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Venus Transit and the Astronomical Unit

Venus Transit and the Astronomical Unit. Biman Basu bimanbasu@gmail.com. Measuring the Universe. Our idea of the structure and size of the Universe has changed drastically over the past centuries . Earth-centred Universe has given way to a Sun-centred Universe.

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Venus Transit and the Astronomical Unit

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  1. Venus Transit and the Astronomical Unit BimanBasu bimanbasu@gmail.com

  2. Measuring the Universe • Our idea of the structure and size of the Universe has changed drastically over the past centuries. • Earth-centred Universe has given way to a Sun-centred Universe. • Ingenious experiments led to the determination of the Earth's shape and size, the Earth-Moon distance, and further to the Sun-Earth distance.

  3. Measuring the Earth • One of the earliest efforts to measure the Earth was by the Greek mathematician and astronomer Eratosthenes around 240 BC. • Using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene (now Aswan, Egypt) on summer solstice, he arrived at the conclusion that the Earth is spherical and has a circumference of about 40,000 km. • The calculation was based on the correct assumption that the Sun is so far away that its rays can be taken as parallel.

  4. Eratosthenes's experiment

  5. Measuring large distances • Measuring the size of the Earth did not involve measuring large distances. • But most astronomical distances are quite large. • To measure them astronomers use a method involving the measurement of parallax - the apparent shift of a nearby object in relation to more distant objects.

  6. What is parallax? • Parallax is the apparent displacement of a relatively close object compared to a more distant background as the location of the observer changes. • Parallax makes it possible for our eyes to perceive depth of field and see objects in three dimensions. • Astronomers use parallax to find distances of astronomical objects.

  7. Parallax due to position of the eyes

  8. Measuring the distance of the Moon using parallax • In 129 BC, the Greek astronomer Hipparchus, used parallax of the Moon during a total solar eclipse to calculate the distance of the Moon from Earth. • He used the observation of the eclipse from two different locations to determine the parallax of the Moon.

  9. Hipparchus's method From Hellespont (Lat. 4020N) the total eclipse could be seen, as the Moon fully covered the Sun from there.

  10. Hipparchus’s method-II However, when viewed from Alexandria (Lat. 3120N), only a partial eclipse could be seen at the same moment due to parallax of the Moon relative to the Sun.

  11. Hipparchus calculations Since A and B differ 9 in latitude and the circumference of Earth is given by 2r, the distance AB is given by (2r/360)×9 where r is the radius of Earth. Similarly, since the distance CD is 1/5 the solar diameter and the Sun subtends an angle of 30' or 0.5 at Earth, the angle  is 0.1, which is the parallax of the Moon’s edge as seen from A and B.

  12. Hipparchus calculations-II From this diagram we can see that AB is also equal to (2R/360)×0.1, where R is the Earth-Moon distance. Therefore, (2R/360)×0.1 = (2r/360)×9 or 0.1R = 9r, which gives R = 90r; that is, the Earth-Moon distance is 90 times the radius of Earth. The distance to the Moon comes out to be 5,73,300 km, which is about 50 per cent higher than the average value of 3,84,400 km.

  13. Finding larger distances • After finding a method to determine the distance to the Moon using parallax, the next step was to find the distance to the Sun. • But determining the parallax of the Sun was difficult, as the distant background stars cannot be seen during daytime. • However, the parallax method could be used to determine the distance of nearby stars. • The first star for which the distance was measured using the parallax method was 61 Cygni in the constellation of Cygnus.

  14. Parallax of 61 Cygni When 61 Cygni was photographed six months apart, it appeared to shift slightly against the background stars because of the shift in Earth's position. From the angle of parallax P the distance d could be calculated.

  15. The Astronomical Unit • The Astronomical Unit (AU) is the average distance between the Sun and the Earth. • It is a convenient unit to use when expressing distances within the solar system. • The AU, as defined in the International Astronomical Union (IAU) system of constants, is equal to 149,597,870 km.

  16. Earth’s orbit around the Sun

  17. Kepler's third law and the AU • By 1619, German astronomer Johannes Kepler had figured out the relative distances of all the planets from the Sun. • For example, if the Earth's distance from the Sun is one astronomical unit (AU), then Mercury’s distance from Sun is 0.38 AU, Venus's is 0.72 AU, Mars's is 1.5 AU, Jupiter’s is 5.2 AU, and so on. • If two planets have orbital periods Pplanet and Pearth, the ratio of their distances aplanet and aearth in AU from the Sun can be worked out from the relationship

  18. Parallax and the AU • Kepler's third law allows one to evaluate the dimensions of the solar system in relative units, e.g. in "astronomical units" (AUs), where 1 AU is the mean Sun-Earth distance. • However, to express the AU in kilometres we need some sort of parallax - some difference in the observed position of some object in the solar system, when seen from two separated points, the distance between which (in kilometres) is known. • The problem is, planetary objects are so enormously distant, that the shift in their apparent position, when viewed from two separated locations on Earth, is extremely small.

  19. Determining the Astronomical Unit • Nevertheless, astronomers have been trying to determine the value of the AU since Kepler’s time and various techniques have been used. • One of the earliest efforts was made in 1672 when the Italian astronomer Giovanni Cassini was able to measure the distance to Mars using parallax when the planet was in opposition; that is, nearest to Earth.

  20. Determining AU using Mars parallax Cassini sent a colleague to French Guiana while he remained in Paris. At an agreed time the two measured the position of Mars against background stars. By comparing the two positions and they could measure the tiny angle of parallax. Knowing this, and the straight distance between the two locations, they could calculate the Earth-Mars distance, which came out to be approx. 74,000,000 km.

  21. Determining AU using Mars parallax-II From Kepler's Third Law it is known that Sun-Mars distance DM = 1.524 times DE (Sun-Earth distance) So, 74,000,000 = DM - DE = 1.524 DE - DE or 74,000,000 = 0.524 DE Finally, we get DE or AU = 74,000,000/0.524 = 141,000,000 km (compared to the modern value of 149,597,870 km); an error of approx. 6%.

  22. Parallax and transits • Parallax of planetary transits can also be used to determine the Sun-Earth distance. • During a planetary transit, the difference in position of the planet, as seen in the background of the solar disc, when observed from two widely separate locations, can be used to determine Earth's distance from the Sun.

  23. What are astronomical transits? An astronomical transit occurs whenever one celestial object, such as a planet or a moon, passes in front of another celestial object. When the Moon passes in front of the Sun it covers the Sun fully because both appear to be of the same size from Earth and we have a solar eclipse.

  24. Planetary transits But when an inner planet like Mercury or Venus passes in front of the Sun it covers only a tiny portion of the Sun's disc (about 1/30th). To viewers on Earth, during such a passage or transit the planet appears as a tiny black dot moving across the solar disc.

  25. Transits of the inner planets • Only the inner planets Mercury and Venus show transits because their orbits are closer to the Sun than Earth’s, and occasionally both come between the Sun and the Earth when they can be seen against the solar disc. • Since both the inner planets occupy orbits between the Earth and the Sun, they would more than likely be seen to pass in front of the solar disk from time to time.

  26. Transits are rare • Mercury comes between the Sun and the Earth every 116 days on average, while Venus does so every 584 days on average. • But transits do not occur as frequently. • On the average, there are 13 transits of Mercury in 100 years compared to only two transits of Venus during the same period.

  27. Transits of Mercury & Venus Being more distant and smaller, Mercury (left) appears much smaller than Venus (right) during transit.

  28. Why transits are so rare • Transits of Mercury and Venus are not quite frequent because their orbits are tilted with respect to that of Earth: Mercury 7.0, Venus 3.23. • In order for a transit to occur, the planet, Sun, and Earth have to be in the same plane on the same side of the solar system. • This happens only when the planets are at any of the two nodes where their orbits cross the Earth's orbital plane.

  29. Orbits of Mercury and Venus

  30. Transits of Venus • Transits of Venus are much rarer than transits of Mercury because the orbital period of Venus is longer than that of Mercury. • Indeed, only seven such events have occurred since the invention of the telescope (1631, 1639, 1761, 1769, 1874, 1882, and 2004). • Transits of Venus show a clear pattern of recurrence at intervals of 8, 121.5, 8, and 105.5 years.

  31. Venus transit cycles • Transits of Venus occur in a 'pair of pairs' pattern that repeats every 243 years. • First, two transits of a cycle take place in December, eight years apart. • There follows a wait of 121 years 6 months, after which two June transits occur, again eight years apart. • The pattern repeats after 105 years 6 months, beginning with two December transits, eight years apart.

  32. Transits of Venus-II • Transits of Venus are only possible during early December and June when the orbital nodes of Venus pass across the Sun. • The last transit of Venus was seen on 8 June 2004 and the next one is due on 6 June 2012. • After the 6 June transit the next transit of Venus will not be seen till the next century, on 11 December 2117; that is, after a gap of 105 years and six months.

  33. Historical transits of Venus • The first person to predict a transit of Venus was the German astronomer Johannes Kepler, who calculated that one would take place on 6 December 1631. • Kepler died in 1630, and there is no record of anyone having seen the 1631 event. • Young English astronomer Jeremiah Horrocks and his friend William Crabtree were the first persons to observe a transit of Venus on 4 December 1639.

  34. Jeremiah Horrocks (1618-1641) Jeremiah Horrocks observing the Venus transit of 4 December 1639.

  35. Horrocks’ observation 1639 Horrocks had calculated that the transit was to begin at approximately 3:00 pm. He had about 35 minutes to observe the transit before sunset at 3.50 p.m. (Published in 1662 by Johannes Hevelius)

  36. Parallax of planetary transits • Parallax causes a planetary transit to look slightly different for two observers at different latitudes on Earth. • Venus does not appear to enter or leave the Sun’s disc simultaneously from two widely different locations, and, observed at the same moment, Venus’ position on the disc of the Sun also differs slightly.

  37. Venus transit parallax From two separate locations on Earth the position of Venus on the solar disc appears different because of parallax.

  38. Edmund Halley and the AU In 1716, the English astronomer Edmond Halley published a paper in the Philosophical Transactions of the Royal Society, describing exactly how the parallax of transits could be used to measure the Sun's distance, thereby establishing the absolute scale of the solar system from Kepler's Third Law. Edmund Halley

  39. Transit of Venus and the AU • Halley’s method involved observing and timing a transit from widely spaced latitudes. • Although the method gave the first reasonable value for the Sun's distance from Earth, his method proved somewhat impractical since contact timings of the required accuracy are difficult to make.

  40. Transit of Venus 1769 • Halley died in 1742, but the transits of 1761 and 1769 were observed from many places around the world and several expeditions were sent to observe the transits. • The transit of 1769 was one of the most extensively observed transits of Venus of that time. • In 1771, French astronomer Jerome Lalande was able to use the combined measurements taken in 1761 and 1769 to determine the average Earth-Sun distance to be 153 ( 1) million km, as against the currently accepted value of 149.60 million km.

  41. Determining the Sun’s distance • The parallax effect gives rise to two ways of obtaining the Sun’s distance from observations of the transit of Venus. i. Timing the start and end of the transit from two stations - Halley’s original 1716 method. ii. Photographing the Sun at the same moment from two stations and measure the northward or southward displacement of Venus due to parallax.

  42. Transit paths of 2004 and 2012 The transits of 1874 and 1882 occurred during ascending nodes, while the transits of 2004 and 2012 occur during the descending node.

  43. Stages in Venus transit 2012

  44. Timing the transit A transit of Venus across the Sun takes about 7 hours, but this time has to be measured to a precision of a few seconds to be of any use. To be useful, the most critical times are the first, second, third, and fourth contact. Unfortunately, an optical phenomenon called the ‘black drop’ effect makes it difficult to time the second and third contacts precisely.

  45. Black drop sequence 1 2 3 4 5 6

  46. Transit timings in India The transit of Venus on 6 June 2012 will start long before Sunrise in India and hence the timing of the 1st and 2nd contacts will not be visible. However, it may be possible to determine the apparent displacement of the position of Venus on the solar disc if observed from two distant latitudes.

  47. View from India at sunrise

  48. Recording position of Venus during transit The best way for amateur astronomers to record the position of Venus during transit would be to project the image of the Sun on a white card using a small telescope. CAUTION: NEVER LOOK AT THE SUN DIRECTLY!

  49. Measuring Venus parallax • For measuring the parallax it is necessary to have at least two simultaneous observations at precisely the same instant from two locations in different latitudes along the same meridian. • Kanyakumari (8.06N, 77.30E) and New Delhi (28.40N, 77.12E) are good examples. • From Kanyakumari, Venus will appear a little northward on the solar disc than from New Delhi.

  50. Locations for observing the transit of Venus

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