The Venus transit

1

• The Venus transit
• and
• the Astronomical Unit calculation
• William THUILLOT
• Institut de mécanique céleste et
• de calcul des éphémérides
• Brandys, May 2004 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
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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
East Elongation
West of the Sun Morning visibility
East of the Sun Evening visibility
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Motion of Venus / Earth if Venus was in the
ecliptic
t (days)
Earth 365.25 j Venus 224.70 j Synodic
period 583.92 j
8
More realistic

• 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
9
Conjunctions / transits
10
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

11
Short history of the Venus transits XVIIth,
Dec.1631, Dec.1639XVIIIth, June 1761, June
1769XIXth Dec. 1874, Dec. 1882
12
Keplers laws

• Each planet describes an ellipse of which the
  Sun is at one of the focus (1605) - areas 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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Keplers third law

• The semi-major axis a
• and the period of revolution T are linked
• by a3/T2constant
• for all the planets (1618).

14
Visibility of the Mercury transit of 1631
15
Gassendi in Paris 1631 Mercury transit
Calculation for Paris hour Sun
(true solar time) 2e contact 5h 06 -21 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 Keplers predictions
• Three other observations in Europe

16
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 Keplers predictions
• Unobservable in Europe (during night) gt
  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

17
Visibility of the Venus transit of 1639
18
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 !

19
First observations of a transit of Venus J.
Horrocks
local time Sun 2e contact 15h15 4 3e
contact 21h30 - 47 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

20
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 s
unset

• Diameter of Venus 1' 16 (Kepler 7)
• Earth-Sun 94 000 000 km

21
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

22
Mean horizontal parallax

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

Mean horizontal parallax

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

23
Parallax of Mars (perihelic opposition in 1672)
Kepler a 3 / T 2 constant (aMars / a
Earth)3 (TMars / TEarth)2 aEarth aMars - D
(Mars-Earth)
Cassini et Richer ps 9.5" ( a 138x 106 km)
Flamsteed ps 10" ( a 130x 106 km)
24
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 gt no problem with longitude. Method
of Delisle The times of contacts are compared
gt more observations but longitudes have to be
known.
25
Method of E. Halley

• 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 gt Parallax to 1/500
  (Halley, 1716)

26
Method of J. Delisle
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 -gt
  longitudes offset

27
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.

28
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 (1733-1779) 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.

29
Le passage du 6 juin 1761
30
The voyage of Chappe dAuteroche
31
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" lt P lt 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.
32
Timing of the internal contacts the black drop
effect"
Uncertainty of the contact measurement 20s to 1
min.
33
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
34
Visibility of the transit of 1769
35
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"lt P lt 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 " . This was a real improvement
regarding the result of 1761 providing a parallax
from 8,28 to 10,60".
36
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.

37
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

38
The observation at Saint-Paul
39
The transit of December 9, 1874
40
The transit of 1882
General circonstances Premie
r 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.

41
The transit of December 6, 1882
42
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.
43
8 June 2004 How the Venus transit will appear
?
44
Description of a transit

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

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
45
Geocentric circumstances
On Tuesday 8 June
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".
46
Local circumstances
Sun rise Meridian transit At 3h 50m UT POSITION
OF THE SUN ON JUNE 8 (PARIS) at 11h 49.7 UT East
South
At Paris T1 first external contact at 5h 20m
06s UTC Z159,8 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 Z228,9 P 212,4 T4
last external contact at 11h 23m
34sUTC Z225,0 P215,6
47
Visibility of the Venus transit on 8 June 2004
48
Mercury transits
Apparent diameter of Mercury 1/158 of the Solar
diameter
49
Venus Transit in 1882
50
Equatorial mount / alt azimuth mount
51
How the Sun-Earth distance will be deduced from
the observations ?
52
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

53
Full parallax effect

• Far from the meridian, parallax effect is not
  simple
• Sun rising the planet is late
• Sun setting the planet is in advance

54
An approximation for two partners
Sun

• 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
• ßS ?ß (( re / rv) 1)
• re ? / (?ß . 0.38248)

dl V dt ?ß dll / h
55
AU online computation
f ( f , X s , X v , p , t ) ?

• Relation between time t and parallax p
• Observers location f
• 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 p of the
  equation
• f (f , X s , X v , p , to ) R s /- R v

56
AU determination the global analysis

• Assuming geographical locations accurately known
• N equations of condition can be written (for N
  timing measurements) involving small corrections
  dX s , d X v , d p , d 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 d p to the Solar
  parallax

a .dXs b .d Xv c .d p d .d(Rs /-Rv )
O - C

• All along the data acquisition (starting from
  June 8), the server will compute the Solar mean
  horizontal parallax p d p using all the data
  gathered
• Numerical values (t), statistics and graphs will
  be produced

57
1770s parallax measurement
58
Parallax measurements since the XVIIIth century
59
Small historic of the Sun-Earth distance
measurement
60
The Astronomical Unit
History of the International Astronomical Union
(IAU) value of AU

• (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

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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
62
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

63
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

64
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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(No Transcript)
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(No Transcript)
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Data acquisition and calculation

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