The Venus transit and the Astronomical Unit calculation

The Venus transit and the Astronomical Unit calculation William THUILLOT Institut de mécanique céleste et de calcul des éphémérides Brandys, May 2004 1 IMCCE/PARIS Observatory

The transit of June 8, 2004 On June 8, 2004, the planet Venus will pass in front of the Sun. Nobody alive today has seen such an event. Why does this event occur ? Why did it retain the attention of the astronomers in the past? What results can we expect? 5 h 40 UTC 11 h 05 UTC 2

The VT-2004 project • Coordinated observations of a rare phenomenon • Educational interest (wide public, schools) • Measurements « easy » to make: timings • Possibility to catch images (if experience…) 3

The VT-2004 project Educational interest • Historical background closely related to the measurement of the Solar System (methods, distances, motions of the celestial bodies, exoplanets…) • preparation of a scientific experiment and measurements with some scientific value • Interest of exchanging information between participants , in particular: üamateurs - schools üamateurs – individuals • succeeding in the measurement of the Earth-Sun distance (…and of the AU) 4

Mechanism • Mini Solar eclipse • Rare event • Difficult to predict in the past (Kepler 1 st) • Rich historical background ü fundamental for : - Confirming the superiority of the Copernician model (Rudolphines Tables) - Measuring the Earth-Sun distance (and the AU) 5

Venus visibility Gibbous phase Superior conjunction Gibbous phase Sun West elongation East Elongation Crescent before The inferior conjunction Inferior conjunction Crescent after the inferior conjunction West of the Sun Morning visibility East of the Sun Evening visibility Fixed Earth 6

Motion of Venus / Earth… if Venus was in the ecliptic 2 6 t (days) 1 0 2 91 3 182 4 273 5 365 6 456 7 547 8 584 4 2 7 7 6 1 3 8 5 3 8 4 7 1 5 Earth 365. 25 j Venus 224. 70 j Synodic period 583. 92 j

More realistic… Nœud descendant Venus • Orbital inclination (/ecliptic) : 3. 4° • Venus at Nodes : . Sun Earth - 7 December (ascending node) - 5 June (descending node) • Conditions for a transit : - conjunction Sun- Venus - Earth (584 d. ) - close to a node 8 • Rare events Noeud ascendant

When transits of Venus can be observed ? • Need of a close aligment of the Sun, Venus and the Earth (duration up to 8 hours) • Very rare events (~ every 120 years, and 8 years after): - Last events : 1874 -1882 - Following events: 2004 - 2012, then in 2117 • The 2004 VT will be well observable from Europe 10

Short history of the Venus transits XVIIth, Dec. 1631, Dec. 1639 XVIIIth, June 1761, June 1769 XIXth Dec. 1874, Dec. 1882 11

Kepler’s laws • Each planet describes an ellipse of which the Sun is at one of the focus (1605) - area’s law – law related to the ratios of semi-major axis • 1627 : Rudolphines Tables • 1629: prediction of a transit of Mercury (november 1631) • more…: prediction of a transit of Venus (december 1631) 12 Kepler (1571 -1630)

Kepler’s third law The semi-major axis a and the period of revolution T are linked by a 3/T 2=constant for all the planets (1618). 13

Visibility of the Mercury transit of 1631 14

Gassendi in Paris 1631: Mercury transit Calculation for Paris hour Sun (true solar time) 2 e contact 3 e contact 5 h 06 10 h 28 -21° +22° Transit of Mercury on Nov 7, 1631 • First observation of a transit • Use of a darkroom ( and may be a lens ) • Observation from Nov 5 (bad weather on 5 and 6) • Starting from the sunrise on Nov 7, Gassendisaw a black spot – Measured diameter of Mercury : 20" (true value : 10") • Error of 5 h from the Kepler’s predictions • Three other observations in Europe Mercurius in sole visus et venus invisa Parissiis anno 1631. 15 "Le rusé Mercure voulait passer sans être aperçu, il était entré plus tôt qu'on ne s'y attendait, mais il n'a pu s'échapper sans être découvert "

Gassendi in Paris 1631: Vénus transit • Gassendi tried also to observe the 1631 Venus transit • Main purpose: to check the Rudolphines Tables (Copernic system) • Error of the Kepler’s predictions • Unobservable : in Europe (during night) => America • Unsuccessful observation of the 1631 Venus transit by Gassendi But in England… • J. Horrocks understood that a second transit of Venus occurs 8 years later • 16 With W. Crabtree: organization of the 1639 observations

Visibility of the Venus transit of 1639 17

Observations of W. Crabtree 1639 • Observations made at Manchester • Cloudy until 3 h 35 10 min of observation possible only ! • Amazed by the transit, he made no measure ! Painting of F. M. Brown, visible at the City Hall of Manchester 18

First observations of a transit of Venus: J. Horrocks 2 e contact 3 e contact sunset local time 15 h 15 21 h 30 15 h 50 Sun + 4° - 47° Transit of Venus on Dec 4. 1639 • Horrocks: First observation of a transit of Venus • Use of a darkroom with a refractor • On Sunday 4 he observed from the morning, through clouds • He stopped observing for religious obligations • At 3 h 15 he continues his observations and the weather became fair 19

J. Horrocks (Venus in Sole Visa) 1639 • He made three measures in a hurry before the sunset t distance (") 3 h 15 864 3 h 35 810 3 h 45 780 3 h 50 sunset Diameter of Venus: 1' 16“ Earth-Sun : 94 000 km 20 (Kepler : 7’)

Transits during the XVIIIth century • A fundamental question : – the determination of the Solar parallax • 1672 : Richer and Cassini (I) : Opposition of Mars • 1677 : Halley observes a Mercury transit (St Helen Island) • 1691: he presents a method to get the Solar parallax from the Venus transits • 1716 : he call for observations for the next Venus transit • expeditions 21

Mean horizontal parallax • • The Sun-Earth distance cannot be directly measured Classical astronomy measures angles R p a Earth Mean horizontal parallax • • 22 Measurement of p and R in order to compute R = 6400 km and a ~ 150 x 106 km Then p ~ 10" ==> difficult to be measured A main problem in the past a

Parallax of Mars (perihelic opposition in 1672) Mars d Paris R Kepler: a 3 / T 2 = constant f Cayenne D (a. Mars / a Earth)3 = (TMars / TEarth)2 a. Earth = a. Mars - D (Mars-Earth) 23 Cassini et Richer ps = 9. 5" ( a = 138 x 106 km) Flamsteed ps = 10" ( a = 130 x 106 km)

Transits during the XVIIIth century • Halley died in 1742 but astronomers remember his call for observations • • • Longitudes are not yet well known. Clocks are not good time keepers. Traveling is slow (sailing). Voyages are very expensive. Nobody has never observed a transit of Venus. Two methods for measuring the parallax : Method of Halley : The durations of the transits are compared => no problem with longitude. Method of Delisle : The times of contacts are compared => more observations but longitudes have to be known. 24

Method of E. Halley c b a • b • a • c • The relative positions of the chords give the parallax • Difficulty to get an accurate measurement – No reference frame available • But these positions are related to the duration of each transit • Angular measurements are replaced by timing measurements – accurate • 25 Requires observing sites far from each other latitudes offset – 1 s. of uncertainty ==> Parallax to 1/500 (Halley, 1716)

Method of J. Delisle Use of the timing offset at the beginning or at the end of the time t Dt Topocentric observation (from the surface of the Earth) event Geocentric view Advantages – Less impact of the meteorological effects – Increasing of the number of sites (partial observations usable) Disadvantages • Timing measurement instead of a duration measurement – need to have absolute timing • Comparaison between sites – need to accurately know the geographic position ! • 26 Requires maximum of timing differences -> longitudes offset

The transit of June 6, 1761 The French • Expeditions for the observation: 2 of these voyages took place in countries allied of France. • César-François Cassini de Thury (1714 -1784) in Vienna (successful observation). • the Abbot Jean-Baptiste Chappe d'Auteroche (1728 -1769) to Tobolsk in Siberia (successful observation). • Alexandre Guy Pingré : Rodrigues Island (north of Madagascar), Thanks to the compagnie des Indes (observation partially successful). • Guillaume Joseph Hyacinthe Jean-Batiste Le Gentil de La Galaisière (1725 -1792), left by sea in order to observe the transit in Indies at Pondichéry. Unfortunately the city of Pondichéry was taken by the English and he saw the transit from the ship, unable to make a measurement; he decided to wait until the next transit in 1769 • Joseph-Jérôme Lefrançois de Lalande (1732 -1807) observed from Luxembourg Palace in Paris. 27

The transit of June 6, 1761 The English two campaigns far from England to observe the event. • Nevil Maskelyne (1732 -1811) went to Sainte-Hélène where he was not able to observe because of clouds. • Charles Mason (1728 -1786), James Bradley and Jeremiah Dixon (17331779) was supposed to observe from Bencoolen (Sumatra). They were not able to make the observation because the French took the city. They observed then at Capetown. • John Winthrop, professor in Harvard went to St-John (Terre-Neuve) where « surrounded by billions of insects " he succeeded to observe the last contact of the transit. 28

Le passage du 6 juin 1761 Projection de Hammer 29

The voyage of Chappe d’Auteroche The travel of Chappe d’Auteroche to Tobol’sk 30

Results from the transit of 1761 • The number of observers was 120, on 62 sites (S. Newcomb, 1959). • Note that some sites of observations were previously selected (Bencoolen, Pondichéry, Batavia) by Halley in 1716. 8. 5" < P < 10. 5" The large error is due to: - a bad knowledge of the longitudes of the sites of observation - the black drop effect which decreases the precision of the measurement of the time of the contacts. Disappointing results : no improvement of the measures from Mars. 31

Timing of the internal contacts: the black drop effect" Sun Before contact Sun Internal contact Sun Expected Sun ~10 s after lcontact Uncertainty of the contact measurement : 20 s to 1 min. 32

The transit of Venus of June 3 -4, 1769 • The organization of the observations for 1769 were made by Lalande in France and Thomas Hornsby in England. • They took benefit from the observations of the transit of 1761. • 27 refractors were used, only 3 were used in 1761. General circonstances First contact with penumbra : le 3 à 19 h 8 m 31. 2 s First contact with shadow : le 3 à 19 h 27 m 6. 7 s Maximum of the transit : le 3 à 22 h 25 m 20. 3 s Last contact with shadow : le 4 à 1 h 23 m 35. 7 s Last contact with penumbra : le 4 à 1 h 42 m 11. 2 s 33

Visibility of the transit of 1769 34

The results from the transit of 1769 • The English made 69 observations and the French 34. • Finally 151 observations, were made from 77 sites. • Four observations of the complete transit were made : Finland, Hudson Bay, California and Tahiti. Author(s) William Smith Thomas Hornsby Pingré et Lalande Pingré Lalande Planmann Hell Lexell Values 8, 6045" (1770) 8, 78" (1770) 9, 2" et 8, 88" (1770) 8, 80 (1772) 8, 55"< P < 8, 63" (1771) 8, 43 (1772) 8, 70" (1773/1774) 8. 68" (1771) et 8, 63" (1772) The conclusion was that the parallax was from 8, 43" to 8, 80 ". This was a real improvement regarding the result of 1761 providing a parallax from 8, 28 to 10, 60". 35

The transits of the XIXth century 36 • The longitudes are now well determined • The clocks are good time keepers. • The travels are faster (steam, Suez channel). • The travels are still expensive • The photographs appeared (Daguerréotype) • The experiences of the XVIIIth century are profitable.

An example: the observation at St-Paul The voyage of Commandant Mouchez at Saint-Paul. • July 1874 : departure from Paris. • August 9: Suez channel. • August 30: arrival in Réunion Island • September 22: arrival in Saint-Paul island in a tempest The probability of fair weather was only 8 to 10% In spite of tempest and bad weather, the observation was a success: 500 exposures of the transit were made 37

The observation at Saint-Paul 38

The transit of December 9, 1874 39

The transit of 1882 General circonstances Premier contact de la pénombre Premier contact de l'ombre Maximum du passage Dernier contact de l'ombre Dernier contact de la pénombre : : : 13 h 49 m 3. 9 s 14 h 9 m 1. 3 s 17 h 5 m 58. 5 s 20 h 2 m 58. 3 s 20 h 22 m 55. 7 s Les Français organisèrent dix missions : • une mission à l'île d'Haïti (d'Abbadie), • une au Mexique (Bouquet de la Grye), • une à la Martinique (Tisserand, Bigourdan, Puiseux), • une en Floride (Colonel Perrier), • une à Santa-Cruz de Patagonie (Capitaine de Frégate Fleuriais), • une au Chili (Lieutenant de vaisseau de Bernardières) , • une à Chubut (Hatt), • une au Rio-Negro (Perrotin, le directeur de l'observatoire de Nice), • une au Cap Horn (Lieutenant de vaisseau Courcelle-Seneuil), • une à Bragado (Lieutenant de vaisseau Perrin). Le Naval Observatory envoya huit expéditions à travers le monde pour observer le passage. 40

The transit of December 6, 1882 41

Reduction of photographs The measures on the plates were made through macro-micrometers with an accuracy of one micrometer. In France, 1019 plates were taken. All the measurements were made two times by two different persons. In fact more than 500 000 measurements were made. 42

8 June 2004 : How the Venus transit will appear ? 43

Description of a transit • The duration of a Venus transit is from 5 to 8 hours t 3 t 1 t 2 t 4 t 1 : 1 st contact t 2 : 2 nd contact t 3 : 3 rd contact t 4 : 4 th contact t 1, t 4 : exterior contacts t 2, t 3 : interior contacts t 1 t 2 : ingress t 3 t 4 : egress Exterior contacts are not easily observable Interior contacts will be more accurate 44

Geocentric circumstances Celestial pole On Tuesday 8 June Polar angle Ecliptic 5 h 13 m 33, 2 s UTC 8 h 19 m 43, 5 s UTC 5 h 32 m 49, 8 s UTC 11 h 25 m 53, 8 s UTC 11 h 06 m 37, 1 s UTC Duration of the general transit : 6 h 12 m 20, 68 s. Duration of the internal transit : 5 h 33 m 47, 26 s. Minimum of the geocentric angular distance : 10' 26, 875". 45

Local circumstances Sun rise At 3 h 50 m UT POSITION OF THE SUN ON JUNE 8 (PARIS) East Meridian transit at 11 h 49. 7 UT South Beginning of the transit at 5 h 20 m 6 s UT Sun height : 12, 4° Sun azimut : 249, 3° Mid event at 8 h 22 m 53 s UT Sun height : 41, 9° Sun azimut : 283, 5° End of the transit at 11 h 23 m 34 s UT Sun height : 63, 5° Sun azimut : 346, 4° At Paris : T 1 : first external contact at 5 h 20 m 06 s UTC Z=159, 8° T 2 : first internal contact at 5 h 39 m 48. s UTC Z= 164, 2° M : maximum at 8 h 22 m 53 s UT center-center : 10’ 40, 9” T 3 : last internal contact at 11 h 4 m 20 s UTC Z=228, 9° T 4 : last external contact at 11 h 23 m 34 s. UTC Z=225, 0° 46 P= 117, 7° P= 121, 0° P= 212, 4° P=215, 6°

Visibility of the Venus transit on 8 June 2004 47

Mercury transits Apparent diameter of Mercury 1/158 of the Solar diameter 48

Venus Transit in 1882 49

Equatorial mount / alt azimuth mount North celestial pole Direction of at T 4 the celestial pole Zenith at T 1 Parallel to equator Venus trajectory on the solar disk as seen in an equatorial frame (for example in a refractor with an equatorial mount) 50 Parallel to horizon Venus trajectory on the solar disk as seen in an horizontal frame (for example in a refractor with a alt-azimuth mount)

How the Sun-Earth distance will be deduced from the observations ? 51

Calculation of the Sun-Earth distance in 2004 For the VT-2004 observations: • • • Locations (longitudes, latitudes) well known Accurate timing (in Universal time) Pedagogic purpose (AU is well known…) Several calculations will be made: • 1 connexion to the VT-2004 web server = 1 timing observation and 1 estimate of the individual measurement 52 • 2 partners: 2 timing observations from far sites • Analysis of the whole campaign: a large number of timing observations

An approximation for two partners Sun Earth Venus A Δβ D βS B re rv Sheet « Calculating the Earth-Sun distance …» • Assumptions: - Two observing locations, centers of the Earth, Venus, Sun are in the same plane 2 l h R - Circular orbits • Measurement of the distance between two chords (re / rv )3 = (Te / Tv) 2 if eccentricities = 0 βS = Δβ (( re / rv) – 1) re = Δ / (Δβ. 0. 38248) 54 dl = V dt Δβ = dl*l / h

AU online computation Sun f ( φ , X s, X v, π , t ) = Δ s Venu • Relation between time t and parallax π • Observer’s location φ Rs Rv • Theory of Venus • Theory of the Earth (Sun) • Radii Δ • The registered users will send their own timing measurements to the vt 2004 web server (same welcome page as registration) • The server will compute the solution π of the equation : 55 f (φ , X s , X v , π , to ) = R s +/- R v

AU determination: the global analysis • Assuming geographical locations accurately known • N equations of condition can be written (for N timing measurements) involving small corrections δX s , δ X v , δ π , δ R to be calculated a. δXs + b. δ Xv + c. δ π + d. δ(Rs +/-Rv ) = O - C • O – C = offset of each timing O with respect to theoretical calculated value C • « Least square » method • determination of correction δ π to the Solar parallax • All along the data acquisition (starting from June 8), the server will compute the Solar mean horizontal parallax π + d π using all the data gathered • Numerical values (t), statistics and graphs will be produced 56

1770’s parallax measurement Authors Values William Smith (1770) 8. 6045" Thomas Hornsby (1770) 8. 78" Pingré et Lalande (1770) 9. 2" and 8. 88" Pingré (1772) Lalande (1771) between 8. 55" and 8. 63" Planmann (1772) 8. 43" Hell (1773/1774) 8. 70" Lexell (1771 / 1772) 57 8. 80" 8. 68“ / 8. 63"

Parallax measurements since the XVIIIth century 58 Method / author Parallax Transits of 1761 and 1769 8. 43" and 8. 80" Transits of 1761 and 1769, Encke (1824) 8. 5776" Transits of 1761 and 1769, (1835) Parallax of Mars, Hall (1862) Parallax of the asteroid Flora, Galle (1875) Parallax of Mars, Gill (1881) Transits of 1874 and 1882, Newcomb (1890) Parallax of the asteroid Eros, Hinks (1900) Parallax of the asteroid Eros, (1941) Radar measurement, NASA (1990) 8. 571 +/- 0. 037" 8. 841" 8. 873" 8. 78" 8. 79" 8. 806" 8. 790" 8. 79415"

Small historic of the Sun-Earth distance measurement 59 Method date parallax " AU in millions km Mars 1672 9. 5 - 10 130 -140 Venus 1761 1769 8. 3 - 10. 6 8. 5 - 8. 9 125 - 160 145 - 155 Mars 1862 8. 84 149 Flora 1875 8. 87 148 Mars 1885 8. 78 150 Venus 1874 - 82 8. 790 -8. 880 148. 1 - 149. 7 Eros 1900 1930 8. 806 8. 790 149. 4 149. 7 radar 1970 8. 79415 149. 5978 Viking+radar 2000 149. 597 870 691

The Astronomical Unit History of the International Astronomical Union (IAU) value of AU (106 km) 60 • De Sitter 1938 : 149. 453 • Clemence 1948 : 149. 670 • UAI 1964 : 149. 600 • UAI 1976 : 149. 597 870 • DE 102 1977: 149. 597 870 68 • DE 200 1982: 149. 597 870 66 • IERS 1992: 149. 597 870 61 • DE 403 1995: 149. 597 870 691

VT-2004 122 years later …VT-2004 • Large number of observers • Modern techniques (GPS, Internet, webcam images, …) • What results will we get in 2004 ? Credits: aknowledgements to P. Rocher (IMCCE) and F. Mignard (OCA) for several frames 61

Data Acquisition and processing of the amateur observations W. Thuillot & J. E. Arlot • Timings : - database and online processing - global analysis and results • Images : - database and pipeline (Ondrejov) • Access to the data base : 62 - observational inputs - registered observers

Data acquistion Timings measurement -Acquisition web page : same welcome page as « registration » - 1 registration = 1 observation = t 1, t 2, t 3 or t 4 - several instruments several registrations - check your profile (geographic coordinates !) - AU and Solar parallax « observed » compared with the true values - comparison with global results (individual /average, dispersion) - global analysis statistics page 63

Data acquistion Images - data base - Position of Venus with respect to the Solar limb can be used - Field of vue must include the least distance to the limb …and the limb itself 64

VT-2004 AU calculation 65

VT-2004 : Geographic overview 66

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Data acquisition and calculation Still in development, but new pages are in test for a week : try the AU calculation ! ! 69