8 minutes for 1 AU. Rømer has in his notebook "Adversaria" a remark from 1706 (page 4 in Kirstine Meyers edition, 1910), where he wonders over Newtons number.

1710 Rømer dies

1713 Newton publish “Principia” 2. edition where he uses the 8 minutes.