1

The Venus transit and

the Astronomical Unit calculation

William THUILLOT

Institut de mécanique céleste etde calcul des éphémérides

Brandys, May 2004 IMCCE/PARIS Observatory

2

The transit of June 8, 2004The 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?

5h40 UTC

11h05 UTC

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The VT-2004 projectThe 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…)

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The VT-2004 project 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:

amateurs - schools amateurs – individuals

• succeeding in the measurement of the Earth-Sun distance (…and of the AU)

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Mechanism Mechanism

• Mini Solar eclipse

• Rare event

• Difficult to predict in the past (Kepler 1st)

• Rich historical background

fundamental for :

- Confirming the superiority of the Copernician model (Rudolphines Tables)

- Measuring the Earth-Sun distance (and the AU)

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Venus visibility Venus visibility

Fixed EarthFixed Earth

SunSun

Inferior conjunctionInferior conjunction

Crescent after Crescent after the inferior conjunctionthe inferior conjunction

West elongationWest elongation

Gibbous phaseGibbous phaseGibbous phaseGibbous phase

Superior conjunctionSuperior conjunction

East East ElongationElongation

Crescent before Crescent before The inferior conjunctionThe inferior conjunction

East of the SunEast of the SunEvening visibilityEvening visibility

East of the SunEast of the SunEvening visibilityEvening visibility

West of the SunWest of the SunMorning visibilityMorning visibility

West of the SunWest of the SunMorning visibilityMorning visibility

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Motion of Venus / Earth… Motion of Venus / Earth… if Venus was in the ecliptic

t (days)

1 0

8 584

EarthEarth 365.25 j365.25 j

VenusVenus 224.70 j224.70 j

Synodic periodSynodic period 583.92 j583.92 j

EarthEarth 365.25 j365.25 j

VenusVenus 224.70 j224.70 j

Synodic periodSynodic period 583.92 j583.92 j

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2

22 91

3 182

4

4

8

84 273

5

5

5 365

6

6

6 456

7

73

3

7 547

8Noeud ascendant

Nœud descendant

More realistic…More realistic…

Earth

Venus

.Sun

• Orbital inclination (/ecliptic) : 3.4°

• Venus at Nodes :

- 7 December (ascending node)

- 5 June (descending node)

• Conditions for a transit :

- conjunction Sun- Venus - Earth (584 d.)

- close to a node

• Rare events

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When transits of Venus can be observed ? 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

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Short history of the Venus transitsShort history of the Venus transits

XVIIth, Dec.1631, Dec.1639XVIIth, Dec.1631, Dec.1639

XVIIIth, June 1761, June 1769XVIIIth, June 1761, June 1769

XIXth Dec. 1874, Dec. 1882XIXth Dec. 1874, Dec. 1882

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Kepler’s lawsKepler’s laws

Kepler (1571-1630)

• 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)

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Kepler’s third lawKepler’s third law

The semi-major axis a and the period of revolution T are linked

by a3/T2=constant for all the planets (1618).

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Visibility of the Mercury transit of 1631Visibility of the Mercury transit of 1631

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Gassendi in Paris 1631: Mercury transitGassendi in Paris 1631: Mercury transit

• 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, Gassendi saw a black spot

– Measured diameter of Mercury : 20" (true value : 10")

• Error of 5h from the Kepler’s predictions

• Three other observations in Europe

Transit of Mercury on Nov 7, 1631

Calculation for Paris hour Sun

(true solar time)

2e contact 5h 06 -21°3e contact 10h28 +22°

"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 "

Mercurius in sole visus et venus invisa Parissiis anno 1631.

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Gassendi in Paris 1631: Vénus transitGassendi 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

• With W. Crabtree: organization of the 1639 observations

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Visibility of the Venus transit of 1639Visibility of the Venus transit of 1639

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Observations of W. Crabtree 1639Observations of W. Crabtree 1639

• Observations made at Manchester

• Cloudy until 3h35 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

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First observations of a transit of Venus: J. HorrocksFirst observations of a transit of Venus: J. Horrocks

• 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 3h15 he continues his observations and the weather became fair

Transit of Venus on Dec 4. 1639

local time Sun2e contact 15h15 + 4°3e contact 21h30 - 47°sunset 15h50

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J. Horrocks (J. Horrocks (Venus in Sole VisaVenus in Sole Visa) 1639) 1639

• He made three measures in a hurry before the sunset

t distance (")

3h15 864

3h35 810

3h45 780

3h50 sunset

Diameter of Venus: 1' 16“ (Kepler : 7’)

Earth-Sun : 94 000 000 km

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Transits during the XVIIIth centuryTransits 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

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Mean horizontal parallaxMean horizontal parallax

aR

Earth

• The Sun-Earth distance cannot be directly measured• Classical astronomy measures angles

moyenne ehorizontalparallaxesin 0 a

R

• Measurement of and R in order to compute a• R = 6400 km and a ~ 150x106 km• Then ~ 10" ==> difficult to be measured• A main problem in the past

Mean horizontal parallax

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Parallax of Mars (perihelic opposition in 1672)Parallax of Mars (perihelic opposition in 1672)

Cayenne

Paris

R

D

DR

2sin2

Mars

Cassini et Richer s = 9.5" ( a = 138x 106 km)

Flamsteed s = 10" ( a = 130x 106 km)

Cassini et Richer s = 9.5" ( a = 138x 106 km)

Flamsteed s = 10" ( a = 130x 106 km)

Kepler: a 3 / T 2 = constant

(aMars / a Earth)3 = (TMars / TEarth)2

aEarth = aMars - D (Mars-Earth)

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Transits during the XVIIIth centuryTransits 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 :Two methods for measuring the parallax :

Method of Halley :Method of Halley : The durations of the transits are compared => no problem with The durations of the transits are compared => no problem with longitude.longitude.

Method of Delisle :Method of Delisle :The times of contacts are compared => more observations but The times of contacts are compared => more observations but longitudes have to be known.longitudes have to be known.

Two methods for measuring the parallax :Two methods for measuring the parallax :

Method of Halley :Method of Halley : The durations of the transits are compared => no problem with The durations of the transits are compared => no problem with longitude.longitude.

Method of Delisle :Method of Delisle :The times of contacts are compared => more observations but The times of contacts are compared => more observations but longitudes have to be known.longitudes have to be known.

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Method of E. HalleyMethod of E. Halley

•a a

•b

b

•c

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

• Requires observing sites far from each other latitudes offset

– 1 s. of uncertainty ==> Parallax to 1/500 (Halley, 1716)

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Method of J. DelisleMethod of J. Delisle

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 !

• Requires maximum of timing differences -> longitudes offset

Geocentric view

Topocentric observation (from the surface of the Earth)

ttime t Use of the timing

offset at the

beginning or at the

end of the event

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The transit of June 6, 1761The transit of June 6, 1761

• ExpeditionsExpeditions for the observation: 2 of these voyages took place in for the observation: 2 of these voyages took place in countries allied of France.countries allied of France.

• César-François Cassini de ThuryCésar-François Cassini de Thury (1714-1784) in (1714-1784) in Vienna Vienna (successful observation). (successful observation).

• the Abbot Jean-Baptiste Chappe d'Auterochethe Abbot Jean-Baptiste Chappe d'Auteroche (1728-1769) to (1728-1769) to Tobolsk in Tobolsk in SiberiaSiberia (successful observation). (successful observation).

• Alexandre Guy PingréAlexandre Guy Pingré : : Rodrigues IslandRodrigues Island (north of Madagascar), (north of Madagascar), Thanks to the compagnie des Indes (observation partially successful). Thanks to the compagnie des Indes (observation partially successful).

• Guillaume Joseph Hyacinthe Jean-Batiste Le Gentil de La GalaisièreGuillaume Joseph Hyacinthe Jean-Batiste Le Gentil de La Galaisière (1725-1792), (1725-1792), left by sea in order to observe the transit left by sea in order to observe the transit in Indies at Pondichéryin Indies at Pondichéry. . Unfortunately the city of Pondichéry was taken by the English and he 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 saw the transit from the ship, unable to make a measurement; he decided to wait until the next transit in 1769until the next transit in 1769

•Joseph-Jérôme Lefrançois de LalandeJoseph-Jérôme Lefrançois de Lalande (1732-1807 (1732-1807) ) observed observed fromfrom Luxembourg Palace in Paris Luxembourg Palace in Paris..

The FrenchThe French

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The transit of June 6, 1761The transit of June 6, 1761

The EnglishThe English

two campaignstwo campaigns far from England to observe the event. far from England to observe the event.

• Nevil MaskelyneNevil Maskelyne (1732-1811) went to (1732-1811) went to Sainte-HélèneSainte-Hélène where he where he was not able to observe because of clouds. was not able to observe because of clouds.

•Charles MasonCharles Mason (1728-1786), (1728-1786), James BradleyJames Bradley and and Jeremiah DixonJeremiah Dixon (1733-1779) was supposed to observe from (1733-1779) was supposed to observe from BencoolenBencoolen (Sumatra). (Sumatra). They were not able to make the observation because the French They were not able to make the observation because the French took the city. They observed then at Capetown.took the city. They observed then at Capetown.

•John WinthropJohn Winthrop, professor in Harvard went to , professor in Harvard went to St-John (Terre-Neuve)St-John (Terre-Neuve) where « surrounded by billions of insects " he succeeded to where « surrounded by billions of insects " he succeeded to observe the last contact of the transit.observe the last contact of the transit.

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Le passage du 6 juin 1761Le passage du 6 juin 1761

Projection de HammerProjection de Hammer

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The voyage of Chappe d’AuterocheThe voyage of Chappe d’Auteroche

The travel of Chappe d’Auteroche to Tobol’skThe travel of Chappe d’Auteroche to Tobol’sk

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Results from the transit of 1761Results from the transit of 1761

• The number of observers was The number of observers was 120120, on , on 62 sites62 sites (S. Newcomb, 1959). (S. Newcomb, 1959).

• Note that some sites of observations were previously selected Note that some sites of observations were previously selected (Bencoolen, Pondichéry, Batavia) by Halley in 1716.(Bencoolen, Pondichéry, Batavia) by Halley in 1716.

The large error is due to:The large error is due to:- a bad knowledge of the longitudes- a bad knowledge of the longitudes of the sites of observation of the sites of observation - the - the black drop effectblack drop effect which decreases the precision of the which decreases the precision of the measurement of the time of the contacts.measurement of the time of the contacts.

8.5" < 8.5" < < 10.5" < 10.5"

Disappointing results : no improvement of the measures Disappointing results : no improvement of the measures from Mars.from Mars.

Disappointing results : no improvement of the measures Disappointing results : no improvement of the measures from Mars.from Mars.

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Timing of the internal contacts: the black drop effect"Timing of the internal contacts: the black drop effect"

Expected

Sun

Uncertainty of the contact measurement : 20s to 1 min.

Internal contact

Sun

~10 s after lcontact

SunSun

Before contact

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The transit of Venus of June 3-4, 1769The transit of Venus of June 3-4, 1769

• The organization of the observations for 1769 were made by The organization of the observations for 1769 were made by Lalande in France and Thomas Hornsby in England. Lalande in France and Thomas Hornsby in England. • They took benefit from the observations of the transit of 1761.They took benefit from the observations of the transit of 1761.

•27 refractors were used, only 3 were used in 1761.27 refractors were used, only 3 were used in 1761.

General circonstancesGeneral circonstancesFirst contact with penumbra : le 3 à 19h 8m 31.2s First contact with penumbra : le 3 à 19h 8m 31.2s First contact with shadow : le 3 à 19h 27m 6.7s First contact with shadow : le 3 à 19h 27m 6.7s Maximum of the transit : le 3 à 22h 25m 20.3sMaximum of the transit : le 3 à 22h 25m 20.3sLast contact with shadow : le 4 à 1h 23m 35.7s Last contact with shadow : le 4 à 1h 23m 35.7s Last contact with penumbra : le 4 à 1h 42m 11.2sLast contact with penumbra : le 4 à 1h 42m 11.2s

General circonstancesGeneral circonstancesFirst contact with penumbra : le 3 à 19h 8m 31.2s First contact with penumbra : le 3 à 19h 8m 31.2s First contact with shadow : le 3 à 19h 27m 6.7s First contact with shadow : le 3 à 19h 27m 6.7s Maximum of the transit : le 3 à 22h 25m 20.3sMaximum of the transit : le 3 à 22h 25m 20.3sLast contact with shadow : le 4 à 1h 23m 35.7s Last contact with shadow : le 4 à 1h 23m 35.7s Last contact with penumbra : le 4 à 1h 42m 11.2sLast contact with penumbra : le 4 à 1h 42m 11.2s

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Visibility of the transit of 1769Visibility of the transit of 1769

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The results from the transit of 1769The results from the transit of 1769

• The English made 69 observations and the French 34. The English made 69 observations and the French 34.

• Finally Finally 151 observations151 observations, were made from , were made from 77 sites77 sites. .

• Four observations of the complete transit were made : Finland, Hudson Four observations of the complete transit were made : Finland, Hudson Bay, California and Tahiti.Bay, California and Tahiti.

Author(s) ValuesAuthor(s) ValuesWilliam Smith 8,6045" (1770) William Smith 8,6045" (1770) Thomas Hornsby 8,78" (1770) Thomas Hornsby 8,78" (1770) Pingré et Lalande 9,2" et 8,88" (1770) Pingré et Lalande 9,2" et 8,88" (1770) Pingré 8,80 (1772) Pingré 8,80 (1772) Lalande 8,55"< P < 8,63" (1771) Lalande 8,55"< P < 8,63" (1771) Planmann 8,43 (1772) Planmann 8,43 (1772) Hell 8,70" (1773/1774) Hell 8,70" (1773/1774) Lexell 8.68" (1771) et 8,63" (1772) Lexell 8.68" (1771) et 8,63" (1772)

Author(s) ValuesAuthor(s) ValuesWilliam Smith 8,6045" (1770) William Smith 8,6045" (1770) Thomas Hornsby 8,78" (1770) Thomas Hornsby 8,78" (1770) Pingré et Lalande 9,2" et 8,88" (1770) Pingré et Lalande 9,2" et 8,88" (1770) Pingré 8,80 (1772) Pingré 8,80 (1772) Lalande 8,55"< P < 8,63" (1771) Lalande 8,55"< P < 8,63" (1771) Planmann 8,43 (1772) Planmann 8,43 (1772) Hell 8,70" (1773/1774) Hell 8,70" (1773/1774) Lexell 8.68" (1771) et 8,63" (1772) Lexell 8.68" (1771) et 8,63" (1772)

The conclusion was that the parallax was from 8,43" to 8,80 The conclusion was that the parallax was from 8,43" to 8,80 "" . This . This was a real improvement regarding the result of 1761 providing a was a real improvement regarding the result of 1761 providing a parallax from 8,28 to 10,60".parallax from 8,28 to 10,60".

The conclusion was that the parallax was from 8,43" to 8,80 The conclusion was that the parallax was from 8,43" to 8,80 "" . This . This was a real improvement regarding the result of 1761 providing a was a real improvement regarding the result of 1761 providing a parallax from 8,28 to 10,60".parallax from 8,28 to 10,60".

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The transits of the XIXth centuryThe transits of the XIXth century

• 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.

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An example: the observation at St-PaulAn example: the observation at St-Paul

•July 1874 : departure from Paris.July 1874 : departure from Paris.•August 9: Suez channel.August 9: Suez channel.•August 30: arrival in Réunion IslandAugust 30: arrival in Réunion Island•September 22: arrival in Saint-Paul island in a tempestSeptember 22: arrival in Saint-Paul island in a tempest

The probability of fair weather was only 8 to 10%The probability of fair weather was only 8 to 10%

In spite of tempest and bad weather, the observation was a In spite of tempest and bad weather, the observation was a success: 500 exposures of the transit were madesuccess: 500 exposures of the transit were made

The voyage of The voyage of Commandant Mouchez at Saint-PaulCommandant Mouchez at Saint-Paul..

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The observation at Saint-PaulThe observation at Saint-Paul

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The transit of December 9, 1874The transit of December 9, 1874

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The transit of 1882The transit of 1882

General circonstancesGeneral circonstances

Premier contact de la pénombre : 13h 49m 3.9sPremier contact de la pénombre : 13h 49m 3.9sPremier contact de l'ombre : 14h 9m 1.3s Premier contact de l'ombre : 14h 9m 1.3s Maximum du passage : 17h 5m 58.5s Maximum du passage : 17h 5m 58.5s Dernier contact de l'ombre : 20h 2m 58.3s Dernier contact de l'ombre : 20h 2m 58.3s Dernier contact de la pénombre : 20h 22m 55.7sDernier contact de la pénombre : 20h 22m 55.7s

General circonstancesGeneral circonstances

Premier contact de la pénombre : 13h 49m 3.9sPremier contact de la pénombre : 13h 49m 3.9sPremier contact de l'ombre : 14h 9m 1.3s Premier contact de l'ombre : 14h 9m 1.3s Maximum du passage : 17h 5m 58.5s Maximum du passage : 17h 5m 58.5s Dernier contact de l'ombre : 20h 2m 58.3s Dernier contact de l'ombre : 20h 2m 58.3s Dernier contact de la pénombre : 20h 22m 55.7sDernier contact de la pénombre : 20h 22m 55.7s

Les Français organisèrent Les Français organisèrent dix missionsdix missions : : • une mission à une mission à l'île d'Haïtil'île d'Haïti (d'Abbadie), (d'Abbadie), • une au une au MexiqueMexique (Bouquet de la Grye), (Bouquet de la Grye), • une à la une à la MartiniqueMartinique (Tisserand, Bigourdan, Puiseux), (Tisserand, Bigourdan, Puiseux), • une en une en FlorideFloride (Colonel Perrier), (Colonel Perrier), • une à une à Santa-Cruz de PatagonieSanta-Cruz de Patagonie (Capitaine de Frégate Fleuriais), (Capitaine de Frégate Fleuriais), • une au une au ChiliChili (Lieutenant de vaisseau de Bernardières) , (Lieutenant de vaisseau de Bernardières) , • une à une à ChubutChubut (Hatt), (Hatt), • une au une au Rio-NegroRio-Negro (Perrotin, le directeur de l'observatoire de Nice), (Perrotin, le directeur de l'observatoire de Nice), • une au une au Cap HornCap Horn (Lieutenant de vaisseau Courcelle-Seneuil), (Lieutenant de vaisseau Courcelle-Seneuil),• une à une à Bragado Bragado (Lieutenant de vaisseau Perrin).(Lieutenant de vaisseau Perrin).

Le Naval Observatory envoya Le Naval Observatory envoya huit expéditionshuit expéditions à travers le monde pour observer le passage. à travers le monde pour observer le passage.

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The transit of December 6, 1882The transit of December 6, 1882

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Reduction of photographsReduction of photographs

The measures on the plates were made through macro-The measures on the plates were made through macro-micrometers with an accuracy of one micrometer.micrometers with an accuracy of one micrometer.In France, 1019 plates were taken. All the measurements were In France, 1019 plates were taken. All the measurements were made two times by two different persons.made two times by two different persons.In fact more than In fact more than 500 000 measurements500 000 measurements were made. were made.

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8 June 2004 : 8 June 2004 :

How the Venus transit will appear ?How the Venus transit will appear ?

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Description of a transitDescription of a transit

• The duration of a Venus transit is from 5 to 8 hours

t1, t4 : exterior contacts

t2, t3 : interior contacts

Exterior contacts are not easily observable Exterior contacts are not easily observable Interior contacts will be more accurate Interior contacts will be more accurate

t1

t1 : 1st contact

t2

t2 : 2nd contact

t3t3 : 3rd contact

t4

t4 : 4th contact

t1 t2 : ingress

t3 t4 : egress

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EclipticEcliptic

Celestial poleCelestial pole

Geocentric circumstancesGeocentric circumstances

5h 13m 33,2s UTC5h 13m 33,2s UTC

5h 32m 49,8s UTC5h 32m 49,8s UTC11h 25m 53,8s UTC11h 25m 53,8s UTC

11h 06m 37,1s UTC11h 06m 37,1s UTC

8h 19m 43,5s UTC8h 19m 43,5s UTC

Polar anglePolar angle

Duration of the general transit : 6h 12m 20,68s. Duration of the general transit : 6h 12m 20,68s. Duration of the internal transit : 5h 33m 47,26s. Duration of the internal transit : 5h 33m 47,26s. Minimum of the geocentric angular distance : 10' 26,875".Minimum of the geocentric angular distance : 10' 26,875".

Duration of the general transit : 6h 12m 20,68s. Duration of the general transit : 6h 12m 20,68s. Duration of the internal transit : 5h 33m 47,26s. Duration of the internal transit : 5h 33m 47,26s. Minimum of the geocentric angular distance : 10' 26,875".Minimum of the geocentric angular distance : 10' 26,875".

On Tuesday 8 JuneOn Tuesday 8 June

46

Local circumstancesLocal circumstances

Mid event at Mid event at 8h 22m 53s UT8h 22m 53s UTSun height : 41,9°Sun height : 41,9°Sun azimut :283,5° Sun azimut :283,5°

End of the transit End of the transit at 11h 23m 34s UTat 11h 23m 34s UTSun height : 63,5°Sun height : 63,5°Sun azimut : 346,4°Sun azimut : 346,4°

Beginning of the transit at Beginning of the transit at 5h 20m 6s UT5h 20m 6s UTSun height : 12,4°Sun height : 12,4°Sun azimut : 249,3°Sun azimut : 249,3°

At Paris :At Paris :T1 : first external contact at 5h 20m 06s UTCT1 : first external contact at 5h 20m 06s UTC Z=159,8° Z=159,8° P= 117,7°P= 117,7°T2 : first internal contact at 5h 39m 48.s UTC T2 : first internal contact at 5h 39m 48.s UTC Z= 164,2°Z= 164,2° P= 121,0°P= 121,0°M : maximum at 8h 22m 53s UT center-center : 10’ 40,9”M : maximum at 8h 22m 53s UT center-center : 10’ 40,9”T3 : last internal contact at 11h 4m 20s UTC T3 : last internal contact at 11h 4m 20s UTC Z=228,9°Z=228,9° P= 212,4°P= 212,4°T4 : last external contact at 11h 23m 34sUTCT4 : last external contact at 11h 23m 34sUTC Z=225,0° Z=225,0° P=215,6°P=215,6°

At Paris :At Paris :T1 : first external contact at 5h 20m 06s UTCT1 : first external contact at 5h 20m 06s UTC Z=159,8° Z=159,8° P= 117,7°P= 117,7°T2 : first internal contact at 5h 39m 48.s UTC T2 : first internal contact at 5h 39m 48.s UTC Z= 164,2°Z= 164,2° P= 121,0°P= 121,0°M : maximum at 8h 22m 53s UT center-center : 10’ 40,9”M : maximum at 8h 22m 53s UT center-center : 10’ 40,9”T3 : last internal contact at 11h 4m 20s UTC T3 : last internal contact at 11h 4m 20s UTC Z=228,9°Z=228,9° P= 212,4°P= 212,4°T4 : last external contact at 11h 23m 34sUTCT4 : last external contact at 11h 23m 34sUTC Z=225,0° Z=225,0° P=215,6°P=215,6°

Sun rise Meridian transit

At 3h 50m UT POSITION OF THE SUN ON JUNE 8 (PARIS) at 11h 49.7 UT

East South

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Visibility of the Venus transit on 8 June 2004Visibility of the Venus transit on 8 June 2004

48

Mercury transitsMercury transits

Apparent diameter of Mercury 1/158 of the Solar diameter

49

Venus Transit in 1882Venus Transit in 1882

50

Equatorial mount / alt azimuth mountEquatorial mount / alt azimuth mount

Venus trajectory on the solar disk as seen in an equatorial frame (for example in a refractor with an equatorial mount)

North celestial pole

Parallel to equator

Venus trajectory on the solar disk as seen in an horizontal frame (for example in a refractor with a alt-azimuth mount)

ZenithDirection of

the celestial pole

at T1

at T4

Parallel to horizon

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

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Calculation of the Sun-Earth distance in 2004Calculation 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

• 2 partners: 2 timing observations from far sites

• Analysis of the whole campaign: a large number of timing observations

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An approximation for two partnersAn approximation for two partnersSun

R2l

h

Sheet « Calculating the Earth-Sun distance …»

• Assumptions:

- Two observing locations, centers of the Earth, Venus, Sun are in the same plane

- 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)

A

B

rv

re

VenusΔβ

Earth

βS

dl = V dt

Δβ = dl*l / h

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AU online computationAU online computation

f ( φ , X s , X v , π , t ) = Δ

• Relation between time t and parallax π

• Observer’s location φ

• Theory of Venus

• Theory of the Earth (Sun)

• Radii

• The registered users will send their own timing measurements to the vt2004 web server (same welcome page as registration)

• The server will compute the solution π of the equation :

f (φ , X s , X v , π , to ) = R s +/- R v

Δ

R sR v

Sun

Venus

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AU determination: the global analysisAU 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

• O – C = offset of each timing O with respect to the 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

a .δXs + b .δ Xv + c .δ π + d .δ(Rs +/-Rv ) = O - C

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1770’s parallax measurement1770’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) 8.80"

Lalande (1771) between 8.55" and 8.63"

Planmann (1772) 8.43"

Hell (1773/1774) 8.70"

Lexell (1771 / 1772) 8.68“ / 8.63"

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Parallax measurements since the XVIIIth centuryParallax measurements since the XVIIIth century

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) 8.571 +/- 0.037"

Parallax of Mars, Hall (1862) 8.841"

Parallax of the asteroid Flora, Galle (1875) 8.873"

Parallax of Mars, Gill (1881) 8.78"

Transits of 1874 and 1882, Newcomb (1890) 8.79"

Parallax of the asteroid Eros, Hinks (1900) 8.806"

Parallax of the asteroid Eros, (1941) 8.790"

Radar measurement, NASA (1990) 8.79415"

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Small historic of the Sun-Earth distance measurementSmall historic of the Sun-Earth distance measurement

Method date parallax AU in " millions km

Mars 1672 9.5 - 10 130 -140

Venus 1761 8.3 - 10.6 125 - 160Venus 1769 8.5 - 8.9 145 - 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 8.806 149.4Eros 1930 8.790 149.7

radar 1970 8.79415 149.5978

Viking+radar 2000 149.597 870 691

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The Astronomical UnitThe Astronomical Unit

(106 km)

• De Sitter 1938 : 149.453

• Clemence 1948 : 149.670

• UAI 1964 : 149.600

• UAI 1976 : 149.597 870

• DE102 1977: 149.597 870 68

• DE200 1982: 149.597 870 66

• IERS 1992: 149.597 870 61

• DE403 1995: 149.597 870 691

History of the International Astronomical Union (IAU) value of AU

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VT-2004VT-2004

Credits: aknowledgements to P. Rocher (IMCCE) and F. Mignard (OCA) for several frames

122 years later …VT-2004

• Large number of observers

• Modern techniques (GPS, Internet, webcam images, …)

• What results will we get in 2004 ?

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Data AcquisitionData Acquisition

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 : - observational inputs - registered observers

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Data acquistionData acquistion

Timings measurement

-Acquisition web page : same welcome page as « registration »

- 1 registration = 1 observation = t1, t2, t3 or t4

- 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

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Data acquistionData 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

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VT-2004 AU calculationVT-2004 AU calculation

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VT-2004 : Geographic overviewVT-2004 : Geographic overview

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Data acquisition and calculationData acquisition and calculation

Still in development,but new pages are in test for a week :

try the AU calculation ! !