1. 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 IMCCE/PARIS Observatory

2. 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?
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…)
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)

5. 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)

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

7. Motion of Venus / Earth… if Venus was in the ecliptic6 2
t (days) 1 4 2 91 7 3
182 3 5 1 8 4
273 5
365 6
456
Earth j
Venus j
Synodic period j 7
547 8
584

8. . More realistic… Orbital inclination (/ecliptic) : 3.4°
Nœud descendant
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
Venus
Earth
Sun .
Noeud ascendant

9. 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 :
Following events: , then in 2117
The 2004 VT will be well observable from Europe

10. Short history of the Venus transits XVIIth, Dec. 1631, Dec
Short history of the Venus transits XVIIth, Dec.1631, Dec XVIIIth, June 1761, June 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)
Kepler ( )

12. and the period of revolution T are linked
Kepler’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).

13. Visibility of the Mercury transit of 1631

14. Gassendi in Paris 1631: Mercury transit
Transit of Mercury on Nov 7, 1631
Calculation for Paris
hour Sun
(true solar time)
2e contact 5h °
3e contact 10h28 +22°
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
"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.

15. 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
With W. Crabtree: organization of the 1639 observations

16. Visibility of the Venus transit of 1639

17. 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 !
Painting of F. M. Brown, visible at the City Hall of Manchester

18. First observations of a transit of Venus: J. Horrocks
Transit of Venus on Dec
local time Sun
2e contact 15h15 + 4°
3e contact 21h °
sunset 15h50
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

19. J. Horrocks (Venus in Sole Visa) 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 : km

20. 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 a R p
Earth
Mean horizontal parallax
Measurement of p and R in order to compute a
R = 6400 km and a ~ 150x106 km
Then p ~ 10" ==> difficult to be measured
A main problem in the past

22. Parallax of Mars (perihelic opposition in 1672)d D
Paris R f
Kepler: a 3 / T 2 = constant
(aMars / a Earth)3 = (TMars / TEarth)2
aEarth = aMars - D (Mars-Earth)
Cayenne
Cassini et Richer ps = 9.5" ( a = 138x 106 km)
Flamsteed ps = 10" ( a = 130x 106 km)

23. 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 a b c• a a • b • 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)

25. Use of the timing offset at the beginning or at the end of the event
Method of J. Delisle Dt
time t
Use of the timing offset at the beginning or at the end of the event
Topocentric observation (from the surface of the Earth)
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

26. 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 ( ) in Vienna (successful observation).
the Abbot Jean-Baptiste Chappe d'Auteroche ( ) 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 ( ),
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 ( ) 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 ( ) went to Sainte-Hélène where he was not able to observe because of clouds.
Charles Mason ( ), James Bradley and Jeremiah Dixon ( ) 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
Internal contact
Sun
Expected
Sun
~10 s after lcontact
Sun
Uncertainty of the contact measurement : 20s 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 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

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

36. 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 : 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 (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 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 t1
t1 : 1st contact t2
t2 : 2nd contact t4
t4 : 4th contact t3
t3 : 3rd contact
t1, t4 : exterior contacts
t2, t3 : interior contacts
t1  t2 : ingress
t3  t4 : egress
Exterior contacts are not easily observable  Interior contacts will be more accurate

44. Geocentric circumstances
Ecliptic
Celestial pole
On Tuesday 8 June
Polar angle
8h 19m 43,5s UTC
5h 13m 33,2s UTC
5h 32m 49,8s 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".

45. Local circumstances East South Sun rise Meridian transit
At 3h 50m UT POSITION OF THE SUN ON JUNE 8 (PARIS) at 11h 49.7 UT
East South
End of the transit
at 11h 23m 34s UT
Sun height : 63,5°
Sun azimut : 346,4°
Beginning of the transit at
5h 20m 6s UT
Sun height : 12,4°
Sun azimut : 249,3°
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 Z=159,8° P= 117,7°
T2 : first internal contact at 5h 39m 48.s UTC Z= 164,2° P= 121,0°
M : maximum at 8h 22m 53s UT center-center : 10’ 40,9”
T3 : last internal contact at 11h 4m 20s UTC Z=228,9° P= 212,4°
T4 : last external contact at 11h 23m 34sUTC Z=225,0° P=215,6°

46. 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
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)
Zenith
Direction of
the celestial pole
at T1
at T4
Parallel to horizon

50. 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
2 partners: 2 timing observations from far sites
Analysis of the whole campaign: a large number of timing observations

52. An approximation for two partners
Sun A B rv re
Venus Δβ D
Earth βS
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 ) R 2l h
dl = V dt
Δβ = dl*l / h

53. AU online computation Sun f ( φ , X s , X v , π , t ) = Δ Venus
R s
R v
Sun
Venus
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

54. 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
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
a .δXs + b .δ Xv + c .δ π + d .δ(Rs +/-Rv ) = O - C
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

55. 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)
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"

56. Parallax 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)
/ "
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)
"

57. Small historic of the Sun-Earth distance measurement
Method date parallax AU in
" millions km
Mars
Venus
Venus
Mars
Flora
Mars
Venus
Eros
Eros
radar
Viking+radar

58. The Astronomical Unit
History of the International Astronomical Union (IAU) value of AU
(106 km)
De Sitter :
Clemence :
UAI :
UAI :
DE :
DE :
IERS :
DE :

59. 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

60. Acquisition and processing of the amateur observations
Data 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

61. 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

62. 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

63. VT-2004 AU calculation

64. VT-2004 : Geographic overview

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