The speed of light calculated by Roemer differs significantly from modern data. According to Roemer, light travels a distance equal to the diameter of the earth’s orbit in 22 minutes. If we take the radius of the earth’s orbit, according to the measurements of D. Cassini, equal to 140 million km, then the speed of light will be 212,000 km / s. If we take the modern value of the astronomical unit of 149.6 million km, then the speed of light according to Römer will be: 227,000 km / s.
According to modern concepts, light takes 16 minutes 38 seconds to overcome the diameter of the earth’s orbit, which corresponds to the speed of light 300,000 km / s.
In reference books and textbooks, this discrepancy is usually hushed up. They simply claim that Roemer obtained a value for the speed of light of about 300,000 km / s.
The correct value of the speed of light, obtained by Roemer, can be found in primary sources [1, 2], in Wikipedia, as well as in historical and popular science literature [4, 5, 6, 7]. But in the latter case, paying for an objective presentation of historical facts, the authors of literary sources are forced to somehow explain the significant difference between the result obtained by Roemer (227,000 km / s) and the current generally accepted value of the speed of light in a vacuum, approximately: 300,000 km / s ., which is 32% higher than the value obtained by Roemer.
This difference could be explained by different properties of the medium in which light propagates. But the authors of the mentioned sources [4, 5, 6, 7] adhere to the postulate of the constancy of the speed of light in a vacuum, and therefore, directly or indirectly, explain the discrepancy between the result of Roehmer and the generally accepted value of the speed of light by the gross Roehmer error. Thus, they belittle the significance of Roemer’s discovery and give him priority only in determining the speed of light in order of magnitude.
In favor of the version of Roemer’s gross error, the literature provides information that Roemer did not give the initial data and the calculation formula, from which he received 22 minutes.
In favor of the same version, the opinion is expressed that the first report on the determination of the speed of light [1] was prepared for publication not by Roemer, but by a reporter who allegedly did not understand most of Roemer’s report.
In development of the same topic, it is reported that Huygens, having familiarized himself with Roemer’s discovery, asked Roemer for additional explanations [4]. This is so, but after understanding the problem, Huygens did not further dispute the meaning obtained by Roemer (22 minutes) and used this meaning in his work “Treatise Lumière”.
Newton took an inconsistent position in relation to the result obtained by Roemer. So in the first publication of “Elements” in 1686 he indicated the value of 22 minutes, but in 1704 in “Optics” he gives the value of the speed of light: 1 AU. in 7 or 8 minutes (which corresponds to the speed of light 356,000 – 312,000 km / s).
Roemer reacted with bewilderment to the estimate of the speed of light given by Newton, but due to his busyness he did not find time to prove his case, and in 1710 he died [4].
James Bradley in 1726-28, measuring the apparent deviation of stars from their position on the celestial sphere, found that the distance from the Sun to the Earth, light can travel in 8 minutes 13 seconds, which corresponds to a speed of 304,000 km / s.
In 1809, the astronomer Jean Baptiste Delambre, repeating Roemer’s observations, found that light should travel from the Sun to the Earth in 8 minutes 12 seconds (ie, at a speed of approximately: 304,000 km / s) [4]. This result also, seemingly, speaks in favor of the version of Roehmer’s error, but without familiarizing yourself with the Delambre calculation method in detail, such a conclusion cannot be drawn.
There are other, more recent publications, where calculations of the speed of light are given, allegedly by Röhmer’s method, but in fact distorting this method, in order to obtain values close to 300,000 km / s.
In the literature, you can find two main ways of distorting the Roehmer method. This is a deliberately incorrect calculation of the path traveled by the light, and a deliberately incorrect calculation of time. For typical examples of such calculations, see [Л 8, pp. 381-382], [Л 9]
To date, no specific errors have been found in Roehmer’s method, but there is an opinion that such errors should be.
In order to dispel this preconceived opinion, we will once again consider the Roemer method and independently evaluate the advantages and disadvantages of this method.
- Research results
To get acquainted with Roemer’s method, we present an excerpt from his first communication (1676) [1]. Figure 1 in all essential details corresponds to the figure given in the first report by Roehmer.
“Let A (see Fig. 1) be the Sun, B – Jupiter, C – the first satellite of Jupiter, which enters the shadow of the planet; he leaves it at point D; let, EFGHLK – the position of the Earth at different distances from Jupiter.
Now suppose that from the Earth, located at point L, the first satellite is visible at the moment of its emergence from the shadow at point D; about 42.5 hours later (that is, after one revolution of this satellite) from the Earth located at point K, the satellite is seen returning to point D.
It is clear that if the light takes time to travel the distance LK, the satellite will be seen returning to the point D later than if the Earth was still at point L “
From this it is already clear that Roemer’s calculation was as follows:
- the time of the satellite exit from the shadow Dt was determined;
- the additional path traversed by the light was determined, in the first approximation, this is the chord LK;
- and the speed of light c was determined from the expression: c = LK / Dt (1)
It is also seen from the diagram (Fig. 1) that the speed of light can also be determined on the FG path section, according to the lead time of the eclipse of the satellite.
In order to determine the delay time of the satellite’s exit from the shadow, it is necessary to know the true orbital period of the satellite, which is equal to the orbital period measured during opposition, when the Earth and Jupiter move parallel to each other. Also, the true orbital period is equal to the average satellite orbital period, calculated from the results of observing the satellite in the sections of the Earth’s orbit located symmetrically relative to the opposition line: A-H-B. Unfortunately, Roemer did not give detailed calculations of the true orbital period of Io’s satellite, relative to the shadow of Jupiter, and did not give a calculation of the delay time for leaving the satellite’s shadow after the n-th number of revolutions. Roemer gave only the final result of the lag time: 10 minutes.
The main disadvantage of the diagram shown in Fig. 1 is that it does not reflect the movement of Jupiter during the Earth’s movement from point L to point K and from point F to point G. Meanwhile, the circumferential velocity of Jupiter is approximately 44% of the circumferential the speed of the Earth and therefore it is impossible to neglect the movement of Jupiter. That is, the scheme shown in Figure 1 is not suitable for making accurate calculations. Apparently, Roemer brought this scheme only to clarify the principle of calculation, and when performing calculations he used a more detailed scheme.
3.1. Determination of the speed of light based on the tabular values of the eclipses of the satellite of Jupiter in 1994-95
In order to form an objective opinion about the results obtained by Roemer, we will carry out a full independent calculation of the speed of light by his method, but based on the later tabular values of the eclipses of the satellite of Jupiter in 1994-1995 and using the Stellarium program 0. 13. 3., to determine the distances between Earth and Jupiter.
3.1.1. Determination of the speed of light according to the results of observations, for: 8 and 95, 8 and 94, 9 and 93, 9 and 94, 10 and 93, – by the revolutions of the satellite of Jupiter, when the Earth is moving away and after the corresponding calls in a symmetrical section of the earth’s orbit, when the Earth is approaching with Jupiter.
First, let us determine the speed of light in the section of the Earth’s escape between 8 and 95 revolutions of the satellite of Jupiter Io, and in the section of the approach of the Earth between 0 and 87 eclipses of the satellite of Io, see Fig. 2.
The figure uses the following designations:
A – the sun;
G0, G67 – observation points in the earth’s orbit for the eclipses of the satellite of Jupiter Io: at the point G0 (95 eclipses before the opposition line) and at the point G87 (8 eclipses before the opposition)
K6, K95 – observation points in the earth’s orbit behind the exit from the shadow of the satellite of Jupiter Io: after the 8th revolution and after the 95th revolution, counting from the line of opposition;
C0, C87 – Io’s moon, entering the shadow of Jupiter, 95 and 8 revolutions before the opposition line;
D8, D95 – Jupiter’s moon emerging from the shadow after the 8th revolution and after the 95th revolution, counting from the line of opposition;
D8 K8- the path traversed by the light reflected from the moon of Jupiter, emerging from the shadow, after the 8th revolution, counting from the line of opposition;
D95 K95- the path traversed by the light reflected from the moon of Jupiter, emerging from the shadow after the 95th revolution, counting from the line of opposition;
L8 K95- an additional (measuring) section of the path traversed by the light, due to the movement of the Earth from point K8 to point K95. Equal to the difference between the segments: D95 K8 and D95 K95;
G0F87 – the measuring distance traveled by the Earth towards the light from point G0 to point G87 is equal to the difference between the segments: C0 G0 and C87 G87;
C0 G0 – the path traversed by the light reflected from the satellite of Jupiter, entering the shadow 95 revolutions before the opposition line;
C87 G87 – the path traveled by the light reflected from the moon of Jupiter, entering the shadow 8 revolutions before the opposition line.
At this image scale, Jupiter’s orbit merges with the positions of Jupiter’s moon entering and exiting Jupiter’s shadow.
The angles: A D8 K8 and A D95 K95, as well as the angles: A C87 G87 and A C0 G0, between the direction of Jupiter’s shadow and the rays of light are approximately equal to each other, which provides the same conditions for observing the satellite.
The opposition between Earth and Jupiter took place on June 1, 1995 at 11:00 a.m.
The exit of the satellite of Jupiter from the shadow after the 8th revolution was recorded on 06.16.95 at 11.54 m. At the same time, the distance from the Earth to Jupiter was: 4.352 AU.
The satellite emerged from the shadow of Jupiter after the 95th revolution took place on 17.11.95 at 11.37 m. The distance from the Earth to Jupiter was: 6.166 AU.
Consequently, the additional (measuring) section of the path L8 K95, traversed by the light, due to the removal of the Earth, was: 1.814 AU. (6.166-4.352 = 1.814).
On a symmetrical plot of earth orbit, as the Earth approached the point of opposition, the zero eclipse of Io’s satellite occurred on 12/14/94 at 8:37 am The distance from the Earth to Jupiter was equal to: 6,292 AU.
The 87th eclipse of the satellite Io took place on 05.17.95 at 0739 hours. The distance from Earth to Jupiter was: 4.366 AU.
Consequently, the measuring section of the path G0 F87, traversed by the Earth towards the light, was: 1.926 AU. (6.292-4.366 = 1.926)
More precisely, the measuring section of the path G0 F87, traversed by the Earth towards the light and the measuring section of the path L8 K95, traversed by the light, due to the removal of the Earth, should be determined as the difference in the distances from the Earth to the satellite of Io, and not as the difference in the distances between the Earth and Jupiter. But this simplification of the calculation introduces an error of the second order of smallness, in comparison with the error of the Io satellite eclipse tables. Therefore, such a simplification of the calculation is acceptable.
The arithmetic mean of the measuring sections: G0 F87 and L8 K95 is equal to: 1.87 A.U. (1.926 + 1.814 / 2 = 1.87)
The time of eighty-seven revolutions of the satellite, from the zero to the 87th eclipse, when the Earth approached the point of opposition, was:
153 days 23 hours 2 minutes.
The time of eighty-seven revolutions of the satellite, from the 8th to the 95th revolution, when the Earth moved away from the point of opposition, was:
153 days 23 hours 43 minutes.
The average time of eighty-seven revolutions, in symmetric parts of the Earth’s orbit relative to the opposition line, was:
153 days 23 hours 22.5 minutes
The lead time of the light signal, due to the approach of the Earth, counted from the average value, was: 20.5 minutes.
The delay time of the light signal, due to the escape of the Earth, counted from the average value, was also: 20.5 minutes.
The delay time of the light signal is proportional to the additional (measuring) path traveled by the light. The lead time of the light signal is proportional to the distance traveled by the Earth towards the light. Therefore, the speed of light can be determined quite accurately using the average value of the change in distance due to the distance and approach of the Earth (1.87 AU) and the average value of the delay (advance) of time, (20.5 minutes), without making corrections to the delay time (advancing) the light signal.
The speed of light is determined as a quotient from the division of the average value of the change in distance (average value of the measuring sections): 1.87 AU, by the average delay (advance) of the light signal: 20.5 minutes. Hence, the speed of light is approximately equal to: 227,000 km / s.
In order to reduce the influence of the errors of tables [3] on the calculation results, calculations were carried out for four more pairs of approximately the same measuring sections, followed by averaging the results obtained: L8 K94 and G1 F87, L9K93 and G2 F86, L9 K94 and G1 F86, L10 K93 and G2 F5.
For the first pair of measurement sites, the average distance is 1.859 AU. The delay (advance) time of the light signal is 21 minutes. The speed of light is approximately equal to 221,000 km / s.
For the second pair of measurement sites, the average distance is 1.839 AU. The delay (advance) time of the light signal is 21 minutes. The speed of light is approximately equal to 218,000 km / s.
For the third pair of measurement sites, the average distance is 1.8535 AU. The delay (advance) time of the light signal is 21.5 minutes. The speed of light is approximately equal to 215,000 km / s.
For the fourth pair of measurement sites, the average distance is 1.83 AU. The time delay, advance, light signal is equal to 20.5 minutes. The speed of light is approximately equal to 223,000 km / s.
Similar results are obtained from other points of the orbit.
In total, the article presents the results of 20 verification calculations of the speed of light by the Roehmer method. The average value of the speed of light for 20 verification calculations was: 223 500 km / s 5%. Which is even slightly less than what Römer did (227,000 km / s)
The scatter of the results of single measurements of the speed of light from the average value, in each of the measuring beams, is explained by a significant error in tables [3], where the time of satellite eclipses was counted with an error of 0.5 minutes.
Roemer fixed the eclipse time of the satellite with an accuracy of seconds, therefore the error of Roemer’s calculations is less than the error of calculations carried out according to the tables [3]
Roemer rounded up the result to minutes (22), therefore, he estimated the maximum error of his calculations 0.5 minutes and there is no reason to believe that he incorrectly estimated the error of his calculations.
From the calculations carried out above, it should be concluded that there is no reason to ascribe an error of 32% to Roehmer in order to adjust the results of his calculations to the generally accepted value of the speed of light.
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Literature
1.”«Démonstration touchant le mouvement de la lumière trouvé par M. Römer de l’Académie Royale des Sciences»“, Journal des Sçavans: 233–36, 1676
2.”«A demonstration concerning the motion of light, communicated from Paris, in the Journal des Scavans, and here made English»“, Philosophical Transactions of the Royal Society of London Т. 12: 893–94, 1677
3. Таблицы затмений спутника Юпитера Ио, ROEMER AND THE VELOCITY OF LIGHT Francis BERTHOMIEU “EAAE Summer schools” Working Group GLEA, France /Википедия/измерение скорости света Рёмером.
4.THE HISTORY OF C By Erling Paulsen/Википедия/измерение скорости света Рёмером.
5. С.Р. Филонович «Самая большая скорость» Библиотечка «КВАНТ» выпуск 27, Москва «Наука» 1983 г.
6. «Классики физической науки» Г.М. Голин, С.П. Филонович, Москва «ВШ» 1989
7. Льоцци Марио «История физики» Москва «Мир» 1970 г.
8. Ландсберг Г. С. Оптика. Учеб. Пособие: Для вузов. – 6-е изд., стереот. – М: ФИЗМАТЛИТ, 2003.
9. А. Удалова и А. Акопян «Затмения Ио и скорость света» Сайт http://elementy.ru
Сокращено полный текст Юрий Гужеля
It turns out that the distance scale in space requires correction!