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Introduction

In the European culture Venus was named after the ancient Roman goddess of love & beauty. It influenced the whole European culture. One of the most famous painting all over the world is Botticelli ’s The Birth of Venus.We often call it the jewel of the sky and it is also known as the morning or evening star. In the Aztec civilization a god called Tlahuizcalpantecuhtli symbolizes Venus. The name means something like the "Lord of the House of Dawn". This god also represent a feathered serpent, Quetzalcoatl . Another great South-American ancient empire, the Mayans paid tribute to Venus as the planet of warfare. That is why some big battles were named after the actual position of the planet. The Mayan astronomers knew that in every   2920 days Venus reaches the same position with the Sun. The Mayans also calculated the synodic period of Venus, it was 594 days. Now we know that its 583.92 days. Extremely precise!

To observe the Venus we must search it in the sky at dawn or at nightfall. As it is situated between the Earth and the Sun, the distance of Earth and Venus varies between 259-240 million kms, so the sizeof the planet changes between 10”-64”. The magnitude is also changing, when it is the brightest then it is -4,6 mag! So it is brighter than the Sirius . Sometimes, when the Earth and the Venus are close some eagle-eyed people can see the Venus not only as a spot. It can reach the definition of the human eye, its bigger than 1'. Other planets’ diameter is always smaller than this. The Venus has got phases like the Mercury and the Moon. The reason is that the position of the Sun, the Earth, and the planet is always changing and we can see different parts illuminated (Figure   2). Sometimes we can observe something like a 3/4 phase on Mars, but not on the other planets. It’s because they are very-very far from us. We look at them from nearly the same direction   where the light comes. In 1672 Giovanni Domenico Cassini observed that the Venus has got a moon. He named Neith after the   goddess of Sais, whose veil no mortal was allowed to rise. Some observations continued until 1892, but these observations were discredited. The „moon” must have been a faint star, and now we know that Venus is moonless.

Figure 2: How the phases arise

We cannot see the surface of the Venus, so it was impossible to say something about the rotary period of the planet on the basis of visual observation. Until 1964 guesses were between 22 hours and 225 days. A very large scale! To measure the clouds with Doppler-effect failed (the clouds and the rotary has a different speed). Like in the case of Mercury only   radio measurements were succesful. They were mainly done at Puerto Rico. It shows, that the planet turns around its axis in about every 243 days. The planet has got a retrograd movement, so it turns „backward”. Only Pluto and Uranus have retrograde rotation, too. It means that on the Venus the   Sun rises on the west and sets down on the East! Scientists don’t know why some planets hava got a retrogad movement, but it is probably the result of a collision with a very large asteroid far in the past. Others say this explanation are not confirmed by the facts.   

               We have the suspicion that the Venus has got an atmosphere for a long time. It’s easy to observe it when it covers a star; it’s fading first for a time and than it vanishes. We can see the star at the Moon and than at the next moment it disappears. And also there are same strange phenomena. We can easily explain them if we assume there is an atmosphere. There is something strange when the phase of Venus appears slightly concave; then the Sun-Earth-Venus geometry indicates that it should be exactly half illuminated. This phenomenon was first explained by a German amateur astronomer Johann Schroeter in 1793. That's what we call it Schroeter's effect. This is because of the light that refracts and get absorbed in the atmosphere. The sulphuric acid droplets by solar radiation results in an atmospheric profile 'inflated' on the day-side of the planet. So near the terminator will contribute towards the observed phase. When the Venus is thin (small phase), at the Polar regions it can have a little "horn". This is also because of the atmosphere.

Until the middle of the 20th century the Venus was known as the sister of Earth, because:

-Young surface on both planet

- They have approximately the same size and mass: if the Earth equals 1, then the   diameter of the Venus is 0.95 and the mass is 0.8

- Their chemical composition and density are nearly the same.

By the help of modern space research we know that these are the only similarities. There were also speculations about the chance of Venusian life. The famous astronomer, Carl Sagan thought there was a chance of primitive creatures exist in the upper clouds. We did know nearly anything about the real Venus until the 1960's. It was very hard to detect anything, because the atmosphere covers everything. We even don’t know the general properties of the planet (its chemcial composition, the surface, the temperature etc). The keys to unlock the Venus’ secrects were the Space Crafts. They went there, took measurements on the location and transmitted them to us authoritative information, that’s why they are very important. The first 2 Venera missions were unsuccessful, but the Venera-3 was the first craft of mankind which reached the atmosphere of another planet! The next Venera missions all succeeded, they took measurements and transmitted datas, the Venera-9 & -10 took photographs from the landing place, too!

The Transit of Venus

The Venus passes directly between the Sun and the Earth, that’s the Venus Transit. We can see it as a dark disk on the Sun. With a „sun-protector” glass we can see the planet with the naked eye. It is very similar to the phenomenon of the Moon passing by the Sun, but the Venus is many more hundred million kilometers away, so it looks very small .

The Venus Transits are rare, the pattern repeats in every 243 years. One pattern contains of 4 transits, with pairs of two transits 8 years apart, separated but long pauses of 121,5 and 105,5 years. This is because at the beginning of the patterns the two planets have return to the same position on their orbit. And 243 sidereal orbital period* of Earth is 88757,3 days and 395 sidereal orbital period of Venus is 88756,9 days. Also the orbit of the Venus is inclined by   3,4° to that of the Earth. So the Venus usually passes over or below the Sun (Figure 9).   But every year Earth crosses the plane of Venus orbit within a few days of 7th June   and   8th December. And also there is no guarantee, when it happens the Venus will be between the Sun and the Earth. They have to be on the „same side of the Solar System”. That is why a Transit is always close to these dates .

Figure 3: When the Transit happens

The phenomenon was extremely interesting, because 19th century astronomers used it to calculate the AU (Astronomical Unit), the distance between Sun and Earth.   Now it has not got any scientific importance. The astronomers have always wanted to know how far it is the Sun from the Earth. This was one of the central problems in astronomy until the 18th century. Aristarchus of Samos , during 3rd century BC, estimated that the Sun is 20 times further from the Earth than the Moon. Tycho Brahe and Copernicus calculated with approximately 8 million kms (1210 Earth radius), then Johannes Kepler realized that if the AU was that small Tycho should observe the geocentric parallax of the Mars, but actually he didn’t. This fact suggested that the AU is minimum 3 times bigger, ~ 24 million kms. Then telescopes meant a big leap and Edmund Halley (1656-1742) guessed in 1716 it was 111 million kms. After Kepler’s law became known astronomers had the data of the planet’s distances ratio, but did not know the standard AU, so they were unable to calibrate the scale. Johannes Kepler was the first to predict a Venus Transit. It happened in 1631. But there was no one to observe it in Europe, it was visible only in America, and nobody checked it out there. Still, in 1631 Pierre Gassendi observed the Transit of Mercury, also predicted by Kepler. He (Kepler) calculated another Venus Transit for 1761, so he said the period was about 130 years.

Finally the first Venus Transit observation was done on 4th December 1639 by Jeremiah Horrocks (1617-1641), later he published his results in a book entitled Venus in Sole Visa in 1661. More than half century later, in 1716 Edmond Halley (on the left) was the one who suggested using the phenomena for calculating the AU. He published the mathematical process and also the data needed for calculation. The only problem was that Halley knew that at the next transits (1761 & 1769) he would be dead for a long time. Here is a little part of Halley’s publication, A new Method of determining the Parallax of the Sun, or his Distance from the Earth :

    „ While I was making my observations about 40 years ago in the island of St. Helena on the stars round the south pole, I happened to observe, with the utmost care, Mercury passing over the Sun's disk: and contrary to expectation, I very accurately obtained, with a good 24-foot telescope, the very moment in which Mercury, entering the sun's limb, seemed to touch it internally, as also that of his going off; forming an angle of internal contact. Hence I discovered the precise quantity of time the whole body of Mercury had then appeared within the sun's disk, and that without an error of one single second of time; for, the thread of solar light, intercepted between the obscure limb of the planet, and the bright limb of the sun, though exceedingly slender, affected my sight, and in the twinkling of an eye, both the indenture made on the sun's limb by Mercury entering into it, vanished, and that made by his going off, appeared. On observing this I immediately concluded, that the Sun's parallax might be duly determined by such observations, if Mercury, being nearer the Earth, had a greater parallax, when seen from the Sun; for, this difference of parallaxes is so very inconsiderable, as to be always less than the Sun's parallax, which is sought; consequently, though Mercury is to be frequently seen within the Sun's disk; he will scarcely be fit for the present purpose. There remains therefore Venus's transit over the Sun's disk, whose parallax, being almost 4 times greater than that of the Sun, will cause very sensible differences between the times in which Venus shall seem to pass over the sun's disk in different parts of our earth. From these differences, duly observed, the sun's parallax may be determined, even to a small part of a second of time; and that without any other instruments than telescopes and good common clocks, and without any other qualifications in the observer than fidelity and diligence, with a little skill in astronomy. For we need not be scrupulous in finding the latitude of the place, or in accurately determining the hours with respect to the meridian; it is sufficient, if the times be reckoned by clocks, truly corrected according to the revolutions of the heavens, from the total ingress of Venus on the Sun's disk, to the beginning of her egress from it, when her opaque globe begins to touch the bright limb of the Sun; which times, as I found by experience, may be observed even to a single second of time .”

The Observation of Jeremiah Horrocks at 4th December 1639

We do not know exactly when he was born, but somewhere between January and July 1618, in a little village, Toxeth Park, near Liverpool. It was believed that his father, James Horrocks,  was a farmer, but actually he was a watchmaker. His mother`s name was Mary Aspinwall. He learned astronomy and mathematics at the Cambridge University. He read every book written by the greatest scientists like Kepler, Tycho Brahe and Gellibrand. When he finished university in 1635 and returned to his hometown, he was 17 years old. He did not graduate, but it was not unusual then, a lot of students had for example financial problems. At Toxeth he meditated on the problems of the planets` movement. He had some cheap instruments, but he also made some for himself. He measured the Venus and he found that it was 10 times bigger than Kepler had thought, and Horrocks was right! He also measured the size of the Moon, and as he had made it for years he found that it is not a constant value ! So for the first time he suggested that the Moon’s orbital around earth is not a circle, but an ellipse. He also observed the Venus and noticed that there were errors in the predicted orbit of the existing astronomical tables.   But his most memorable discovery happened on 4th December, 1639. Kepler did not predict this transit, but Horrocks thought that he had been wrong. Kepler failed to discover that the transits have an 8 year pairing, because he calculated with the Earth being a spot, not an extended ball so Kepler had left it for Horrocks. From his observations he calculated that it would happen on 24th November, around 3 pm at Much Hoole, where he was a curate. He made a card with an 6 inch circle and he rated it for 360 degrees. He directed his telescope to the Sun and waited for a little black point. Around 3:15 pm he beheld that spot. The spot`s diameter was about 30 times smaller than that of the Sun. He watched the movement of the planet for 30 minutes, but then the Sun disappeared under the horizon. He wrote the following about his observations :

    “ I carefully watched it on 24th from sunrise to nine o’clock, and from a little before ten until noon, and also at one in the afternoon, being called away in the intervals by business of the highest importance which, for these ornamental pursuits, I could not with propriety neglect. But during all this time I saw nothing in the Sun except a small and common spot… This evidently had nothing to do with Venus. About fifteen minutes past three in the afternoon, when I was again at liberty to continue my labors, the clouds, as if by divine interposition, were entirely dispersed, and I was once more invited to the grateful task of repeating my observations. I then beheld a most agreeable spectacle, the object of my sanguine wishes, a spot of unusual magnitude and of a perfectly circular shape, which had already fully centered upon the Sun’s disc on the left, so that the limbs of the Sun and Venus precisely coincided, forming an angle of contact. Not doubting that this was really the shadow of the planet, I immediately applied myself sedulously to observe it .”

His friend William Crabtree also observed the 30 minute transit, but no other observers were noticed. With his little information he guessed the distance between the Sun & the Earth. He got to 9 4951296 kms. It is not so accurate now, but at that time this was the most accurate estimate. He published his results in the book Venus in Sole Visa ( see the frontpage at left), in 1661. The next step to the correct value was the next transit in 1761 more than a century later! Because of his interest in Horrocks’ work, Dr John Wallis collected and edited the astronomer’s works, and published them in 1672 under the title: Jeremaie Horrocci Liverpoliensis Angli ex Palinate Lancastiae Opera Posthuma , it is the most detailed authenticity .

 

The Transit of 6th June, 1761 & 9th Dec, 1769

At Horrocks time, Halley did not publish his new ideas about the calculation of the AU (it only happend in 1716). But since then, a new generation of astronomers had picked up the challange, and waited for the big chance of 1761 & 1769. Travelling was still a big problem, astronomers had to carry heavy   equipments on long voyages whose duration was not rarely more than one year. Halley’s technique resulted another problem: it needed highly accurate coordinants from the place of the observation. It meant more instruments and more time to take the necessary measurements. But everybody wanted to find out the correct figure of AU. So big observing plans were born all over Europe. The most interesting brainchild of a journey was to get around the world: from North-America across Siberia to India .

Some authors said there were 176 scientists watching the Transit at more than 117 different places!** It was an international project, it was like space programs in modern times: a few brave adventurers/astronomers were supported by the military and the goverment(s) and with plenty of money. It is important to note here, that most of the astronomers were French and English, and in 1761 there was a war between these two country: the Seven Year War. So each observer was given a permission to pass behind the enemy lines. The greatest project was organised by   French Joseph-Nicolas Delisle , who set up an observation network with 62 stations! He also founded a school of astronomy at St. Petersbourg in Russia at request of Peter Czar the Great . For his memory there is crater called Delisle on the Moon.

               Inspite of the huge number of observers the project was unsuccesful. Scientists were simply not prepared for it, they did not know what they had expected to happen. Probably the most influencisl phenomea were the refraction of the atmosphere and the mysterius Black Drop effect . But Mikhail V. Lomonosov , the Russian astronomer, discovered the very bright edge of the Venus. Other astronomers had expected a completely dark dish. Lomonosov noticed that the phenomenon means that the planet has an atmosphere !

               But the most unlucky of all the scientists was the French Le Gentil who travelled to India, but during the first transit he was still on the sea (he wanted to dock at Pondicherry, but the English amry had occupied it 4 months before). He was adamant on this point. He decided to wait there for the next transit, that is for another 8 years. First he stayed at Mauritius, and studied the territory’s botany, zoology, geology, antrophology etc. Then he left for Manila (a Spanish area) in May, 1766, but the local governer, Don Jose Raon , did not like him, so he left again. In February 1768 he finally arrived at Pondicherry where he started to build an observatory. Everything went fine, and finally the day of the Transit had come! With some clouds actually ... Because of the weather he was not able to observe the phenomenon after travelling more than 70,000 miles, and spending more than 9 years abroad. He wrote in his journal :

    " I was more than two weeks in a singular dejection and almost did not have the courage to take up my pen to continue my journal; and several times it fell from my hands, when the moment came to report to France the fate of my operations ."

After all he finally arrived in France on 8th October, 1771 that is after 11years, 6 months, 13 days. Rumors of his death had spread, so the Academy gave his chair to someone else, and his family looted his estate .

 

The Black Drop effect

    The Black Drop effect means that the Venus appears to be stuck to the line of the Sun. Something similar to a „small bridge” appears between the two circles and it takes much-much harder affects to allocate the exact moment of the contacts (see the Cook erxpedition's famous drawing). It appears only at the interior contacts, at the 1st & the 4th contact when the phenomenon gets lost in the black background. Halley believed that advanced astronomers would be able to estimate the contact within 1 second, but he was false. The agitating atmosphere (dust, convection mainly) and the black Drop brings the accuracy back to within 30-40 seconds. Today the Black drop does not influence accuracy so much: now we have got much better telescopes than in the 18th century .

               What causes the Black Drop? A theory says that it is result of the atmosphere of the Venus, but that is not true because we can see this effect at the Mercury Transit, too, while the Mercury does not have an atmosphere! In 2001 Bradley Schaefer re-analaysed the question and he got to the conclusion that the Black Drop is mainly the effect of seeing. The diffraction and refraction effects are very small. It was easy to check the theory at the Transit of Mercury on 15 th November, 1999. We should not forget that this planet has no atmosphere, and it was observed with the TRACE (a space craft which has got a 30cm diameterd telescope) , so there could not have been atmosphere effects. Now, if the Black Drop is not only caused by seeing   it must still be visible from the space with less intensity. Glenn Schneider and his colleages completed the analysis. You can see the pictures in Figure 11. We can see the Black Drop unequivocally but wanly. So atmosphere is not necessarily responsible for the effect but its influence is dramatic . The biggest non-atmospherical effect is the darker edge of the Sun. It makes the Mercury’s lighting asymmetrical. Scientists have calculated the diffraction effects, too, but they found their influence is much smaller. So it is a natural effect which is hitched up by the atmosphere. Of course, the quality of the telescope can hitch the influence, too .

               The next Venus Transit occured on 3rd June, 1769. And the international science research continued. By this time the Seven Year War had ended, so it was safe to travel. Again there were a lot of observers, mainly the same astronomers who made the observations in 1761, naturally, there came some new ambitious scientists to join. Because of the few places their observations were carried out I want only to write in details about the expedition of Maximilian Hell & Captain Cook , because it was their observartions that finally led to the exact AU calculation .

The story of Captain James Cook

He set sail from Plymouth in 1768. His mission was to circumnavigate the globe and explore the Southern Pacific Islands. The scientist Joseph Bank and the astronomer Charles Green were also on deck of the ship, H.M.S. Endeavor . After more than 7 months sailing, they dropped anchor in Matavia Bay, at the isand of Tahiti (the natives called the island Otahete). It was the third European vessel on the island, and it had a warm welcome by the aborigines. Actually the sailors were especially interested in the local women. They had not seen women for more than 7 months! And the native women were very pretty. They liked iron nails, they could use it for a lot of things. So aboriginal womens maked love for iron nails. And the Endeavor was a wodden ship, so it was held together with iron nails. And slowly the nails from the ship started to disappear. It had only been 2 years before that the H.M.S. Dolphin (with Captain Samuel Wallis on board) nearly fell apart because of the sailors’ sudden passion for carpentry. Cook did not want to fall into the same pit: he issued strict orders to stop the businessing:

    "1st. To endeavor by all proper means to cultivate a friendship with the Natives, by showing them every kind of civility & regard. 2nd. No Iron Tools, Nails large or small, shall be given to the Natives in exchange for anything but Provisions and Refreshments, as it has been found that these are the most valuable articles in their Eyes..."

           

1.The Ship Was in great Danger    2. The Captain Himself

The astronomers and the crew set up an observatory on a high spot, which is still called Point Venus. The weather was wonderful on the day of the transit. Green succesfully observed the phenomena, including the Black Drop. The very hot air, full of convection just hitched up the doubtfullness of   the measurements. After all Green was able to take time moments, and they were posted to Hell. Unfortunately Green got sick and died during the second part of the mission. James Cook returned to England succesfully, he had circumnavigated the Earth, and this established the Captain`s name as an outstanding explorer.

The Story of Maximilan Hell

                Maximillam Hell (at right on a stamp) was a Hungarian Jesuit monk. In the 18th century priests were not conversant with not only one branch of sciences but with science id general, so he worked on a lot of problems, he was a Renaissance man. But his true love was astronomy. He observed the Transit of 1761, but he was unable to catch the exact moment of the contects. He published his results in his astronomical year-book, Ephemerides Astronomicae . He was the court astronomer of Maria Theresa . He was hung up by the inaccuracy of the measurements of 1761, and the next Transit was not visable from Vienna. He wanted to calculate the AU from the measurements of other astronomers. But in 1767 the Danish king invited him to the island of Vardö in the North in order to make the requested observations there. Hell hesitated a lot because he was in his fifties and at that time a long trip took a long time and much risk. On the other hand he knew Vardo was an excellent place for observation: from May to August the Sun does not fall under the horizon. He took another monk John Sajnovics with him, and they started their trip on 28th April, 1768. Hell had made calculations if he would be able to observe the transit. So he made up a complete scientific program including the study of the climate, local folk art, zoology etc. , as other scientistd did in a distant land. Hell built an observatory on the island and accomplished his „North Science Program” while he had waited for the Transit. The two scientists for example   mapped the island. A Danish astronomer Borgrewing was also at Hell’s observatory. Hell noted that on the very day 10 minutes before the transit there were terrible clouds in the sky, but just a few minutes before the first contact they disappeared. And again, 10 minutes after the 3rd & 4th contact clouds covered the Sun, but at he time of the contacts there were no disturbing effect, they were able the measure the time of the contacts with maximum accuracy. They had a strike of luck, they were the only ones to succeed in Europe!

As Hell returned to Vienna he got the results of Captain Cook (their method requested two measurements taken as far from each other as possible), and he got the Solar Parallax as 8,70” (now we know that is 8, 80). Finally he published his results in 1770 Observatio transitus Veneris... with the details of the astronomical side of the mission. The   scientific documentation of the journey, the Expeditio Litteraria , had never been accomplished because the Jesuit order dismissed him. Only the table of contects were written. During the journey the scientists noticed that the Lappish language and clothing is very similar to that of Hungarian. Hell encouraged Sajnovics to study these phenomena   and later Sajnovics wrote a book about his findings. This was the first book of high standards about the Finno-Ugrian linguistic relationship. That was also a very important recognition of the mission, especially here in Hungary.

Maximilian Hell: Observatio Transitus Veneris ante discum Solis die 3. Junii

The following text is a translation from Latin into Hungarian by Ferenc Pzinger (revised by Gyorgy Gabor Csaba) The English tranlation is the author`s work. Since I am not a native English speaker I cannot recapture the language of the 18th century. So here I can only give a word by word translation but I want to show the extremely precise preparations of Hell’s observation. I tried to choose the most important parts but it was a very hard decision. I choose parts which is required to get the precise moments of the contects.

    „Since the ball of the Sun, the Moon or the Venus are significantly far from the Earth, for the observer from the Earth they optically appear as flat disks or circular plates, whose edge is bordered like a circle; from the optical contact of these celestial bodies we must discourse as we do the ostensible contact of   two physical bodies: We can state that two circles, whether the same or different, have an exterior optical contact, if their optical edges are conversely fixed up, that there is no space between their adjacent outline, but they have only one common physical point, namely, that the observer can see the outline of one of them falling totally out of the other’s outline.   Namely, if a part of   the contour   of one of them is inside that of the other`s contour then we call it secant, and not tanget, to adjudge it, so it is apparently necessary, that the observer has to see both circles` circumference. Since if he sees only one of the outline, and the other’s outline is invisible for him, then how can he judge if they are opticaly adjacent and that there is no any optical interval between them?   After all nobody can compare two optically palpable thing, if he can only see one of them, and the other one is simply invisible for him. So I declare, that it is completely impossiple to observe the first contact of the Moon’s disk at the beginnig of the Solar Eclipse, even more the first contect of the Venus` disk with the Sun’s disk at Venus Transit.... That is to say: it is impossible to observe the first contact of the ball of the Venus and the Sun.”

„It is said that two different circles have an interior contact when the smaller one gets into the bigger one, when the smaller circle’s outline optically so much near to the bigger circle’s inner outline, that both circumference seem intact, but there is no optical interval between the smaller and the bigger circle’s outline. So if the first interior contact of the Venus with the Sun ’s inner outline, {then} I am enough brave to declare, that in my opinion the first interior contact of the dark Venus disk with the bright outline of the Sun is possible to be narrowly between 15 or 10 seconds - I would not use the verb to observe (later I will show the physical impossibility of it), but to estimate.”

Then Hell explains in details that the contact happens when ab = cd (we will able to see it only when its totally inside, but don't move forward to the center of the Sun)

    „If the observer has to estimate only with his eyes, that the ab and dc diameter of the Venus are the same, namely that the Venus` outline is a circle now, then it is easy to understand, that estimating this circle this way must have some requisited errors, namely because of the Venus` slow movement, it is physicaly beyond possibility to declare the exact time moment, with the naked eye, when the Venus` cd diameter is equal with the ab diameter, or, what is the same, accord the exact time when the Venus` outline passes into the precise circle; and it is not much easier to allocate the exact time as far as the Venus cd diameter, though it is a little smaller than the ab diameter. Insofar as the observer cannot be infallible with this time data, that it is easy to foult one arc second in the comparison of the two diameters. Let`s suppose that the minimum error of the most practised observer that he can commit while estimating   the Venus’ circumference, is roughly 1 arc second, so he can miss the 1/58 part of the Venus’s diameter {just think how difficult it is just to keep this exactitude}, while he believes that he correctly estimates the ab and the cd diameter equal; in this case I can assert: the observer determing the accurate time of the contact necessarily lapses 15 time seconds and with this date he estimates the moment of the optical contact as it really happened   and because of the Venus’s observed movement is in one minute, namely in 60 seconds on its ellipse compared to that of the Sun, its progress is with 4 arc seconds, it is clear that it moves 1 arc second during 15 time seconds. As thus the observer cannot estimate the Venus` circumference within 1 arc second with the naked eye, consequently he cannot be sure about the occurance of the contact within approximately 15 seconds.”

    „But if we declare that the precise time of the first contact happens we catch sight of the Sun’s shiny filament, as it said, at the dark circumference of the Venus, then it is easy to understand why we can observe this moment with more accuracy than the other optical contact mentioned above, and at the same time it also becomes clear, that the very moment when this bright filament of   the Sun flashes during the enterance of the Venus, it will not be the real moment of the interior optical contact, but it happens later, so it occurs after the real optical contact.”

    „So the word contact, which is used to describe the Transit of Venus by the observers, is very doubtful and ambiguous, and we have proved it with explaining the moment of the exterior contact; whereas according to some observers the interior contact happens when the outline of the Sun and the Venus are like circles, while others use the word   contact to describe the moment when they observe the bright filament of the Sun at the Venus dark circumference, which moments are apparently different, so it is clear that if these observers use the same word> contact, then this word is doubtful and ambiguous, because we don not know the method, namely the definition of the contact, whether they use the first or the second meaning of the word contact. This ambiguity of the world contact must lead to important differences between observations though made at the same site.

    "Because of the first definiton of the first interior contact does not to allow us to be more accurate than 15 or at best 10 seconds in the exactness of the observed time; conversely the second method of observing the contact, namely when the Sun’s shiny filament appears, allows much closer - 4 or 5 seconds, sometimes 2 or 3 seconds - borders between the measurements, since observes at the same place have to observe the Sun’s filament at the same time, so the observations and the performance of the telescopes made for this observation, as I discoursed it in the Ephemerides in 1765, are completely rebut, that in the course of the observation of the bright filament at the interior contact can even have some second deflection, although this moment comes later than the real optical interior contact, therefore it is right that astronomers usually take it as a law, that at these very important measurements, at the calculation of the Sun’s parallax, they do not use the first but the second definition of   the word contact.”

Other astronomers challenged Hell’s calculation, but he refused the indictments in 1773 in Ephemerides (his astronomical year-book). It was the famous French scientists, Lalande who took the offensive, but later he recognized that he was false. Karl Littrow, the later leader of the Vienna’s Observatory, accused Hell with adulteration, because his notes were full of corrections, and he wrote them in different color ink. And the public lined up with Littrow . So astronomers accepted Johann Franz Encke ’s calculation for the AU. They were much less precise than Hell’s data... More than a century later an American scientist, Newcomb proved Hell had been wright: the corrections did not affect the calculations (he simply corrected the slips of the pen), and they were written in similar ink. Littrow was color blind!

So Hell managed to give a very accurate value for the AU, but he was forgetten because of the accusations! I think Hell still hasn’t got the appreciation he deserves, I reckon him as one of the biggest astronomers of the 18 th century.

The calculation

     The parallax is the movement of the background when we change the perspective. If we shift our viewpoint, the position of the object (compared to the background changes) is changing. If we use it for a star than it iss called stellar parallax. It was Bessel in 1838 who first measured the stellar parallax. It is easy to use for measuring distances.   For the same „ change of viewpoint” the farthest star will change its position less than a closer one.

The parallax can be use to calculate distances, with a little bit of trigonometry

Just hold out your arm and point your thumb somewhere. Now close your left eye, and study where it is „in the background”. Now close your right eye, and notice the differenceIt is this observation and recalling the konwledge of our High School math lessons that we need for the calculation. So the Solar parallax is nothing else but the different positions of the Sun seen from the Earth's core and another point one Earth radius away. Or simply the angle subtended with the Sun by the Earth's radius. Now look on the 14th Figure!

 

- Point A & B are two different observation stations (the lines from A are red, the lines from B are green)

- ß2 is the Solar Parallax

- C is the Center of the Sun

-D is the distance of the Venus from two different positions of the Sun

-Dv is Venus’ distance

- AU is the requested astronomical unit

All triangles summed angles are equal, and the two angles at point O are equal, because they are bordered by the same two lines, so

α1 + α2 = ß1 + ß2

Reduce the equalition and you’ll get:

α2 - ß2 = ß1 - α1

And by the definition of d the equation in the upper line d equals:

d = α2 - ß2 = ß1 - α1

Reduce the equation to this form (remember they are similar triangles):

d = ß2( (2 / ß2 ) - 1 )

Here, let`s stop for a moment:

Venus’ Parallax:              α2 = AB/ (AU-Dv)

Sun’ Parallax:    ß2 = AB/AUSo their quotient is:2 / ß2 = AU/(AU-Dv)

Substitute it to the equation above:

d = ß2(( AU / (AU-Dv)) -1)

Reduce the equation, and you’ll get:

d = ß2AU/(AU-Dv)

So:

ß2 = d / (Dv/(AU-Dv))

Or:

ß2 = d (( AU/DV) – 1)

Now we have got the Solar Parallax! Now we need Kepler’s Third Law here!

(R1/R2)3 = (P1/P2)2

Where R stans for Radius and P is forPeriod, and please note that we know the siderical periods of the planets

( AU / Dv )³ = (365.25 / 224.7)²

AU / Dv = 1.38248

Substitude this to the equation of the Solar Parallax!

ß2 = d(( AU / Dv ) – 1) = d*0.38248

And by the Parallax:

AU = AB / ß2

The Transits of 9th December, 1874 & 6th December, 1882

                More than a century passed after the last Venus Transit. The technial improvement was huge during the last century. The clocks and the measurement of the coordinates of the Earth, and the efficiency of all the scientific instruments developed a lot. Even the telescopes went through a great evolution. But the most significant invention was photography. The number of the observers grew, too. More and more astronomers were brave enough to travel big distances. The technology to take photos of the Sun was invented by Warren De La Rue in the middle of 19th century. Taking photographs was very important, but it did not result in a revolution of the data of the AU. Hell’s calculation was the end of a time. The next really more accurate data were only acquired with radar measurements. Naturally, they got closer to the value that we accept now. Hell’s calculations were on the edge of error.

In 1874 There were six French expeditions all over the globe. The most interesting one was lead by J. Janssen ( he travelled to Japan), who took a   "photographic revolver", and took 48 exposures during the transit.   England organized 5 expeditions by Sir George Airy , and a private expedition by Lord Lindsay to Mauritius. Americans set out 8 expeditions and the congress give the organisers $177000. But most of the expeditions were organized in Russia, 24 observation stations were buitt. Hundreds of photos were taken, but only a few were scientifically valuable. A new technology, the spectroscopy was also made use of. Lomonosov inspired their usage to detect elements in the atmosphere, but they were unsuccesful attemps. There seemed to be a lot of water in the atmosphere. Again, as scientists did not know what to look for, most of the measurements were inaccurate, it did not help them if they read what scientist had written about the Transit a century before.

The best scientists from several nations travelled all over the globe. I only want to concentrate on the most famous observer of 1882, that is the expedition organized by the Naval Observatory at Washington D.C.. The observatory was led by the most honored American astronomer in the 19th century: Prof. Simon Newcomb ( his picture on the left). With his value, he proved Hell's true against his attackers. As a respect of his work there is a Newcomb crater on Moon. First they wanted to travel to South-Africa, but finally they stay at home. They used the garden of the American Huguenot Seminary. Newcomb encouraged everybody to set up his/her own equipment and take measurements. But now here is a part of a letter written by Mary Elizabeth Cummings , one of girls who observed the Transit together with the professional astronomers:

    "I must tell you of our telescope before I close. Some of you perhaps know that it is the one through which we had a few peeps when pupils of Mt. Holyoke. When it was no longer needed there, Mr Williston kindly presented it to the South African daughter of Mt. Holyoke. An observatory was erected for it in our garden, and the telescope was mounted under the direction of Dr Gill, the Astronomer Royal, from Cape Town. It was scarcely in order when the "Transit of Venus Expedition" from the United States, arrived in Cape Town, and soon after decided upon Wellington as the best astronomical station for their purpose. Our garden was selected as the best site, all things considered, and four buildings were erected. Prof Newcomb, the Chief of the Expedition, instructed the pupils in Miss Ferguson's astronomy class and several of us teachers, in the art of reading time quickly on the chronometer, and several of us were invited to share the practice of the astronomers, in observing an artificial transit of Venus, by means of an apparatus invented by one of the party. The actual transit took place the day before our anniversary and in the midst of the examinations and hurry of anniversary week, and to several of us teachers was the most important event, as it had been arranged that we should observe it through our own telescope, which was in excellent condition and gave a splendid view of all that could be seen."

Because of actions like this one described in the letter there was an enormous public interest in this transit. Nearly all newspapers announced latest events of the Transit on the frontpage. People on the street were talking about it, and everybody expected a bright sky. Next day articles were published, like this one:

"Many of the residents of San Francisco were noticed yesterday with a piece of smoked glass to their eye, looking curiously at the sun, between the hours of about sunrise and noon, during which time Venus was visible; and even under these disadvantages without the aid of a suitable telescope, it was still a grand and beautiful spectacle. All who missed a view of the transit of Venus are to be commiserated, for should they live to be 100 year old the chance will not come again." (San Francisco Chronicle)

    It took a long time to process the thousands of photos taken of the transit, and only a few astronomers had the trust to do the calculations, probably only Newcomb and the other famous scientist of the century, William Harkness . Newcomb published his results in 1891:   the Sun’s parallax is 8.80 +/- 0.051", so the AU (average value) is: 149,189 million kms. Harkness` value was 8.809" +/- 0.0059", but he never published it. However, the international scientific community accepted Newcomb’s value in 1896.   It is important to note here that Newcomb „only” specified the value, the real breakthrough had been achieved by Maximillan Hell. However, Newcomb finally closed the hunt for the AU by the Venus Transit. A Photo from 1882 on the right.

Our Transit:

                As we realized that the Venus was getting closer, we started to study this episode in the history of science. It happend in about March. Then „we” means my physics teacher, a few guys from the school, who were interested in astronomy and myself. We met with Hell’s story and we liked it very much, that is why I have translated some of them (see above). We want a little bit to simulate his work, as a kind of honour. We slowly prepared for the phenomon, we counted the remaining days. We were unable to care about our end-of-term marks, just to concentrate on the year’s most momentous moment! We said: we did not want to belong to the part of the people on Earth who would not see it, we did not want to miss the chance to see it!

  A week before the Transit we tested the whole equipment, the telescope & mount as well. We used an old, but excellent Zeiss refractor (80/840) with a telemator mount, we projected the Sun’s face. Everything went all right. We planned to make the observation from the garden of the school, but we do not have a GPS to measure the correct value of our coordinates, but on the basis of a map of   the district we were able to diagnose it with more accuracy than on heavens-above.com. During the transit we used a DCF 77 clock, it uses the radio signals of the atomic clock at Frankfurt. We worried the most about the weather. If clouds cover the Sun, everything goes for nothing. We started to understand the feelings of Le Gentil! Our B plan was to travel as far as it was necessary. With webcams we observed the whole country to see where there was sunshine.

On the great day I woke up at 4 o’clock to check to weather, and as I looked out of the window it seemed wonderful: blue sky, no clouds anywhere. I head for the school in the morning.   In a few minutes everybody arrived. We set up the equipment on the field, and waited. We projected the Sun’s face and first we just looked for Sun spots, and kept looking at the clock: how many minutes still remain? 2 minutes before the estimated contact we were silently waiting, then a small black knob appeared (see the exact values below)! We waited for the second contact, and than it was easy to discover the notorious Black Drop Effect and the atmosphere.

Between the 2nd & 3rd contact we organized a demonstration for the school. All classes visited us in the garden in small groups, we told them the story of every famous Transit observer, and told them why it was so important. Then we projected the scene for them and they were able to see that mystic black spot on the Sun’s face. We counted the number of those who looked at the phenomenon at us, and finally it turned out that we showed it to 412 persons!

For the 3rd & 4th contact we stopped the visitors coming in order to maximum concentration. We saw the Black Drop again, and the atmosphere (it was especially bright for the second time). We weren’t able to catch accuratelly the 4th contect, a cumulus appeared in front of the Sun. On the whole it was a day to remember, nearly everything went perfectly, there is nothing to grumble about. I hope the Transit of 2012 will be as successful as this one, unfortunately it will not be visable from Budapest, but we are willing to travel as far as it is necessary to see it again. ( Pictures in the Gallery!)

Results:  

Observers: Gyorgy Gabor Csaba; Balazs Szigeti; Andras Donath (we take the measurements)

Method: We projected the Sun’s Face

Equipment : Zeiss 80/840 Telemator, we didnt use the RA motor drive

Location: The yard of the Vere Peter’s High School (E 19º 05’ 00” ; N 47º 35’ 00”)

Clock: DCF 77  

1st Contect : 5h : 20 min : 44 sec We observe it quite late, because of the bad seeing, the Sun’ circumference was waving. We also noticed after the contect the atmosphere of the planet  

2nd Contec t: 5h : 33min : 16 sec We noticed the Black drop effect. And soon we realized that something went wrong... see below  

School Demonstration for 412 people (We collected thier names)  

3rd Contect :   11h : 03min : 41 sec This is the avrage value, Andras observed it 1 sec before, Mr. Csaba at the timeand I observed it 1 sec later. We noticed the black effect from 11h : 01min : 56sec. We also catch the atmosphere at   11h : 01min : 35sec and for the second time it was much brighter than first time.  

4th Contect : 11h : 22min : 12-20 sec                A cumulus disturbed us.

 

    I have done the calculations to get „my AU”. For the second contect, I’m sure its a clerical error, a little bit annoying, but not a tragedy. For my luck not I was the writer! Strange the big differnce too, because we measured the right value at the 3rd contect, or probably the clock get an inaccurate value... However I calculated for the second contect a Hungarian Avrage Value from other observers around my city. Its 5h : 38min : 56-57 sec (I calculated with 56). For the 3rd contect I calculated with my value, because its good. First I picked up an South observer’s value. I find the home page of Jacky Francoise ( http://www.astrorun.com/~fjacky/VT.html ) during Internet. I calculated with his values. We weren’t at the same longitudes, but I calculated the distance with the doctrine of the sphere First I get a strange value,   than I found the mistake: a sign convection error. I re-calculated, and I get the Value:

Solar Parallax : 8.82º

AU =149 1176 82kms

    Compare to the corect value 149 59 78 70 km, the difference is 480 188 km. Not bad, but can be better... To get this value was somewhere the end of Our Transit. The next transit will happen 6th June, 2012 (only 8 years!).   It has no longer a scientific magnitude, but does not seem to lose the interest of the professional and amateur astronomers. I do not know why, probably the rareness of it, or as a kind of respect for the past time astronomers. But after seeing it once I am already waiting for it returning in 2012.. unfortunately I do not have the chance to see the one in 2117...

 

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