The Venus transit and the Astronomical Unit calculation

1 Brandys, May 2004 William THUILLOT Institut de mécanique céleste et de calcul des éphémérides 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?

2 5h40 UTC 11h05 UTC

3

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…)

4

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…) • 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)

5

Mechanism

• Mini Solar eclipse • Rare event • Difficult to predict in the past (Kepler 1st) • Rich historical background  fundamental for : - Measuring the Earth-Sun distance (and the AU)

6

Venus visibility

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

7 7 3

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

2 6 1 t (days) 0 4 7 2 8 5 1 6 1 5 2 91 3 182 4 273 3 8 5 365 4 Earth Venus Synodic period 365.25 j 224.70 j 583.92 j 6 456 7 547 8 584

More realistic…

Nœud descendant Venus 8 •

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

Sun .

Noeud ascendant Earth

When transits of Venus can be observed ?

• Need of a close aligment of the Sun, Venus and the Earth (duration up to 8 hours) 10 • 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

11

Short history of the Venus transits

XVIIth, Dec.1631, Dec.1639

XVIIIth, June 1761, June 1769 XIXth Dec. 1874, Dec. 1882

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)

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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).

14

Visibility of the Mercury transit of 1631

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Gassendi in Paris 1631: Mercury transit

Calculation for Paris

hour Sun 2e contact 3e contact (true solar time) 5h 06 10h28 -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, 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

Mercurius in sole visus et venus invisa Parissiis anno 1631.

"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 16 But in England… • J. Horrocks understood that a second transit of Venus occurs 8 years later • With W. Crabtree: organization of the 1639 observations

17

Visibility of the Venus transit of 1639

Observations 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 !

18 Painting of F. M. Brown, visible at the City Hall of Manchester

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First observations of a transit of Venus: J. Horrocks

2e contact 3e contact sunset local time 15h15 21h30 15h50 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 3h15 he continues his observations and the weather became fair

J. Horrocks (

Venus in Sole Visa

) 1639

• He made three measures in a hurry before the sunset 20 t 3h15 3h35 3h45 3h50 distance (") 864 810 780 sunset  Diameter of Venus: 1' 16“ (Kepler : 7’)  Earth-Sun : 94 000 000 km

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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

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Mean horizontal parallax

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

sin

p 0 

R



parallaxe

a

Measurement of p and

R

in order to compute a R = 6400 km and a ~ 150x10 6 Then p ~ 10" km ==> difficult to be measured A main problem in the past

horizontal e moyenne

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Parallax of Mars (perihelic opposition in 1672)

2

R

sin f 2 

D

d Mars d Paris

R

f Cayenne

D

Kepler: a 3 / T 2 = constant (a Mars / a Earth ) 3 = (T Mars / T Earth ) 2 a Earth = a Mars

-

D (Mars-Earth)

Cassini et Richer Flamsteed p s = 9.5" ( a = 138x 10 6 km) p s = 10" ( a = 130x 10 6 km)

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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.

b a • • • c

Method of E. Halley

c b a 25 • • • 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. Delisle

time t Topocentric observation (from the surface of the Earth) D t Use of the timing offset at the beginning or at the end of the 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 !

Requires maximum of timing differences -> longitudes offset

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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 Siberia (successful observation).

(1728-1769) to Tobolsk in • 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 until the next transit in 1769 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 •Joseph-Jérôme Lefrançois de Lalande from Luxembourg Palace in Paris .

(1732-1807 ) observed

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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 able to observe because of clouds. where he was not •Charles Mason (1728-1786), James Bradley 1779) was supposed to observe from and Bencoolen Jeremiah Dixon (1733 observed then at Capetown.

(Sumatra). They were not able to make the observation because the French took the city. They •John Winthrop , professor in Harvard went to last contact of the transit.

St-John (Terre-Neuve) where « surrounded by billions of insects " he succeeded to observe the

Projection de Hammer 29

Le passage du 6 juin 1761

The voyage of Chappe d’Auteroche

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

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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 - the black drop effect the time of the contacts.

of the sites of observation which decreases the precision of the measurement of Disappointing results : no improvement of the measures from Mars.

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

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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 19h 8m 31.2s First contact with shadow : le 3 à 19h 27m 6.7s Maximum of the transit : le 3 à 22h 25m 20.3s

Last contact with shadow : le 4 à 1h 23m 35.7s Last contact with penumbra : le 4 à 1h 42m 11.2s

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Visibility of the transit of 1769

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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) Values William Smith 8,6045" (1770) Thomas Hornsby 8,78" (1770) Pingré et Lalande 9,2" et 8,88" (1770) Pingré 8,80 (1772) Lalande 8,55"< P < 8,63" (1771) Planmann 8,43 (1772) Hell 8,70" (1773/1774) Lexell 8.68" (1771) et 8,63" (1772) The conclusion was that the parallax was from 8,43" to 8,80 real improvement regarding the result of 1761 providing a parallax from 8,28 to 10,60".

" . This was a

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The 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-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

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The observation at Saint-Paul

39

The transit of December 9, 1874

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The transit of 1882

General circonstances Premier contact de la pénombre : 13h 49m 3.9s

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

Les Français organisèrent dix missions : • une mission à l'île d'Haïti (d'Abbadie), • une au Mexique • une à la Martinique • une en Floride • une à Santa-Cruz de Patagonie • une au Chili • une à Chubut (Bouquet de la Grye), (Colonel Perrier), (Lieutenant de vaisseau de Bernardières) , (Hatt), • une au Rio-Negro • une au Cap Horn (Tisserand, Bigourdan, Puiseux), (Capitaine de Frégate Fleuriais), (Perrotin, le directeur de l'observatoire de Nice), (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.

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The transit of December 6, 1882

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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.

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8 June 2004 : How the Venus transit will appear ?

Description of a transit

• The duration of a Venus transit is from 5 to 8 hours 44 t 1 t 2 t 3 t 4 t 1 : t 2 : t 3 : t 4 : 1 st 4 th contact 2 nd contact 3 rd contact 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

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Geocentric circumstances

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

Sun rise At 3h 50m UT East

Local circumstances

POSITION OF THE SUN ON JUNE 8 (PARIS) Meridian transit at 11h 49.7 UT South

46 Beginning of the transit at 5h 20m 6s UT Sun height : 12,4° Sun azimut : 249,3° End of the transit at 11h 23m 34s UT Sun height : 63,5° Sun azimut : 346,4° Mid event at 8h 22m 53s UT Sun height : 41,9° Sun azimut :283,5° At Paris : T1 : first external contact at 5h 20m 06s UTC T2 : first internal contact at 5h 39m 48.s UTC M : maximum at 8h 22m 53s UT center-center : 10’ 40,9” T3 : last internal contact at 11h 4m 20s UTC T4 : last external contact at 11h 23m 34sUTC Z=159,8° P= 117,7° Z= 164,2° P= 121,0° Z=228,9° P= 212,4° Z=225,0° P=215,6°

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Visibility of the Venus transit on 8 June 2004

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Mercury transits

Apparent diameter of Mercury 1/158 of the Solar diameter

49

Venus Transit in 1882

Parallel to equator

Equatorial mount / alt azimuth mount

North celestial pole Direction of the celestial pole at T1 at T4 Zenith

Parallel to horizon 50

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

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

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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 • 2 partners: 2 timing observations from far sites • Analysis of the whole campaign: a large number of timing observations

54 Earth A D B

An approximation for two partners

Sun Venus β S Δβ r e r v

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 (r e / r v ) 3 = (T e / T v ) 2 if eccentricities = 0 β S = Δβ (( r e / r v ) – 1) r e = Δ / (Δβ . 0.38248) 2l h R dl = V dt Δβ = dl*l / h

AU online computation

55 Sun 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 R v R s Δ • 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 , t o ) = R s +/- R v

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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 .

δX s

+

b

.

δ X v

+ c .

δ

π + d .

δ

(R

s

+/-R

v

) = O - C • 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

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1770’s parallax measurement

Authors Values

William Smith (1770) Thomas Hornsby (1770) Pingré et Lalande (1770) Pingré (1772) Lalande (1771) Planmann (1772) Hell (1773/1774) Lexell (1771 / 1772) 8.6045" 8.78" 9.2" and 8.88" 8.80" between 8.55" and 8.63" 8.43" 8.70" 8.68“ / 8.63"

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Parallax measurements since the XVIIIth century

Method / author Parallax

Transits of 1761 and 1769 Transits of 1761 and 1769, Encke (1824) 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) 8.43" and 8.80" 8.5776" 8.571 +/- 0.037" 8.841" 8.873" 8.78" 8.79" 8.806" 8.790" 8.79415"

59 Small historic of the Sun-Earth distance measurement Method date Mars Venus Venus Mars Flora 1672 1761 1769 1862 1875 Mars Venus Eros Eros radar Viking+radar 1885 1874 - 82 1900 1930 1970 2000 parallax " 9.5 - 10 8.3 - 10.6

8.5 - 8.9

8.84

8.87

8.78

8.790-8.880

8.806

8.790

8.79415

AU in millions km 130 -140 125 - 160 145 - 155 149 148 150 148.1 - 149.7

149.4

149.7

149.5978

149.597 870 691

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The Astronomical Unit

History of the International Astronomical Union (IAU) value of AU (10 6 km) • De Sitter • Clemence • UAI • UAI • DE102 • DE200 • IERS • DE403 1938 : 149.453

1948 : 149.670

1964 : 149.600

1976 : 149.597 870 1977: 149.597 870 68 1982: 149.597 870 66 1992: 149.597 870 61 1995: 149.597 870 691

VT-2004

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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

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Data Acquisition

Acquisition and processing of the amateur observations

W. Thuillot & J.E. Arlot

•Timings : •Images : - database and online processing - global analysis and results - database and pipeline (Ondrejov) •Access to the data base : - observational inputs - registered observers

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Data 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 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 calculation

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VT-2004 : Geographic overview

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Data acquisition and calculation

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