Slide1:
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
The transit of June 8, 2004: 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
The VT-2004 project: 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…)
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)
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)
Venus visibility : Venus visibility East Elongation East of the Sun
Evening visibility West of the Sun
Morning visibility
Motion of Venus / Earth… if Venus was in the ecliptic: 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
More realistic…: More realistic… . 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
Conjunctions / transits: Conjunctions / transits
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
Short history of the Venus transits XVIIth, Dec.1631, Dec.1639 XVIIIth, June 1761, June 1769 XIXth Dec. 1874, Dec. 1882: Short history of the Venus transits XVIIth, Dec.1631, Dec.1639 XVIIIth, June 1761, June 1769 XIXth Dec. 1874, Dec. 1882
Kepler’s laws: 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’s third law: 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).
Visibility of the Mercury transit of 1631: Visibility of the Mercury transit of 1631
Gassendi in Paris 1631: Mercury transit: Gassendi 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 Calculation for Paris
hour Sun
(true solar time)
2e contact 5h 06 -21°
3e contact 10h28 +22°
Gassendi in Paris 1631: Vénus transit: 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
Visibility of the Venus transit of 1639: Visibility of the Venus transit of 1639
Observations of W. Crabtree 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 !
First observations of a transit of Venus: J. Horrocks: First 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
local time Sun
2e contact 15h15 + 4°
3e contact 21h30 - 47°
sunset 15h50
J. Horrocks (Venus in Sole Visa) 1639: 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 : 94 000 000 km
Transits during the XVIIIth century: 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
Mean horizontal parallax: Mean horizontal parallax The Sun-Earth distance cannot be directly measured
Classical astronomy measures angles
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
Mean horizontal parallax
Parallax of Mars (perihelic opposition in 1672): 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)
Transits during the XVIIIth century: 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.
Method of E. Halley: 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 ==> Parallax to 1/500 (Halley, 1716)
Method of J. Delisle: Method 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) time t Use of the timing offset at the beginning or at the end of the event
The transit of June 6, 1761: The transit of June 6, 1761 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. The French
The transit of June 6, 1761: 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.
Le passage du 6 juin 1761: Le passage du 6 juin 1761
The voyage of Chappe d’Auteroche: The voyage of Chappe d’Auteroche
Results from the transit of 1761: 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.
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. 8.5" < P < 10.5" Disappointing results : no improvement of the measures from Mars.
Timing of the internal contacts: the black drop effect": Timing of the internal contacts: the black drop effect" Uncertainty of the contact measurement : 20s to 1 min.
The transit of Venus of June 3-4, 1769: 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
Visibility of the transit of 1769: Visibility of the transit of 1769
The results from the transit of 1769: 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 " . This was a real improvement regarding the result of 1761 providing a parallax from 8,28 to 10,60".
The transits of the XIXth century: 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.
An example: the observation at St-Paul: An example: the observation at St-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
The voyage of Commandant Mouchez at Saint-Paul.
The observation at Saint-Paul: The observation at Saint-Paul
The transit of December 9, 1874: The transit of December 9, 1874
The transit of 1882: 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.
The transit of December 6, 1882: The transit of December 6, 1882
Reduction of photographs: 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.
8 June 2004 : How the Venus transit will appear ?: 8 June 2004 : How the Venus transit will appear ?
Description of a transit: Description 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 Interior contacts will be more accurate t1 t2 : ingress t3 t4 : egress
Geocentric circumstances: Geocentric circumstances 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". On Tuesday 8 June
Local circumstances: Local circumstances 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° Sun rise Meridian transit
At 3h 50m UT POSITION OF THE SUN ON JUNE 8 (PARIS) at 11h 49.7 UT
East South
Visibility of the Venus transit on 8 June 2004: Visibility of the Venus transit on 8 June 2004
Mercury transits: Mercury transits Apparent diameter of Mercury 1/158 of the Solar diameter
Slide49: Venus Transit in 1882
Equatorial mount / alt azimuth mount: Equatorial mount / alt azimuth mount
How the Sun-Earth distance will be deduced from the observations ?: How the Sun-Earth distance will be deduced from the observations ?
Calculation of the Sun-Earth distance in 2004: 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
Full parallax effect: 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
An approximation for two partners: 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
βS = Δβ (( re / rv) – 1)
re = Δ / (Δβ . 0.38248) dl = V dt
Δβ = dl*l / h
AU online computation: AU 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
AU determination: the global analysis: 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 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
1770’s parallax measurement: 1770’s parallax measurement
Parallax measurements since the XVIIIth century: Parallax measurements since the XVIIIth century
Small historic of the Sun-Earth distance measurement: Small historic of the Sun-Earth distance measurement
The Astronomical Unit: The 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
VT-2004: VT-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 ?
Data Acquisition: 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
Data acquistion: 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
Data acquistion: 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
VT-2004 AU calculation: VT-2004 AU calculation
VT-2004 : Geographic overview: VT-2004 : Geographic overview
Data acquisition and calculation: Data acquisition and calculation Still in development,
but new pages are in test for a week :
try the AU calculation ! !