A Century of Light-Bending Measurements: Bringing Solar Eclipses into the Classroom
AA Century of Light-Bending Measurements: Bringing SolarEclipses into the Classroom
Emanuele Goldoni a, ∗ , Ledo Stefanini a a Accademia Nazionale Virgiliana, 46100 Mantova, Italy
Abstract
In 1919, Eddington and Dyson led two famous expeditions to measure the bending of lightduring a total solar eclipse. The results of this effort led to the first experimental confirmationof Einstein’s General Relativity and contributed to create its unique and enduring fame.Since then, similar experiments have been carried out all around the world, confirming thepredictions of the General Relativity. Later, developments in radio interferometry provideda more accurate way to measure the gravitation deflection. We believe that - after morethan a century - starlight deflection caused by the Sun’s gravity still represents a simple andintuitive way to introduce high-school students to General Relativity and its effects. To thisaim, we gathered measurements taken during eight eclipses spanning from 1919 to 2017, andwe created a single dataset of homogeneous values. Together with the whole dataset, thisarticle provides a blueprint for a possible group activity for students, useful to introduce thetheory in physics classes with a playful approach.
Keywords:
Physics, Educational, Teaching, Laboratory, General Relativity
1. Introduction
The first decades of the last century saw the emergence of two of the greatest scientificrevolutions: the Theory of Relativity and Quantum Mechanics. The former was the exclusivework of Albert Einstein, while the latter was the joint work of Erwin Schr¨odinger and WernerHeisenberg. These two fundamental theories for our life were born almost simultaneously,but had very different roots. Quantum Mechanics was meant to give rational structure to agreat collection of experimental facts that did not fit in the classical theories of mechanicsand electromagnetism. On the other hand, General Relativity came from a deep need tocollect the space-time stage of physical phenomena in an aesthetic synthesis. Einstein workedon this huge project for about ten years starting from 1906, passing through great hopesand atrocious disappointments, before arriving at a mathematically simple and aestheticallydazzling synthesis of its theory.In 1911 Einstein himself suggested the idea that light could be influenced (and bent) by agravitational field: he calculated that the observed position of a star whose light passed near ∗ Corresponding author: [email protected]
February 5, 2020 a r X i v : . [ phy s i c s . e d - ph ] F e b he Sun’s limb would change by 0 .
87 arcsec. Since 1912, a few expeditions were scheduled toconfirm (or disprove) General Relativity. Luckily for the famous physicist, bad weather andwar prevented the astronomers from making any observations [1]. In 1915, in fact, Einsteinfound that the general Principle of Equivalence needed a modification of the Newtonian lawof gravitation and adjusted his predictions: the correct light displacement value was not thesame as the Newtonian result, but twice as large (1 .
75 arcsec).At the end of the Great War, a new opportunity for an experimental verification ofGeneral Relativity arose: a solar eclipse on May 29, 1919 was going to happen just whenthe Sun would have been in front of unusual bright stars belonging to the Hyades cluster.The English Royal Society, in the person of the astronomer Arthur Eddington, seized theopportunity and arranged two expeditions to take accurate pictures [2].The results, confirming Einstein’s generalized relativity theory, were presented by Ed-dington to the Royal Society of London and made the front page of many worldwide news-papers. Headlines like “Revolution in science: new theory of the universe: Newtonian ideasoverthrown” (Times) and “Lights all askew in the heavens: Einstein’s theory triumphs”(The New York Times) transformed the father of General Relativity into a global celebrity.Although the 1919 experiment had an immediate impact on Einstein’s popularity, theacceptance of his theory by the worldwide scientific community was slower: the high uncer-tainty in Eddington’s measurements and a poor understanding of general relativity amongother scientists at the time fuelled a controversy that surrounded for years the outcome ofthe expeditions.During the 1920s, scepticism about General Relativity theory and its predictions contin-ued until new observations provided much more convincing statistical data, settling (rela-tively) the matter. Optical measurements of light deflection during eclipses continued untilthe 70s, when radio interferometry provided a more accurate way to measure the gravitationdeflection.No more expeditions have been organized after 1973, but in 2017 the amateur astronomerDonald Bruns replicated the eclipse experiment using commercially available equipment andobtaining a result in perfect agreement with Einstein’s predictions. As Burn commented onhis achievement, “
While there is no new science resulting from this experiment, the hopes ofthe 20th century astronomers have been realized ” [3].In November 2019, a series of public lectures organized by the Accademia NazionaleVirgiliana and the local chapter of AIF (Associazione per l’Insegnamento della Fisica) tocelebrate the anniversary of the famous Dyson’s announcement prompted us to gather allthe data taken by astronomers during the years. A careful bibliographic research led us tocollect different sets of measurements, but we had not been able to find a single datasetcontaining all the values. In 1960 H. Von Kl¨uber summarized the results obtained by eclipseexpeditions until 1959 and represented graphically the measures [4]. Unfortunately, hisarticle only includes low-resolution plots and does not to provide the numerical values.Hence, we transcribed all the measurements from the original papers, we harmonized thevalues and we created a single dataset of homogeneous observations. Finally, we decided torelease it publicly, believing it could be useful for teachers.In this article we briefly describe the expeditions which provided the measurements and2e suggest a possible playful activity for students based on our dataset. We hope thatplaying with the same data that Eddington, Dyson, Freundlich and Van Biesbroeck handledin the past could make physics appear less scaring to students and could inspire the nextgeneration of scientists.
2. The Expeditions
Our database includes the measurements collected by astronomers during total eclipsesin 1919, 1922, 1929, 1947, 1952, 1973, and 2017. Three notable expedition are still missingin our project. The results obtained during the eclipse of 21 September 1922 by Campbelland Trumpler, [5] and by Dodwell and Davidson [6] are currently under analysis and will beintegrated in the future. In addition, we have not been able to find the original article byA. Mikhailov on the eclipse in USSR in June 1936.A brief description of the eight considered expeditions will follow: for more details onthe technical equipment used, the methodology applied and the anecdotes of these scientificmissions we suggest to refer to the original articles pointed in the references.We are aware that, quite often, the methodologies used in the original works were laterdisputed by other scientists and new values were derived from the same observation [4]. Inall cases, we preferred to stay with the original measurements.
The first observation of the effect of General Relativity was carried out by British as-tronomers during the eclipse of May 29, 1919 [2, 7]. Two expeditions were organized: ArthurEddington and Edwin Turner Cottingham went to the island of Pr´ıncipe, while the secondteam - formed by Andrew Crommelin and Charles Rundle Davidson - camped in Sobral,Brazil. Both expeditions observed stars belonging to the Hyades cluster in the constellationof Taurus, a region of the sky containing relatively bright stars.On the day of the eclipse, Eddington took 16 plates but he had to face a sky full of clouds,which significantly reduced the quality of the images: when developed, 9 plates showed nosigns of stars, and 4 plates had only faint, diffused marks. Luckily, clouds thinned for awhile during the eclipse an two plates were usable. The analysis of the only five visible starsprovided a deflection of 1 . ± .
30 arcsec.On the side of the Ocean, Sobral was favoured by fine weather and the team captured 19plates with its main instrument, an astrographic telescope, plus 8 pictures using the backupinstrument, a smaller 4-inch lens. However, the images obtained with the main instrumentwere diffused and apparently out of focus: hence, the authors decided to discard them,although they yielded to 0 .
93 arcsec, a deflection very close to the Newtonian (and notEinstein’s) prediction. The second instrument, the 4-inch lens, performed well: its narrowerfield of view provided less stars on its plates, but the quality of images was higher and gavea deflection value of 1 . ± .
16 arcsec. 3 a) The astrograph used in 1929 by the Pots-dam observers. (Photo from [4]) (b) The equipment used by D. Bruns in 2017.(Photo from [3])
Figure 1: Nowadays, Einstein’s theory can be verified with high accuracy using cheaper and smaller equip-ment. It is indeed fascinating how astronomers successfully managed to move tons of fragile material acrossthe world during the first half of the past century.
The Canadian astronomers Clarence Augustus Chant and Reynold Kenneth Young ledan expedition to Wallal, western Australia, to observe the solar eclipse of September 21, 1922[8]. The Canadian party captured two plates during the eclipse, while the night comparisonplates were kindly captured by Campbell and Trumpler, members of the so-called Lickexpedition. On each eclipse plate, 18 stars were used to compute the light displacement: theobtained mean values ranged from 1 .
42 arcsec to 2 .
16 arcsec, depending on the actual starsused for computation. Although the results agreed with the value predicted by Einstein, theaccuracy of measurements was not sufficient to be considered decisive.
In 1929 the Potsdam observatory organized an expedition to Takengon, North Sumatra(now Indonesia) [9]. During the total solar eclipse of May 9, four images of the solarenvironment as well as three control plates were obtained. The astronomers noticed a veryclear deflection of the light near the Sun. However, considering the displacement of 18 stars,they obtained an average value of 2 . ± .
10 arcsec at the Sun edge, which is noticeablylarger than the theoretical value. 4 .2. Matukuma, 1939
The total solar eclipse of June 19, 1936, gave Japanese astronomers an excellent opportu-nity for General Relativity verification. The expedition of the Tohoku Imperial University,led by professor Matukuma of the Astronomical Institute, placed their observations camp atKosimizu, Abasiri [10]. Totality lasted less than two minutes, and during that time only oneplate was taken. Ten stars within the Taurus constellation were recognized on the plate, buttwo of them were near the edges and could not be measured with enough accuracy. Aboutsix months later, two comparison plates (called No. 115 and 119) were taken at Sendai. Theaverage deflection value was 1 ,
71 arcsec. However, measurement from plate 119 were quiteunreliable: the author suggested an error while developing, drying or measuring the controlplate.
In 1947 the Belgian-American astronomer George Van Biesbroeck took part in an expe-dition to Bocajuva, Brazil, to observe the total solar eclipse of May 20 [11]. At the timeof the eclipse, the Sun was located in front of one of the extended dark regions in Taurus.This lead to an unfavourable distribution of the stars: none of them was within less than2.3 solar radii from the Sun’s edge. Moreover, the auxiliary field stars were distorted due tothe heating of the plane-parallel semi-transparent plate in front of the objective. Two plateswere taken in May and two check plates were acquired in August: 51 stars were considered,leading to a mean Einstein of 2 . ± .
27 arcsec.
In 1952 George Van Biesbroeck travelled to Kartoum, Sudan, to make a new test [12] withthe same equipment previously used in Brazil in 1947. On February 25, 1952 the astronomerexposed two plates. Differently from the first attempt, this time the plane-parallel plate waskept well shielded from the Sun and ventilated by an electric fan to insure equal distributionof temperature. Unfortunately, images were affected by the vibrations of the telescope dueto a “ gusty wind ” and many stars that were faintly visible had to be omitted. In total, a firstplate showed 9 well measurable stars in the eclipse field, while a second had 11 measurablestars around the equatorial constellation of Aquarius. Analysing the data, the astronomerobtained a relativity constant equal to 1 . ± .
10 arcsec.
The Department of Astronomy and the Department of Physics of the University of Texasat Austin, in collaboration with the Department of Physics of Princeton University, sent anexpedition to Chinguetti Oasis, Islamic Republic of Mauritania, to observe the Einstein shiftat the total solar eclipse of June 30, 1973 [13, 14]. The eclipse lasted around six minutesand took place in a rich Milky Way field near the Gemini constellation. Three plates wereobtained during the eclipse, while three sets of night-time plates of the same field wereacquired five months later with the identical equipment.All the plates were given to Burton F. Jones at the Royal Greenwich Observatory, whocarried out careful plate reductions. During his analysis, Jones assigned to faint stars a much5ower weight than the bright stars, computing weight as a function of magnitude. Eventually,39 stars were considered and the computed light deflection value was 1 . ± .
18 arcsec
In 2017, Donald G. Bruns measured stars’ deflection during the the August 21, 2017 totalsolar eclipse using high-quality amateur astronomical equipment [3]. A portable refractor,a CCD camera, and a computerized mount were set up in Casper, Wyoming, USA. A totalof 45 images of the sky surrounding the Sun were acquired during totality. Two differenttechniques were used to analyse the data and two calibration fields were used to determinethe plate scales. A total of 20 stars were considered for measuring the deflection value,and the final result was 1 . ± .
060 arcsec - a value in perfect agreement with GeneralRelativity and with the smallest uncertainty ever reported for this kind of experiment.Bruns acknowledges that one of the key improvements that simplified this experimentwas the availability of accurate absolute star positions. Hence, this experiment had lessobstacles; nonetheless, it showed that nowadays Einstein’s theory can be a pleasant learningexperience without facing the costs, the risks and the difficulties encountered in the past bylarge expeditions.
3. Raw and Processed Data
As mentioned above, the aim of our work is the creation of a single, homogeneous datasetof all measurements acquired since 1919 during solar eclipses. The outcome of our efforts isa 170-lines table, structured as shown in Table 1.
Author (Year) Star ID Distance Deflection
Table 1: Excerpt of our dataset: distance and measured deflection are provided for each star.
The first column identifies the year and the main observer who provided the data (seeSection 2 for more information on the expeditions). The second column contains the ID ofthe star: for older catalogues, we converted the references to a more recent catalogue (SAO,Tycho, or Bonner Durchmusterung) and we wrote the identifier in a string compatible bothwith the SIMBAD Astronomical Database [15] and the educational program Stellarium [16].The last two columns contain the distance of the star from Sun - expressed in solar radii -and the measured deflection, expressed in arcsec .6his table contains only one value for each star: when multiple measurements whereavailable for one star, we averaged them to obtain a single value. Combined with thishomogeneous database of measurements, we provide all the original values as separate files.Hence, the raw value are still available for further analysis.We decided to make all data freely available online using the collaborative platformGitHub - this platform is widespread, reliable, and offers a simple way to signal issue andsuggest edits. The whole dataset of measurements is available for download at [17].The dataset is provided in CSV format, so that is can be easily imported by most ofspreadsheet programs, data analysis tools, and programming languages (Figure 2). In ad-dition, a folder for each expedition contains the raw values in CSV format, a brief text doc-ument describing how the data has been processed when adding them to the main dataset,plus a link to the original article. When additional scripts have been used to process themeasurements, we published the source code within the appropriate folder.
Distance from Sun (solar radii) D e f l e c t i on ( a r cs e c ) Einstein L=1.751Bruns (2017)Jones (1972)Biesbroeck (1952)Dyson (1919)
Figure 2: Sample plot combining measurements taken in 1919, 1952, 1972, and 2017 - comparing the resultsobtained during the last century is a matter of minutes when they are all available in single database.
4. Classroom Activity
Here we propose a possible group activity for high-school students. We believe it is veryimportant to be as much general (and anonymous) as possible when presenting the task,in order to keep students unbiased toward the data. We also suggest to create a playfullearning environment, starting the lesson more or less as follows: “Two famous scientists Aand B have proposed two alternative theories for an important astronomical phenomenon.According to A, the actual value should be . ; on the contrary, B’s theory leads to . .The scientific community is split: different teams around the world have been asked to carry ut experiments and gather useful data. Today we have received all the values obtained onthe field. Now we have been asked to analyse them and choose which theory is the right one(or if both are wrong). The world is waiting for us!” Then, each group of students will receive a portion the data coming from an expedition,and they will let be free to analyse the data using the methods and the tools they are morecomfortable with (such as graphical interpolation, spreadsheet, ad-hoc computer programs,etc.). Eventually, after a few days, they will be asked to present their conclusions to theclassroom.We believe that the combination of historical, numerical and team-work factors rep-resents an opportunity both to present General Relativity theory in physics classes in anengaging way and to show how scientists tried during the last century to verify (or disprove)a fundamental theory.
5. Conclusion
More than one hundred years since its first observation, the idea that Sun’s gravitymakes “ lights all askew in the heavens ” is still fascinating. To celebrate the centenary ofthe first observation of gravitational bending for starlight that grazes the Sun, we collecteddozens of measurements taken from 1919 to 2017 in single dataset of homogeneous values.Together with the whole dataset, now freely available on-line, we suggested a playful activityfor high-school students. We would like to extended this work including more activities andexercises: hence, we invite the reader to use the data with young scientists and to provideus feedback and suggestions.
Acknowledgements
We would like to thank Davide Cavalca and Gabriele Marangoni for giving the pa-per a critical reading and for providing several helpful comments. We are also grateful tothe Accademia Nazionale Virgiliana and to the Mantova chapter of AIF (Associazione perl’Insegnamento della Fisica, the Italian association for physics teaching) for their supportand for giving us the opportunity to meet several teachers and to exchange ideas with them.
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