Venus transit

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A transit of Venus (from Latin transitus , passage ',' pre-transition '), also transit of Venus or Venus Passage , is a past drawing of the planet Venus in front of the sun . With telescope, sometimes freiäugig observable (with glasses), phenomenon occurs in about 243 years, only four times (after 8, further 121½, another 8 and further 105½ years) because Venus and Earth's orbit are a little inclined towards each other.

After the Venus passages in 1874, 1882 and 2004, the last one took place on June 6, 2012 between about 0:00 a.m. and 7:00 a.m. CEST . The next one won't happen again until December 11, 2117.

During transit, Venus has an apparent diameter of 1 (1/30 of the solar disk ) and, in contrast to the sunspots, appears completely black. Historically, the precise measurement of such passages was of great importance for determining the distance between earth and sun ( astronomical unit ) and gave rise to many expeditions and measurement campaigns by important institutes and scientists. Since 1900, distances in the solar system have been determined using near-Earth asteroids (NEA), today using space travel and radar methods.

Sunrise with Venus in front of the sun: Dresden , June 6, 2012, 4:53 a.m. (UTC + 2). As a result of the stratification of the atmosphere near the horizon, the sun appears distorted and Venus, which is a dark point in front of the sun, doubles.


The transit of Venus on June 8, 2004
The incline of Venus' orbit

During a Venus transit, the sun, Venus and earth are exactly in one line. The principle of this rare planetary constellation is the same as that of a solar eclipse , in which the moon moves in front of the sun and darkens it. However, due to the great distance between Earth and Venus, a Venus transit does not cause any darkening on Earth. In contrast to the moon, Venus covers only a tiny fraction (approx. One thousandth) of the sun's surface. It seems to move as a tiny deep black disc over the course of several hours westward over the sun.

The penultimate Venus passage occurred on June 8, 2004. For Vienna or Frankfurt am Main , it lasted from 7:20 am to 1:23 pm CEST . At the time of transit, the distance between Venus and Earth was more than 42 million kilometers, and from Venus to the sun about 109 million. Because of the good weather, the phenomenon could be observed in large parts of Europe. Prism binoculars or a telescope were not absolutely necessary for this; a protective film for the eyes was sufficient. Coordinated parallel measurements were also carried out in South Asia and Australia.

A Venus transit is a very rare event of which there are only two in 130 years, alternately after a short interval of eight and a long interval of over 100 (depending on the node 105 or 122) years. The interval between five transits is therefore periodic and is about 243 years, 1 day and 22 hours. The last one took place on June 5 and 6, 2012, the penultimate on June 8, 2004, the predecessor of which was observed on December 6, 1882. There was not a single passage of Venus in the 20th century. A Venus transit is therefore actually an astronomical event of the century and due to its rarity it is a heavenly spectacle that is worth observing. However, you have to use suitable, heat-safe solar filters , otherwise you could go blind .

The reason for the rarity of the Venus transit is the inclination of the Venus orbit towards the earth's orbit plane by 3.4 °. This is why Venus does not stand sufficiently precisely between the earth and the sun in every lower conjunction , but "passes" above or below the sun in 98–99 out of 100 cases. With identical orbital planes, the passage of Venus could be observed every 1.6 years.

This lower conjunction occurs at intervals of 579 to 589 days when Venus "overtakes" the earth on its orbit closer to the sun. She changes from the role of the evening star to that of the morning star. Nine months later she is then behind the sun (upper conjunction). The planet Mercury, which is closest to the Sun, has a similar, but much faster cycle of 116 days ( synodic orbital period).

The inner planets Venus and Mercury

Seen from Earth, there are two planets where a planetary transit can occur: Mercury and Venus, whose orbits are within the Earth's orbit. Analogous to the transit of Venus, one speaks of the transit of Mercury when the planet named after the winged divine messenger stands exactly between us and the sun. Mercury transits occur much more frequently than with Venus - in the 21st century alone there are fourteen: The first of these took place on May 7, 2003, the 14th will occur on November 10, 2098. While Venus passages in our epoch take place in June and December, Mercury passages take place in May and November. This is related to the position of the orbital planes and their intersection lines ( nodes ). However, the lines of intersection between the planes of the Earth's orbit and Venus' orbit continue to move slowly, which means that the times of the Venus transit slowly shift to later dates in the year. From the year 4700 onwards, Venus transits will take place in January and July and no longer in December and June.

Sequence of a Venus transit

Scheme of the four contacts and the drop phenomenon

A planet transit in front of the sun has four contacts.

The first contact is the contact of the planet disk with the sun. A few seconds later, knowing the exact position on the solar disk, you can see the indentation. The second contact is the point in time when the disc is completely in front of the sun and no piece of sun can yet be seen between the planet and the edge of the disc. Then the planet appears to be moving in front of the sun. The third and fourth contact is the reverse of the second and first contact. Since the exact position of the planet in front of the disk is known when it exits, the exit can always be observed exactly to the end.

Shortly before the second and after the third contact, the Lomonosov effect can be observed, which can be traced back to the diffraction of the sun's rays through the upper layers of the Venusian atmosphere.

The drop phenomenon can often be observed immediately after the second and before the third contact . When observed through a telescope or on photos, Venus does not appear circular, but rather deformed like a drop towards the edge of the sun. However, the cause of the phenomenon is not - as previously claimed - the evidence of the dense Venusian atmosphere, but lies in the limited resolving power of every optical arrangement required for observation , such as a photo lens or a telescope.

Historical passages of Venus

Venus Transit

Middle transit date
Time ( UTC )
Beginning center The End
May 9, 1650 BC Chr. 21:54 00:45 3:35
May 6, 1642 BC Chr. 14:26 18:02 21:32
December 7, 1631 3:51 5:19 6:47
4th December 1639 14:57 18:25 21:54
June 6, 1761 2:02 5:19 8:37
June 3, 1769 19:15 22:25 1:35
December 9, 1874 1:49 4:07 6:26
December 6, 1882 13:57 17:06 20:15
June 8, 2004 5:13 8:20 11:26
5th / 6th June 2012 22:09 1:29 4:49
December 11, 2117 23:58 2:48 5:38
December 8, 2125 13:15 16:01 18:48
Venus transit recorded on December 6, 1882 (US Naval Observatory Library); this photo of the American transit expedition is probably one of the oldest photographs of Venus.
Memorial stones of the German Venus expedition of 1874

Johannes Kepler had calculated a passage through Venus for the first time, that of 1631. This could not be seen from Europe, since for all European observers the sun was below the horizon at the time of passage. The scientific potential of the event has not yet been recognized. Kepler died in 1630, the subsequent passage of 1639 could not be predicted with Kepler's orbit data, as they were a few hours too inaccurate. The Englishman Jeremia Horrocks was able to recognize and correct these inaccuracies in calculations in October 1639 on the basis of Kepler's and other information. He determined that another round would follow soon. This transit of Venus on December 4, 1639 was the first documented observation by Jeremiah Horrocks himself and William Crabtree . In the short preparation time, Horrocks was only able to alert his friend Crabtree in time for a second observation.

Determination of the earth-sun distance (astronomical unit AU)

In astronomy, people learned relatively early to measure angular distances between astronomical objects with ever greater accuracy. What could not be measured at first, however, were the distances between the heavenly bodies. As soon as such a distance had been determined, the remaining distances in the planetary system could also be determined, since the relationships between the planetary distances were already known due to Kepler's Third Law .

It was customary to express the distance to the sun in terms of its horizontal parallax, i.e. by half the angle by which the sun appears shifted in front of the fixed star background when it is viewed simultaneously from two opposite locations on earth (appears at the full angle also the diameter of the earth viewed from the sun). The modern value of the half angle is 8.794148 , corresponding to a length of 149,597,870 km for the astronomical unit .

History of solar parallax

Aristarchus was the first to find a method, in principle correct, to determine the parallax of the sun based on the angles in the right-angled triangle earth-moon-sun at a crescent moon, but received the unsatisfactory result from today's point of view that the sun is more than 18 times but less than 20 Times as far away as the moon (in reality it is about 390 times as far away). Hipparchus determined from the geometry of the lunar eclipses an already considerably better solar parallax of 3 '. This value was traditionally used until the late 16th century.

While studying Tycho Brahe's Mars observations, Kepler noticed that no Mars parallax could be measured with the means at that time, i.e. that the even smaller solar parallax could not be greater than 1 '. The Mars opposition of 1672 was observed at the same time by Jean Richer in Cayenne and GD Cassini in Paris , who derived a solar parallax of 9 12 " from the measured Mars parallax , but with a considerable scatter of the individual values .

Lacaille was able to compare the position measurements of Mars and Venus he made at the Cape of Good Hope between 1751 and 1754 with European observations and obtained a solar parallax of 10.20 ″. These and all other parallax determinations (most of them in opposition to Mars) remained on the verge of measurability, so that until the 18th century the only consensus that could be established was the view that solar parallax must be less than about 15 ".

Halley's method

The transit of Venus was historically the first way to precisely determine distances in the solar system. The transit was observed from different points on earth that are as far apart as possible in a north-south direction. From the different points it was observed that Venus passed differently close to the center of the sun, seen from the North Pole somewhat lower, from the South Pole somewhat higher (" parallax "). In the end, the distance between the earth and the sun could be calculated from the known distance between the observation points on earth.

Comparison of the simultaneously observed Venus positions during the transit of 1769, for a southern observer in Tahiti and a northern observer in Vardø (Norway).

Edmond Halley had recognized in 1716 that during a transit the parallax of Venus could also be determined much more accurately by time measurements instead of angle measurements. As an example, the graphic on the right shows the positions of Venus in front of the solar disk during the transit of 1769, as presented to observers in Tahiti (Pacific) and in Vardø (Norway). Seen from Tahiti, Venus passed through a more northerly and thus shorter chord on the solar disk because of the observer's location in the southern hemisphere . The lateral offset of both tendons could be determined by angle measurements, but above all by comparing the transit times observed at both locations.

In addition, when viewed from Tahiti, Venus apparently moved faster across the solar disk than when viewed from Vardø, as the observer on Tahiti was closer to the equator and covered a larger arc during the observation due to the rotation of the earth. In addition, Vardø was on the far side of the earth during the transit, but could see the midnight sun over the pole. While Vardø moved in the same direction as Venus, overtaking the earth, as a result of the earth's rotation, Tahiti was carried in the opposite direction. As a result, the apparent speed of Venus in front of the solar disk was reduced for Vardø, but increased for Tahiti. For this reason, too, Venus entered later and earlier for the observer in Tahiti than for the observer in Vardø.

The difference between the Venus parallaxes for the two observers could therefore be determined by time measurements, which at that time were in principle already possible with an accuracy of one second. The comparison of the parallax measurements of several observers who were as far apart as possible from one another at known locations then made it possible to determine the distance to Venus by triangulation. The results of the evaluations were the diameter of the sun and the radii of the planetary orbits of Earth and Venus. In the future, the mean radius of the earth's orbit was used as the astronomical unit AE, especially for dimensions within the planetary system. With one of the two determined planetary orbits and the easily and reliably determinable orbital times of the planets, the radii of the other planetary orbits could be calculated with the help of Kepler's third law. Since it was expected to be able to observe the contact times with an uncertainty of only a few seconds, a Venus transit would have made it possible to determine the solar parallax with an accuracy of at least 1/100 ″.

Since Halley's method required measuring the duration of the entire transit, its application was limited to those observation sites for which both entry and exit were visible. Delisle developed a method that could also evaluate the observation of individual transit phases, provided that observations from at least two locations were available for a phase. This greatly expanded the number of possible observation locations. Halley's method, however, had the advantage of not requiring precise knowledge of the difference in length between the stations being compared, while for Delisle's method the coordinates of the observation location - in particular the geographical longitude  , which at that time could only be determined with great effort - had to be measured as precisely as possible.

The passages of Venus in the 18th and 19th centuries

The Passage of Venus in 1761, observed by James Ferguson


Following the suggestion of Halley and especially later Delisle, expeditions were sent to sometimes very remote places. Le Gentil traveled to Pondicherry in India (where he arrived after the passage due to political unrest, then stayed in the country to watch the passage of 1769, but was prevented from doing so by clouds), Pingré to the island of Rodrigues east of Madagascar, Maskelyne to St. Helena , Planman to Kajaani , Chappe to Tobolsk , Rumowski to Selenginsk . Together with other expeditions and numerous European observers, useful results from a total of 72 stations were finally available.

Thus, for the first time, the solar parallax was clearly in the realm of measurability. Due to the inconsistent instrumentation, different observation methods , but above all the unexpected drop phenomenon , which made the timing of the second and third contact very uncertain, the accuracy of the results remained far below expectations. For example, Pingré received 10 12 ″, Short 8 12 ″, Hornsby 9 12 ″, etc.

The apparition of Venus at the edge of the sun observed by James Cook and Charles Green in Tahiti in 1769


Numerous expeditions were again equipped for this passage. James Cook , accompanied by Green and Solander, observed in Tahiti , Alexandre Guy Pingré in Haiti , Jean Chappe in Baja California , Rittenhouse in Norriton and the Viennese court astronomer Maximilian Hell as the northernmost observer in Vardø . Euler organized a large observation network in Russia, with the Swiss Jean-Louis Pictet and Jacques-André Mallet observed on behalf of the St. Petersburg Academy on the Kola peninsula . A total of 77 stations provided usable observation data.

The results were significantly better this time, but different evaluators still received noticeably different results due to different calculation methods and different ways of combining the data, for example

Planman Lalande Lexell Bright Maskelyne Hornsby Pingré you Séjour
8.43 ″ 8.50 ″ 8.68 ″ 8.70 ″ 8.72 ″ 8.78 ″ 8.80 ″ 8.84 ″
mean 8.681 ″ ± 0.052 ″

Encke subjected all of the data from 1761 and 1769 to a joint evaluation using the newly developed adjustment calculation and obtained a solar parallax of 8.578 ″ ± 0.077 ″, corresponding to an astronomical unit of 153.4 million km.


A German expedition observed in 1874, the Venus of Isfahan from

The passage of Venus in 1874 was relatively unfavorable for astronomical measurements. It remained invisible from almost all of Europe, long transit times could only be observed from Asia and short transit times from Australia, the islands of the South Pacific and the southern Indian Ocean (here in particular the Kerguelen Archipelago). Yet another 60 expeditions were sent out; the German science expedition was led by Karl Nikolai Jensen Börgen in order to at least gain experience with the more modern instruments.

It was found, however, that even observers provided with standardized instruments at the same location measured the contact times by ten or more seconds differently, and that the photographic position measurements used for the first time lagged behind the accuracy of traditional micrometer measurements.

The travelogue of the German expedition - with their ship SMS Gazelle - was published in 1889.


In preparation for the 1882 passage, an international commission issued proposals for uniform instrumentation and observation methods. In particular, it was stipulated that in the event of a drop phenomenon, the time to be determined should be the final breaking of the “ribbon” (upon entry) or its first appearance (upon exit). 38 expeditions made their way, mainly to the northernmost and southernmost parts of the American continent.

Newcomb , whose processing of the 1761 and 1769 passes gave a solar parallax of 8.79 ″ ± 0.05 ″, got a value of 8.79 ″ ± 0.02 ″ after adding the data from 1874 and 1882. Thus, the method of the Venus transits lagged well behind the expectations of astronomers, and even behind the observation of the Mars opposition: Gill had received a solar parallax of 8.78 ″ ± 0.01 ″ from the Mars opposition in 1877.

In 1896, astronomers agreed during a conference on the consistency, the ephemeris km an average value obtained from the Venus passages and other provisions of 8.80 "to use, according to an astronomical unit of 149,500,000.

In the 20th century there was no transit of Venus, the results were refined with the help of near-Earth opposition positions of the minor planet Eros , during which parallax measurements could be obtained. During the opposition in 1900/1901, Eros came within 48 million kilometers of the earth; the parallax measurements yielded a solar parallax of 8.8006 ″ ± 0.0022 ″ (1 AU = 149,488,000 ± 38,000 km). In 1931, an even more favorable opposition brought Eros to within 26 million kilometers of the earth; the observations from 24 observatories resulted in a solar parallax of 8.7904 ″ ± 0.0010 ″ (1 AU = 149,675,000 ± 17,000 km). For 40 years, distances in the planetary system have also been measured with radar .


The earth needs a sidereal year of T sidE = 365.256 days to orbit the sun once; Venus needs T sidV = 224.70 days. It follows that a certain position of both planets to each other - for example the lower conjunction - is repeated after a synodic period of mean T synV = 583.9169 days.

Eight years

So even though Venus (on average) goes through its lower conjunction every 584 days, it still rarely passes in front of the solar disk. Since the orbit of Venus is inclined by 3.4 ° to the Earth's orbit, Venus - seen from Earth - can move past the Sun at a distance of more than 8 ° (16 apparent solar diameters) during a lower conjunction .84 °. In order for a passage of Venus to occur, the sun, Venus and earth must be almost exactly in one line, so earth and Venus must be in close proximity to the common intersection of their orbital planes (the so-called node line ). The earth crosses the nodal line around June 7th (in this knot Venus traverses the earth's orbit plane from north to south, "descending knot") and around December 6th (from south to north, "ascending knot").

If a transit of Venus takes place on a given date, the next opportunity for a transit arises eight years later . Then on the one hand an integer number of earth years has passed (namely eight: 8 ×  T sidE = 2922.0480 days), so the earth is again close to the node. On the other hand, this period corresponds almost exactly to an integer number of synodic Venus periods (namely five: 5 ×  T synV  = 2919.5845 days) and Venus goes through a lower conjunction again, is therefore again close to the earth and thus also close to the node.

After four uneventful lower conjunctions at other points on the orbit, earth and Venus meet again near the knot in the fifth . The coincidence is not exact, however, because it takes Earth 2.46 days longer to reach the knot again than it takes Venus to reach the conjunction again (2922.0480 days versus 2919.5845 days). During the conjunction, Venus and Earth are still some way from the knot, and Venus appears 22 arc minutes more north (if at the descending knot) or south (if at the ascending knot) than in the last pass.

If the last passage went through the center of the solar disk, Venus misses the sun on the new opportunity that has now arisen, since it is now 22 'north or south, but the solar disk only has a radius of 16'. However, if the last passage went far enough south (or north) through the solar disk, so that it is still hit after a shift of 22 ′ to the north (or south), another passage occurs, this time through the other half of the sun. At the next opportunity, eight years later, the sun will inevitably be missed (the shift by 2 × 22 ′ is larger than the solar diameter of 32 ′). Venus transitions occur either individually or in a pair with an interval of eight years. Then the node passage and conjunction drift further and further apart, so that no passage can take place for a long time.

243 years

A longer period in which the sidereal earth years and the synodic Venus periods each come up almost exactly as an integer is 243 years: 243 ×  T sidE ≈ 152 ×  T synV . 243 years after a passage, another passage occurs under very similar circumstances. For example, the passes of June 3, 1769 and June 6, 2012 both took place at the descending node and ran through the northern part of the solar disk.

121.5 and 105.5 years

The passages of Venus show different periodicity patterns over the millennia

While the place of conjunction circles the orbit in the course of its above-mentioned drift, it also hits the opposite node and also enables passages there. In these cases, the periodicity of the passages must be expressed by a half- integer number of sidereal earth years and an integer number of synodic Venus periods. Possible pairings are e.g. B. 121.5 ×  T sidE ≈ 76 ×  T synV and 105.5 ×  T sidE ≈ 66 ×  T synV . Other pairings are also conceivable (e.g. 113.5 ×  T sidE ≈ 71 ×  T synV ), but cannot occur here, as the sub-periods must add up to 243 years. This is (currently) the case with the occurrence of the sub-periods 8 + 105.5 + 8 + 121.5 = 243.

In the long term, due to the variable planetary orbits, other periodicity patterns also appear. The graphic opposite shows all lower conjunctions of Venus for the years -18109 to +21988; the millennium from 2001 to 3000 is highlighted in gray. Conjunctions without transit are shown as light points, conjunctions with transit as dark points. Each line consists of 152 conjunctions, the number of conjunctions in a transit cycle of 243 years. While the period of 243 years is retained, there are different sub-periods in the course of time.

During the period of May 22nd, 427 BC. By November 23, 424 AD, both 8-year pairs were replaced by a single transit, the periodicity pattern was 121.5 + 121.5. The May runs then occurred in pairs, while the November runs remained single. The current pattern, 8 + 105.5 + 8 + 121.5, began on December 7, 1631 and will end on June 14, 2984. On December 18, 3089 a series with paired June rounds and single December rounds will begin; this pattern 129.5 + 8 + 105.5 will end on December 25, 3818.

Special forms of the Venus transit

Children watch the 2012 transit of Venus in Dili

Grazing transit

In principle it is possible for Venus to pass the edge of the sun during a transit. Here it can happen that for some areas of the earth Venus passes completely in front of the sun and for others only partially. Such passages are very rare: the last such passage took place on December 6, 1631. The next such passage of Venus will not take place until December 13, 2611.

It is also possible that a passage through Venus will be visible as a partial passage from some areas of the earth, while for observers in other parts of the earth the planet Venus passes the sun. The last such transit took place on November 13th, Greg. 541 BC Around 1:36 pm ( UT ), the next such passage of Venus will take place on December 14, 2854.

Simultaneous transits

The simultaneous occurrence of Mercury and Venus passages is not possible in the near future and in the past due to the different node positions. However, the position of the railway nodes is slowly changing. Since the orbital nodes of Mercury and Venus move at different speeds, such events will be possible in the distant future, but only in the year 69163 and in the year 224508. In contrast, the simultaneous occurrence of a solar eclipse and a passage of Venus is already possible on April 5, 15232.

On June 4, 1769, a total solar eclipse occurred just five hours after the end of Venus' passage, which could be seen at least as a partial solar eclipse in Europe, the northernmost parts of North America and in North Asia. This was the shortest time interval between a planetary transit and a solar eclipse in historical time.

Notes on observation

Global visibility of the transit of Venus from 5./6. June 2012

We strongly advise against observing the sun or a planetary transit with the naked eye or with self-made filters. In the case of self-made filters made of untested materials, there is no certainty whether harmful but invisible ultraviolet and infrared components of sunlight will be filtered out. Above all, one should never look into the sun with the naked eye (not even with sunglasses or the like) through prism binoculars or telescope , as the sunlight is so focused that the retina of the eye is immediately destroyed or severely damaged. When observing directly through a telescope, it is essential to use suitable solar filters in front of the objective - not in front of or behind the eyepiece.

The easiest way to make solar observations is to project the image of the sun onto white paper. The telescope is aimed at the sun using its shadow and the paper is held 10–30 cm behind the eyepiece. The sun then appears as a bright circular area and is brought into focus by turning the eyepiece. Venus or Mercury move over the surface as a small, dark disc over the course of hours.

This projection method is also very suitable for observing sunspots . However, you have to be careful that the telescope does not overheat, which would cause the lenses or mirrors to burst. The telescope's finderscope must be covered, as the bundled radiation from the sun is sufficient to destroy the viewfinder crosshair or to burn holes in clothing.

In addition, observatories offer the possibility of observing the process with the help of professional instruments during Venus transits (as well as other important astronomical events).

Pictures of the process from June 8, 2004

Pictures of the process from June 6, 2012

See also


  • Gudrun Bucher: The trace of the evening star - The adventurous exploration of the transit of Venus , Scientific Book Society, Darmstadt 2011, ISBN 978-3-534-23633-6 .
  • SJ Dick: Venus in front of the sun , Spectrum of Science 6/2004, pp. 24–32.
  • Hilmar W. Duerbeck : The German transit of Venus expeditions of 1874 and 1882: organization, methods, stations, results. In: Journal of Astronomical History and Heritage, Volume 7, 2004, Number 1, pp. 8-17, pdf .
  • Alexander Moutchnik : Research and teaching in the second half of the 18th century . The natural scientist and university professor Christian Mayer SJ (1719–1783) (Algorism, Studies on the History of Mathematics and Natural Sciences, Vol. 54), Erwin Rauner Verlag, Augsburg, 523 pages with 8 plates, 2006, ISBN 3-936905-16- 9 .
  • Marco Peuschel: Conjunctions, coverings and transits - The little almanac of the planets . Self publication . Engelsdorfer Verlag, Leipzig 2006, ISBN 3-939144-66-5 . (The small almanac of the planets contains the Mercury transits from 1800 to 2700 and from Venus between 1000 and 10000. Furthermore, there are also mutual overlaps between the planets from 1500 to 4500, also between Jupiter and Saturn).
  • Andrea Wulf : The hunt for Venus and the measurement of the solar system , Bertelsmann, Munich 2012, ISBN 3-470-10095-0 .

Web links

Commons : Transit of Venus  - collection of images, videos and audio files
Wiktionary: Venus transit  - explanations of meanings, word origins, synonyms, translations

Event December 9, 1874

Event June 8, 2004:

Venus transit animation

Event June 6, 2012:

Individual evidence

  1. The cycle of the passages of Venus ,
  2. ^ The Imperial Navy and the Passage of Venus from 1874. ( Memento from November 4, 2014 in the Internet Archive ) Bundesarchiv
  3. a b c Fred Espenak: Transits of Venus, Six Millennium Catalog: 2000 BCE to 4000 CE. NASA, February 11, 2004, accessed July 13, 2012 .
  4. ^ Robert H van Gent: Transit of Venus Bibliography. Retrieved September 11, 2009 .
  5. ^ Paul Marston: Jeremiah Horrocks — young genius and first Venus transit observer . University of Central Lancashire, 2004, pp. 14-37.
  6. ^ Nicholas Kollerstrom: William Crabtree's Venus transit observation. (PDF; 149 kB) In: Proceedings IAU Colloquium No. 196, 2004. International Astronomical Union, 2004, accessed May 10, 2012 .
  7. PK Seidelmann (Ed.): Explanatory Supplement to the Astronomical Almanac. University Science Books, Mill Valley 1992. ISBN 0-935702-68-7 .
  8. ^ A. van Helden: Measuring the Universe. University of Chicago Press. Chicago, London 1985. ISBN 0-226-84882-5 . P. 7
  9. ^ R. Wolf: Handbook of astronomy, its history and literature. F. Schulthess, Zurich 1892. (Reprint Olms: ISBN 978-3-487-05007-2 ) Par. 438 ( online (PDF file; 16.28 MB)).
  10. ^ R. Wolf: Handbook of astronomy, its history and literature. F. Schulthess, Zurich 1892. (Reprint Olms: ISBN 978-3-487-05007-2 ) Par. 439 ( online (PDF file; 16.28 MB)).
  11. ^ R. Wolf: Handbook of astronomy, its history and literature. F. Schulthess, Zurich 1892. (Reprint Olms: ISBN 978-3-487-05007-2 ) Par. 441 ( online (PDF file; 16.28 MB)).
  12. ^ R. Wolf: Handbook of astronomy, its history and literature. F. Schulthess, Zurich 1892. (Reprint Olms: ISBN 978-3-487-05007-2 ) Par. 444 ( online (PDF file; 16.28 MB)).
  13. ^ A. van Helden: Measuring the Universe. University of Chicago Press. Chicago, London 1985. ISBN 0-226-84882-5 . P. 163.
  14. ^ Edmond Halley: Methodus Singularis Quâ Solis Parallaxis Sive Distantia à Terra, ope Veneris intra Solem Conspiciendoe, Tuto Determinari Poterit. In: Philosophical Transactions. Vol. 29, No. 348, June 1716, pp. 454-464, JSTOR 103085 , (In English: A new Method of determining the Parallax of the Sun, or his Distance from the Earth. In: The Philosophical Transactions of the Royal Society of London, from their Commencement, in 1665, to the Year 1800; Abridged. Vol. 6, 1809, ZDB -ID 241560-4 , pp. 243-249 ).
  15. a b R. Wolf: Handbook of astronomy, its history and literature. F. Schulthess, Zurich 1892. (Olms reprint: ISBN 978-3-487-05007-2 ) Par. 448 ( online (PDF file; 16.28 MB)).
  16. Venus transit 2004, parallax measurement with the help of solar granulation. At:
  17. Sun distance, simple calculation , (PDF; 158 kB).
  18. Using a transit of Venus to determine the Astronomical Unit: a simple example.
  19. a b c d e R. Wolf: Handbook of astronomy, its history and literature. F. Schulthess, Zurich 1892. (Olms reprint: ISBN 978-3-487-05007-2 ) Par. 449 ( online (PDF file; 16.28 MB)).
  20. ^ Prof. Richard Pogge: Lecture 26: How far to the Sun? The Venus Transits of 1761 & 1769. Retrieved September 25, 2006 .
  21. ^ R. Wolf: Handbook of astronomy, its history and literature. F. Schulthess, Zurich 1892. (Reprint Olms: ISBN 978-3-487-05007-2 ) Par. 450 ( online (PDF file; 16.28 MB)).
  22. a b R. Wolf: Handbook of astronomy, its history and literature. F. Schulthess, Zurich 1892. (Reprint Olms: ISBN 978-3-487-05007-2 ) Par. 451 ( online (PDF file; 16.28 MB)).
  23. a b S. Débarbat: Venus transits - A French view. In: DW Kurtz (Ed.): Transits of Venus: New Views of the Solar System and Galaxy. IAU Colloquium No. 196. Cambridge University Press. Cambridge 2004. ISBN 0-521-84907-1 doi: 10.1017 / S1743921305001250 .
  24. a b G. Bucher: The trace of the evening star. WBG, Darmstadt 2011, ISBN 978-3-534-23633-6 , p. 186.
  25. Eli Maor: Venus in Transit. Princeton University Press, Princeton 2004, ISBN 0-691-11589-3 , p. 55.
  26. It is 1 / T synV = 1 / T sidV - 1 / T sidE .
  27. The approximately 8.8 ° are calculated from the 3.4 * by equating the absolute height with representation by means of the tangent, see Venus positions # Visibility !
  28. MJ Neumann: Venus in front of the sun. Stars and Space June 2004, p. 22 ( online ).
  29. a b Eli Maor: Venus in Transit. Princeton University Press, Princeton 2004, ISBN 0-691-11589-3 , p. 59
  30. Eli Maor: Venus in Transit. Princeton University Press, Princeton 2004, ISBN 0-691-11589-3 , p. 60.
  31. a b R. Wolf: Handbook of astronomy, its history and literature. F. Schulthess, Zurich 1892. (Reprint Olms: ISBN 978-3-487-05007-2 ) Par. 446 ( online (PDF file; 16.28 MB)).
  32. a b c Eli Maor: Venus in Transit. Princeton University Press, Princeton 2004, ISBN 0-691-11589-3 , p. 63.
  33. ^ J. Meeus: Astronomical Tables of the Sun, Moon and Planets. 2nd ed., Willmann-Bell, Richmond 1983-1995, ISBN 0-943396-45-X , chap. XIV.
  34. a b Hobby Q&A: Sky & Telescope. August 2004, p. 138. See J. Meeus; A. Vitagliano: Simultaneous transits. In: The Journal of the British Astronomical Association 114 (2004), no.3.
  35. ^ Fred Espenak: Transits of Mercury, Seven Century Catalog: 1601 CE to 2300 CE. NASA, April 21, 2005, accessed July 13, 2012 .
  36. Dr. Hans Zekl: Double Transits - When can Venus and Mercury be seen in front of the Sun at the same time?, accessed on July 13, 2012 .
  37. Jérôme de La Lande , Charles Messier: Observations of the Transit of Venus on June 3, 1769, and the Eclipse of the Sun on the Following Day, Made at Paris, and Other Places. Extracted from Letters Addressed from M. De la Lande, of the Royal Academy of Sciences at Paris, and FRS to the Astronomer Royal; And from a Letter Addressed from M. Messier to Mr. Magalhaens . In: Philosophical Transactions (1683-1775) . 59, No. 0, 1769, pp. 374-377. bibcode : 1769RSPT ... 59..374D . doi : 10.1098 / rstl.1769.0050 .
  38. Venus Traps. In: FAZ . December 19, 2011, p. 26.
  39. Menso Folkerts (ed.): Algorism. Studies in the history of mathematics and the natural sciences.
  40. ^ Table of contents ( Memento from July 22, 2012 in the Internet Archive ), (PDF; 106 kB).
Passages in our solar system
Venus earth Mars Jupiter Saturn Uranus Neptune
Mercury Mercury Mercury Mercury Mercury Mercury Mercury
  Venus Venus Venus Venus Venus Venus
    earth earth earth earth earth
      Mars Mars Mars Mars
        Jupiter Jupiter Jupiter
  moon Deimos     Saturn Saturn
    Phobos       Uranus
This version was added to the list of articles worth reading on April 12, 2005 .