The Venus transit
and
the Astronomical Unit calculation
William THUILLOT
Institut de mécanique céleste et
de calcul des éphémérides
Brandys, May 2004
1
IMCCE/PARIS Observatory
The transit of June 8, 2004
On June 8, 2004, the planet Venus will pass in front of the Sun. Nobody
alive today has seen such an event.
Why does this event occur ?
Why did it retain the attention of the astronomers in the past?
What results can we expect?
5h40 UTC
11h05 UTC
2
The VT-2004 project
• Coordinated observations of a rare phenomenon
• Educational interest (wide public, schools)
• Measurements « easy » to make: timings
• Possibility to catch images (if experience…)
3
The VT-2004 project
Educational interest
• Historical background closely related to the
measurement of the Solar System (methods,
distances, motions of the celestial bodies,
exoplanets…)
• preparation of a scientific experiment and
measurements with some scientific value
• Interest of exchanging information between
participants , in particular:
amateurs - schools
amateurs – individuals
• succeeding in the measurement of the Earth-Sun
distance (…and of the AU)
4
Mechanism
• Mini Solar eclipse
• Rare event
• Difficult to predict in the past (Kepler 1st)
• Rich historical background
 fundamental for :
- Confirming the superiority of the Copernician
model (Rudolphines Tables)
- Measuring the Earth-Sun distance (and the AU)
5
Venus visibility
Gibbous phase
Superior conjunction
Gibbous phase
Sun
West elongation
East
Elongation
Crescent before
The inferior conjunction
Inferior conjunction
Crescent after
the inferior conjunction
West of the Sun
Morning visibility
East of the Sun
Evening visibility
Fixed Earth
6
Motion of Venus / Earth… if Venus was in the ecliptic
2 6
t (days)
1
0
2
91
3
182
4
273
5
365
6
456
7
547
8
584
4
2
7
7
6
1
3
8
5
3
8
4
7
1 5
Earth
365.25 j
Venus
224.70 j
Synodic period
583.92 j
More realistic…
Nœud descendant
Venus
• Orbital inclination (/ecliptic) : 3.4°
• Venus at Nodes :
Sun
.
Earth
- 7 December (ascending node)
- 5 June (descending node)
• Conditions for a transit :
- conjunction Sun- Venus - Earth (584 d.)
- close to a node
•  Rare events
8
Noeud ascendant
When transits of Venus can be observed ?
• Need of a close aligment of the Sun, Venus and the Earth
(duration up to 8 hours)
• Very rare events (~ every 120 years, and 8 years after):
- Last events : 1874-1882
- Following events: 2004 - 2012, then in 2117
• The 2004 VT will be well observable from Europe
10
Short history of the Venus transits
XVIIth, Dec.1631, Dec.1639
XVIIIth, June 1761, June 1769
XIXth Dec. 1874, Dec. 1882
11
Kepler’s laws
• Each planet describes an ellipse of which the Sun is at one of the
focus (1605) - area’s law – law related to the ratios of semi-major axis
• 1627 : Rudolphines Tables
• 1629: prediction of a transit of Mercury (november 1631)
• more…: prediction of a transit of Venus (december 1631)
12
Kepler (1571-1630)
Kepler’s third law
The semi-major axis a
and the period of revolution T are linked
by a3/T2=constant
for all the planets (1618).
13
Visibility of the Mercury transit of 1631
14
Gassendi in Paris 1631: Mercury transit
Calculation for Paris
hour
Sun
(true solar time)
2e contact
3e contact
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.
15
"Le rusé Mercure voulait passer sans être aperçu, il était entré plus tôt
qu'on ne s'y attendait, mais il n'a pu s'échapper sans être découvert "
Gassendi in Paris 1631: Vénus transit
•
Gassendi tried also to observe the 1631 Venus transit
•
Main purpose: to check the Rudolphines Tables (Copernic system)
•
Error of the Kepler’s predictions
•
Unobservable : in Europe (during night) => America
•
Unsuccessful observation of the 1631 Venus transit by Gassendi
But in England…
•
J. Horrocks understood that a second transit of Venus occurs 8
years later
•
16
With W. Crabtree: organization of the 1639 observations
Visibility of the Venus transit of 1639
17
Observations of W. Crabtree 1639
•
Observations made at Manchester
•
Cloudy until 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
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
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“
Earth-Sun : 94 000 000 km
20
(Kepler : 7’)
Transits during the XVIIIth century
• A fundamental question :
– the determination of the Solar parallax
• 1672 : Richer and Cassini (I) : Opposition of Mars
• 1677 : Halley observes a Mercury transit (St Helen Island)
• 1691: he presents a method to get the Solar parallax from
the Venus transits
• 1716 : he call for observations for the next Venus transit
• 
21
expeditions
Mean horizontal parallax
•
•
The Sun-Earth distance cannot be directly measured
Classical astronomy measures angles
R
a
p
Earth
R
sin p 0 
a
22
 Mean
parallaxe
horizontal
e moyenne
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
Parallax of Mars (perihelic opposition in 1672)
2 R sin
f
2
 Dd
Mars
d
Paris
R
Kepler: a 3 / T 2 = constant
f
Cayenne
D
(aMars / a Earth)3 = (TMars / TEarth)2
aEarth = aMars - D (Mars-Earth)
23
Cassini et Richer
ps = 9.5" ( a = 138x 106 km)
Flamsteed
ps = 10"
( a = 130x 106 km)
Transits during the XVIIIth century
•
Halley died in 1742 but astronomers remember his call for observations
•
•
•
•
•
Longitudes are not yet well known.
Clocks are not good time keepers.
Traveling is slow (sailing).
Voyages are very expensive.
Nobody has never observed a transit of Venus.
Two methods for measuring the parallax :
Method of Halley :
The durations of the transits are compared => no problem with longitude.
Method of Delisle :
The times of contacts are compared => more observations but
longitudes have to be known.
24
Method of E. Halley
c
b
a
•
b•
a
•
c
•
The relative positions of the chords give the parallax
•
Difficulty to get an accurate measurement
– No reference frame available
•
But these positions are related to the duration of each transit
•
Angular measurements are replaced by timing measurements
– accurate
•
25
Requires observing sites far from each other  latitudes offset
– 1 s. of uncertainty ==> Parallax to 1/500 (Halley, 1716)
Method of J. Delisle
Use of the timing
offset at the beginning
or at the end of the
time t
Dt
Topocentric observation
(from the surface of the
Earth)
event
Geocentric view
Advantages
– Less impact of the meteorological effects
– Increasing of the number of sites (partial observations usable)
Disadvantages
•
Timing measurement instead of a duration measurement
–  need to have absolute timing
•
Comparaison between sites
–  need to accurately know the geographic position !
•
26
Requires maximum of timing differences -> longitudes offset
The transit of June 6, 1761
The French
• Expeditions for the observation: 2 of these voyages took place in
countries allied of France.
• César-François Cassini de Thury (1714-1784) in Vienna (successful observation).
• the Abbot Jean-Baptiste Chappe d'Auteroche (1728-1769) to Tobolsk in
Siberia (successful observation).
• Alexandre Guy Pingré : Rodrigues Island (north of Madagascar),
Thanks to the compagnie des Indes (observation partially successful).
• Guillaume Joseph Hyacinthe Jean-Batiste Le Gentil de La Galaisière (1725-1792),
left by sea in order to observe the transit in Indies at Pondichéry.
Unfortunately the city of Pondichéry was taken by the English and he
saw the transit from the ship, unable to make a measurement; he decided to wait
until the next transit in 1769
•Joseph-Jérôme Lefrançois de Lalande (1732-1807) observed
from Luxembourg Palace in Paris.
27
The transit of June 6, 1761
The English
two campaigns far from England to observe the event.
• Nevil Maskelyne (1732-1811) went to Sainte-Hélène where he was not
able to observe because of clouds.
•Charles Mason (1728-1786), James Bradley and Jeremiah Dixon (17331779) was supposed to observe from Bencoolen (Sumatra). They were
not able to make the observation because the French took the city. They
observed then at Capetown.
•John Winthrop, professor in Harvard went to St-John (Terre-Neuve)
where « surrounded by billions of insects " he succeeded to observe the
last contact of the transit.
28
Le passage du 6 juin 1761
Projection de Hammer
29
The voyage of Chappe d’Auteroche
The travel of Chappe d’Auteroche to Tobol’sk
30
Results from the transit of 1761
• The number of observers was 120, on 62 sites (S. Newcomb, 1959).
• Note that some sites of observations were previously selected (Bencoolen,
Pondichéry, Batavia) by Halley in 1716.
8.5" < P < 10.5"
The large error is due to:
- a bad knowledge of the longitudes of the sites of observation
- the black drop effect which decreases the precision of the measurement of
the time of the contacts.
Disappointing results : no improvement of the measures from
Mars.
31
Timing of the internal contacts: the black drop effect"
Sun
Before contact
Sun
Internal contact
Sun
Expected
Sun
~10 s after lcontact
Uncertainty of the contact measurement : 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)
William Smith
Thomas Hornsby
Pingré et Lalande
Pingré
Lalande
Planmann
Hell
Lexell
Values
8,6045" (1770)
8,78" (1770)
9,2" et 8,88" (1770)
8,80 (1772)
8,55"< P < 8,63" (1771)
8,43 (1772)
8,70" (1773/1774)
8.68" (1771) et 8,63" (1772)
The conclusion was that the parallax was from 8,43" to 8,80 " . This was a
real improvement regarding the result of 1761 providing a parallax from
8,28 to 10,60".
35
The transits of the XIXth century
36
•
The longitudes are now well determined
•
The clocks are good time keepers.
•
The travels are faster (steam, Suez channel).
•
The travels are still expensive
•
The photographs appeared (Daguerréotype)
•
The experiences of the XVIIIth century are profitable.
An example: the observation at St-Paul
The voyage of Commandant Mouchez at Saint-Paul.
•July 1874 : departure from Paris.
•August 9: Suez channel.
•August 30: arrival in Réunion Island
•September 22: arrival in Saint-Paul island in a tempest
The probability of fair weather was only 8 to 10%
In spite of tempest and bad weather, the observation was a
success: 500 exposures of the transit were made
37
The observation at Saint-Paul
38
The transit of December 9, 1874
39
The transit of 1882
General circonstances
Premier contact de la pénombre
Premier contact de l'ombre
Maximum du passage
Dernier contact de l'ombre
Dernier contact de la pénombre
:
:
:
:
:
13h 49m 3.9s
14h 9m 1.3s
17h 5m 58.5s
20h 2m 58.3s
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 500 000 measurements were made.
42
8 June 2004 :
How the Venus transit will appear ?
43
Description of a transit
•
The duration of a Venus transit is from 5 to 8 hours
t4
t3
t1
t2
t1 :
1st contact
t2 :
2nd contact
t3 :
3rd contact
t4 :
4th 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
Celestial pole
On Tuesday 8 June
Polar angle
Ecliptic
5h 13m 33,2s UTC
8h 19m 43,5s 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
Sun rise
At 3h 50m UT
POSITION OF THE SUN ON JUNE 8 (PARIS)
East
Meridian transit
at 11h 49.7 UT
South
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°
End of the transit
at 11h 23m 34s UT
Sun height : 63,5°
Sun azimut : 346,4°
At Paris :
T1 : first external contact at 5h 20m 06s UTC
Z=159,8°
T2 : first internal contact at 5h 39m 48.s UTC
Z= 164,2°
M : maximum at 8h 22m 53s UT center-center : 10’ 40,9”
T3 : last internal contact at 11h 4m 20s UTC
Z=228,9°
T4 : last external contact at 11h 23m 34sUTC
Z=225,0°
46
P= 117,7°
P= 121,0°
P= 212,4°
P=215,6°
Visibility of the Venus transit on 8 June 2004
47
Mercury transits
Apparent diameter of Mercury 1/158 of the Solar diameter
48
Venus Transit in 1882
49
Equatorial mount / alt azimuth mount
Direction of
North celestial pole
at T4
the celestial pole
Zenith
at T1
Parallel to equator
Venus trajectory on the solar disk as seen in an
equatorial frame (for example in a refractor with an
equatorial mount)
50
Parallel to horizon
Venus trajectory on the solar disk as seen in an
horizontal frame (for example in a refractor with a
alt-azimuth mount)
How the Sun-Earth distance will be
deduced from the observations ?
51
Calculation of the Sun-Earth distance in 2004
For the VT-2004 observations:
•
•
•
Locations (longitudes, latitudes) well known
Accurate timing (in Universal time)
Pedagogic purpose (AU is well known…)
Several calculations will be made:
•
1 connexion to the VT-2004 web server = 1 timing observation
and 1 estimate of the individual measurement
52
•
2 partners: 2 timing observations from far sites
•
Analysis of the whole campaign: a large number of timing
observations
An approximation for two partners
Sun
Earth
Venus
A
Δβ
D
βS
B
re
rv
Sheet « Calculating the Earth-Sun distance …»
• Assumptions:
- Two observing locations, centers of the Earth,
Venus, Sun are in the same plane
2l
h
R
- Circular orbits
• Measurement of the distance between two chords
(re / rv )3 = (Te / Tv) 2 if eccentricities = 0
βS = Δβ (( re / rv) – 1)
re = Δ / (Δβ . 0.38248)
54
dl = V dt
Δβ = dl*l / h
AU online computation
Sun
f ( φ , X s, X v, π , t ) =Δ
• Relation between time t and
parallax π
• Observer’s location φ
Rs
Rv
• Theory of Venus
• Theory of the Earth (Sun)
• Radii
Δ
• The registered users will send their own timing measurements to
the 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
55
AU determination: the global analysis
• Assuming geographical locations accurately known
• N equations of condition can be written (for N timing measurements)
involving small corrections δX s , δ X v , δ π , δ R to be calculated
a .δXs + b .δ Xv + c .δ π + d .δ(Rs +/-Rv ) = O - C
• O – C = offset of each timing O with respect to 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
56
1770’s parallax measurement
Authors
Values
William Smith (1770)
8.6045"
Thomas Hornsby (1770)
8.78"
Pingré et Lalande (1770)
9.2" and 8.88"
Pingré (1772)
Lalande (1771)
between 8.55" and 8.63"
Planmann (1772)
8.43"
Hell (1773/1774)
8.70"
Lexell (1771 / 1772)
57
8.80"
8.68“ / 8.63"
Parallax measurements since the XVIIIth century
58
Method / author
Parallax
Transits of 1761 and 1769
8.43" and 8.80"
Transits of 1761 and 1769, Encke (1824)
Transits of 1761 and 1769, (1835)
8.5776"
8.571 +/- 0.037"
Parallax of Mars, Hall (1862)
Parallax of the asteroid Flora, Galle (1875)
Parallax of Mars, Gill (1881)
Transits of 1874 and 1882, Newcomb (1890)
8.841"
8.873"
8.78"
8.79"
Parallax of the asteroid Eros, Hinks (1900)
Parallax of the asteroid Eros, (1941)
Radar measurement, NASA (1990)
8.806"
8.790"
8.79415"
Small historic of the Sun-Earth distance measurement
59
Method
date
parallax
"
AU in
millions km
Mars
1672
9.5 - 10
130 -140
Venus
Venus
1761
1769
8.3 - 10.6
8.5 - 8.9
125 - 160
145 - 155
Mars
1862
8.84
149
Flora
1875
8.87
148
Mars
1885
8.78
150
Venus
1874 - 82
8.790-8.880
148.1 - 149.7
Eros
Eros
1900
1930
8.806
8.790
149.4
149.7
radar
1970
8.79415
149.5978
Viking+radar
2000
149.597 870 691
The Astronomical Unit
History of the International Astronomical Union
(IAU) value of AU
(106 km)
60
• De Sitter
1938 :
149.453
• Clemence
1948 :
149.670
• UAI
1964 :
149.600
• UAI
1976 :
149.597 870
• DE102
1977:
149.597 870 68
• DE200
1982:
149.597 870 66
• IERS
1992:
149.597 870 61
• DE403
1995:
149.597 870 691
VT-2004
122 years later …VT-2004
• Large number of observers
• Modern techniques (GPS, Internet, webcam images, …)
• What results will we get in 2004 ?
Credits: aknowledgements to P. Rocher (IMCCE) and F. Mignard (OCA) for several frames
61
Data Acquisition
Acquisition and processing of
the amateur observations
W. Thuillot & J.E. Arlot
•Timings :
- database and online processing
- global analysis and results
•Images :
- database and pipeline (Ondrejov)
•Access to the data base :
62
- observational inputs
- registered observers
Data acquistion
Timings measurement
-Acquisition web page : same welcome page as « registration »
- 1 registration = 1 observation = 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
63
Data acquistion
Images
- data base
- Position of Venus with respect to the Solar limb can be used
- Field of vue must include the least distance to the limb
…and the limb itself
64
VT-2004 AU calculation
65
VT-2004 : Geographic overview
66
67
68
Data acquisition and calculation
Still in development,
but new pages are in test for a week :
try the AU calculation ! !
69