The Transit of Venus
John S. Reid
Cruickshank Lecturer in Astronomy
Department of Physics
University of Aberdeen
Public interest
Venus crossing the
face of the Sun
 A rare phenomenon

¾
¾
¾
Telescopic view by US
Naval Observatory of
1882 transit
Last seen in 1882
Visible without a
telescope
An annular eclipse of
the Sun by Venus
Courtesy: www.williams.edu/astronomy/
eclipse/transits/
Astronomical interest
 Refine
elements of Venus’s orbit using
observed timing
¾ 17th
century result
 Determine
system
¾ 18th
 Find
the absolute scale of the solar
century result
an accurate value for 1 AU
¾ 19th
century interest
¾ 1 AU is the metre-stick for the Universe
Solar system and Kepler’s laws

The relative sizes of the
orbits in the solar system
are given by Kepler’s 3rd
law
¾

Sun
a3 ∝ (planetary year)2
What is the absolute size?
¾
Average
distance a
1 AU is average distance
between Earth and Sun
Planet
a
Mercury
0.387
Venus
0.723
Earth
1.00
Mars
1.524
Jupiter
5.203
Parallax of a planet
 You
can find the distance of a planet, P, if
you can measure its parallax angle from
separated points, A and B, on the Earth
Parallax angle
P
Distance
Definition: Parallax angle = AB/Distance
Hence:
Distance = AB/Parallax angle
B
A
Earth
Method was tried for Mars
 Observe
position of Mars against the fixed
background of stars
Mars
¾ Difficult
¾ Parallax
Earth
from 1 Earth radius is 20" at best
¾ Can use Earth’s rotation and observe change
in Mars’ position from evening to pre-dawn
Enter Venus
 Venus
is closest planet to Earth and
in principle best for parallax
¾ Closest
is typically 0.28 AU
 Measure
parallax against background
of Sun’s disk
¾ When
at greatest elongation
from Sun (46º), Venus
~2.5 times further from Earth
Venus orbit
46º
E
V
Sun
0.28 AU
The master plan
 Use
the Sun’s disk as a calibrated screen
 Observe the transit from different locations
on Earth
 Measure the parallax of Venus
 Scale the solar system and hence
determine 1 AU in terms of metres
Observed
from
St Helena
Observed
from
Aberdeen
Side view
Earth
Venus
Sun’s disk
The refinement
 Use
the curved edge of the Sun and time
the ingress and egress of Venus to
deduce which chord Venus travelled on
¾ Clocks
are more accurate
than telescope angles
Sun
Alignments of Earth, Venus & Sun
 The
Earth, Venus & Sun are in a line
looking down on the solar system every
583.9 days (1.6 years = 8/5 years)
¾ Venus
orbits 2+ times
¾ Earth orbits 1+ time
2
4
E
V
3
Earth year: 365.25630 days
Venus year: 224.70078 days
S
5
The problem
 Venus’s
orbit is tilted at 3.39º with respect
to the Earth’s orbit
 In reality, only 2 points in Venus’s orbit are
in the plane of the Earth’s orbit
¾ Descending
node N
¾ Ascending node N'
E
Plane of
Earth’s orbit
N'
V
3.39º
S
N
Line of nodes
View
from
Earth to
Venus
The optics
 Earth
must be in the central shadow cone
of Venus to see Venus in front of the Sun
Sun
V
E
Shadow cone
 Some
Line of sight to
Venus and Sun
of shadow cone must be in the
plane of Earth’s orbit for transit to be seen
The transit season
 The
Plane of
Venus’s
orbit
2004
transit season lasts ~3.5 days
Shadow
cone
N
E
What would be
seen
Earth’s orbit
~1 day for shadow cone
1.8 days for Earth
The alignments
 Suppose
a transit occurs in one year, how
long before the next one?
 Earth-Venus-Sun alignment shifts 2.4 days
(earlier) after 8 years
2012
¾ Hence
after 8 years a second transit
will occur on the other side of the node
N
Earth’s orbit
E
~2.4 days
What would be
seen
Then what?
 There
are no transits for a long time
¾ When
the Earth passes through the line of
nodes, Venus has already been there
The ~8 year alignments occur progressively
earlier, before the Earth reaches the node
 The alignment ‘spokes’ retreat clockwise

E
N
E
V
2.4° per 8
years
4
4
S
2
2
N'
3
3
55
243 years between repeat pairs

Alignment directions every 8 years less
2.4 days
2, alignment after 1.6
years
Alignment 153 ≡ 243 years
N
32
Sun
153
62
72
123
N'
alignment 72 ≡
113.5 years
93
V
63
33
E
3 , alignment after 3.2 years
The ascending node transits
 71
transits (113.5 years) after the first one,
the shadow cone passes close to the
ascending node N'
1874
& 2117
¾ Another
Earth’s orbit
pair of transits will be seen
What
would be
seen
N'
E
Venus moving shadow cone
Series of
transits every
243 years
 Ascending
node series
Return to 2004 transit
(2012 transit occurs 2.4 days earlier, mainly during our night)
Expected sight

Clouds allowing!
Courtesy: http://www.eso.org/outreach/pressrel/pr-2004/images/vt-anim.gif
Venus’ track across the Sun
 Why
is Venus’ track 8.7º to the ecliptic?
→ 29.78 km s-1
N
E
→ 48.55 km s-1
↓ 2.87 km s-1
0.52×106 km
 Venus
track across the Sun is the Earth’s
track across the shadow cone
¾ Velocity
of Earth relative to shadow cone
19 km s-1
¾ Max duration ~7.6 hr
¾ 2004 transit ~ ¾ max ~ 5½ hr
8.7º
Illustrating the
parallax in transits
experienced at
different latitudes
on Earth
Parallax effects
Earth & central
shadow cone to
scale
Aberdeen (57ºN)
St Helena (15ºS)
Equatorial
rotational speed
0.46 km s-1
Each point
in the shadow
cone corresponds
to Venus
appearing at a
different place on
the Sun’s disk
Details of June 8th transit
Sun
Approximate BST
timings shown for
Aberdeen
Ecliptic
0640
7
8
BST
9
10
11
12
Observing the Spectacle
 Directly
¾ Venus
– use eclipse glasses
will be a very small dot
 Project
using
binoculars/telescope
 Photograph with ~200 mm
telephoto lens, or longer
¾ remember
the solar filter!
Jeremiah Horrocks (1619 – 1641)


Horrocks predicted the 1639 transit and observed it, as did
his friend Wm Crabtree
Horrocks deduced improved orbital parameters for Venus
William Crabtree, Horrock’s friend
24th Nov 1639
Old-style calendar
James Gregory (1638 – 1675)
Brilliant mathematician &
astronomer from Drumoak
 First suggested that
observation of the
transit of Venus
could determine
the scale of the
solar system

Courtesy: University of Aberdeen
Edmond Halley (1656 – 1742)
Halley observed the transit of Mercury and
worked out the details of finding the solar
distance from the Transit of Venus observations
Plantation house 1812
St Helena
6th June 1761 transit

A big international
effort
Charles Mason (1730 1786)
 Jeremiah Dixon (1733
- 1779)

Transit of
Venus from
ceiling of the
Paris
Observatory
Nevil Maskelyne (1732 – 1811)
unsuccessful at St Helena
http://www.bdl.fr/Granpub/Promenade/
pages6/608.html
3rd June 1769 Transit

Charles Green’s
& James Cook’s
observations from
Tahiti were successful
James Cook
Pictures courtesy:
http://www.transitofvenus.org/historic.htm
Venus Point
David Gill
(1843 – 1914)
Sir David Gill KCB,
FRS, PRAS, etc.
 One of the 19th
century’s foremost
observational
astronomers
 Her Majesty’s
astronomer at the
Cape of Good Hope

Enter Lord Lindsay

Founder of the Dun Echt
observatory
¾ ~15

km West of Aberdeen
This observatory was
among the best equipped in
the world, turning out highly
professional astronomy
Heliometer dome ↓
David Gill at the
Cape Observatory
Results

1761: “solar parallax” 8.28" to 10.20"
¾

1769: “solar parallax” 8.43" to 8.80"
¾

Equivalent solar distances (159 – 129)×106 km
Equivalent solar distances (156 – 149)×106 km
19th century re-analysis
¾
Encke (1825): 8.577"
z
Widely used but later discredited
19th century: “solar parallax”
End
8.78"
 Modern value: “solar parallax” 8.794148"

¾
Equivalent solar distances 149.598×106 km
References


David Sellers The Transit of Venus [Maga Velda Press,
Leeds, 2001]
Eli Maor June 8 2004: Venus in transit [Princeton Univ.
Press, 2000]

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit4/venussun.html

http://www.transitofvenus.org/historic.htm
http://www.venus-transit.de/links.html library of refs


VT-2004 international observing programme seeking active
participation of amateurs from around the globe
¾
http://www.vt-2004.org/
Photographic animation of the
1882 transit
http://skyandtelescope.com/observing/objects/sun/article_1187_1.asp