Venus Transit and the
Astronomical Unit
Biman Basu
bimanbasu@gmail.com
Measuring the Universe

Our idea of the structure of the
Universe has changed drastically over
the past centuries.

Earth-centred Universe has given way
to a Sun-centred Universe.

Ingenious experiments led to the
determination of the Earth's shape and
size, the Earth-Moon distance, and
further to the Sun-Earth distance.
2
Measuring the Earth

One of the earliest efforts to measure the Earth
was by the Greek mathematician and
astronomer Eratosthenes around 240 BC.

Using trigonometry and knowledge of the
angle of elevation of the Sun at noon in
Alexandria and Syene (now Aswan, Egypt) on
summer solstice, he arrived at the conclusion
that the Earth is spherical and has a
circumference of about 40,000 km.

The calculation was based on the correct
assumption that the Sun is so far away that its
rays can be taken as parallel.
3
Eratosthenes's experiment
4
Measuring the distance of the Moon

In 129 BC, another Greek astronomer
Hipparchus, used the coverage of the Sun
by the Moon during a total solar eclipse to
calculate the distance of the Moon from
Earth, which came to about 90 times the
radius of Earth.

Although the calculated distance was
substantially larger than the actual
distance, the method showed how
parallax could be used to measure
distances of astronomical objects.
5
Hipparchus's method
 From Hellespont (Lat. 4020N) the total
eclipse could be seen, as the Moon fully covered
the Sun.
 Viewed from Alexandria (Lat. 3120N), only
a partial eclipse could be seen at the same
moment due to parallax of the Moon.
6
Hipparchus calculations
Since A and B differ 9 in latitude and the
circumference of Earth is given by 2r, the distance
AB is given by AB = (2r/360) × 9 where r is the
radius of Earth.
Similarly, since the distance CD is 1/5 the solar
diameter and the Sun subtends an angle of 30' or 0.5
at Earth, the angle  is 0.1, which is the parallax of
the Moon as seen from A and B.
7
Hipparchus calculations-II
Here AB = (2R/360) × 0.1 where R is the EarthMoon distance.
Therefore, (2R/360) × 0.1 = (2r/360) × 9 or 0.1R
= 9r, which gives R = 90r; that is, the Earth-Moon
distance is 90 times the radius of Earth.
The distance to the Moon comes out to be 5,73,300
km, which is about 50 per cent higher than the
average value of 3,84,400 km.
8
What is parallax?

Parallax is the apparent displacement of a
relatively close object compared to a more
distant background as the location of the
observer changes.

Parallax makes it possible for our eyes to perceive
depth of field and see objects in 3-dimensions.

Astronomers use parallax to find distances of
planets and stars.

Parsec is a unit of distance used in astronomy,
equal to about 3.25 ly, which corresponds to the
distance at which the mean radius of the Earth's
orbit subtends an angle of one second of arc.
9
Parallax due to position of the eyes
10
Parallax of nearby stars
When the stars are photographed six months
apart, some of the nearby stars appear to shift
slightly because of the shift in Earth's position.
11
Solar parallax
Solar parallax is defined as the angle
subtended by the radius of the Earth at the
centre of the Sun.
Its value has been computed to be about 8.8
arcseconds.
12
Astronomical transits
An astronomical
transit occurs
whenever one
celestial object,
such as a planet or
a moon, passes in
front of another
celestial object.
When the Moon passes in front of the Sun it
covers the Sun fully because both appear to
be of the same size from Earth.
13
Planetary transits
But when an inner
planet like Mercury
or Venus passes in
front of the Sun it
covers only a tiny
portion of the Sun's
disc.
To viewers on Earth, during such a passage
or transit the planet appears as a tiny black
dot moving across the solar disc.
14
Transits of the inner planets

Only the inner planets Mercury and Venus
show transits because their orbits are closer
to the Sun than Earth’s and occasionally both
come between the Sun and the Earth when
they can be seen against the solar disc.

Transits of Venus are much fewer than
transits of Mercury.

On the average, there are 13 transits of
Mercury in a century compared to only two
transits of Venus during the same period.
15
Transits of Mercury & Venus
Being more distant and smaller, Mercury (left)
appears much smaller than Venus (right)
during transit.
16
Conditions for transit

Since both the inner planets occupy
orbits between the Earth and the Sun,
they would more than likely be seen to
pass in front of the solar disk from time
to time.

Mercury comes between the Sun and
the Earth every 116 days on average,
while Venus does so every 584 days on
average.
17
Conditions for transit-II

But transits of the two planets are not as
frequent because their orbits are tilted with
respect to that of Earth: Mercury 7.0,
Venus 3.23.

In order for a transit to occur, the planet,
Sun, and Earth have to be in the same plane
on the same side of the solar system.

This happens only when the planets are at
any of the two nodes where their orbits
cross the Earth's orbital plane.
18
Orbits of Mercury and Venus
19
Transits of Venus

Transits of Venus are much rarer than
transits of Mercury because the orbital
period of Venus is longer than that of
Mercury.

Indeed, only seven such events have
occurred since the invention of the
telescope (1631, 1639, 1761, 1769, 1874, 1882,
and 2004).

Transits of Venus show a clear pattern of
recurrence at intervals of 8, 121.5, 8, and
105.5 years.
20
Transits of Venus-II

Transits of Venus are only possible during
early December and June when the orbital
nodes of Venus pass across the Sun.

The last transit of Venus was seen on 8
June 2004 and the next one is due on 6
June 2012.

After the 6 June transit the next transit of
Venus will not be seen till the next
century, on 11 December 2117; that is, after
a gap of 105 years and six months.
21
Historical transits of Venus

The first person to predict a transit of
Venus was the German astronomer
Johannes Kepler, who calculated that one
would take place on 6 December 1631.

Kepler died in 1630, and there is no record
of anyone having seen the 1631 event.

Young English astronomer Jeremiah
Horrocks and his friend William Crabtree
were the first persons to observe a transit
of Venus on 4 December 1639.
22
Jeremiah Horrocks (1618-1641)
Jeremiah Horrocks observing the Venus
transit of 4 December 1639.
23
Horrocks’ observation 1639
Horrocks had
calculated that
the transit was
to begin at
approximately
3:00 pm. He
had about 35
minutes to
observe the
transit before
sunset at 3.50
p.m.
(Published in 1662 by Johannes Hevelius)
24
Venus transit cycles

Transits of Venus occur in a 'pair of pairs'
pattern that repeats every 243 years.

First, two transits of a cycle take place in
December, eight years apart.

There follows a wait of 121 years 6 months,
after which two June transits occur, again
eight years apart.

The pattern repeats after 105 years 6
months, beginning with two December
transits, eight years apart.
25
Earth’s orbit around the Sun
26
The Astronomical Unit

The Astronomical Unit (AU) is the
average distance between the Sun and
the Earth.

It is a convenient unit to use when
expressing distances within the solar
system.

The AU, as defined in the International
Astronomical Union (IAU) system of
constants, is equal to 149,597,870 km.
27
Kepler's third law and the AU

According to Kepler's Third Law, the square of
the orbital period of a planet (P) is
proportional to the cube of the semi-major axis
(a) of its orbit measured in AU; that is, P²  a³.

If two planets have orbital periods P1 and P2,
the ratio of their distances a1 and a2 from the
Sun can be worked out.

Kepler's Third Law thus allows one to evaluate
the dimensions of the solar system in relative
units, e.g., in "astronomical units" (AUs),
where 1 AU is the mean Sun-Earth distance.
28
The heliocentric model

The heliocentric model uniquely specifies the
relative distances (from the Sun) to the planets
according to Kepler’s Third Law, as follows:
Mercury (0.38 AU), Venus (0.72 AU), Mars (1.5
AU), Jupiter (5.2 AU), and Saturn (9.5 AU).

The challenge then becomes determining the
absolute distance to any one planet.

If a parallax measurement could be accurately
obtained for any single planet, all the other
distances including the AU would be trivial to
calculate using Kepler’s laws.
29
Determining the Astronomical Unit

Astronomers have been trying to determine
the value of the AU since Kepler’s time and
various techniques have been used.

In 1716, the English astronomer Edmond
Halley published a paper in the
Philosophical Transactions of the Royal
Society, describing exactly how the parallax
of transits could be used to measure the
Sun's distance, thereby establishing the
absolute scale of the solar system from
Kepler's Third Law.
30
Edmund Halley (1656-1742)
31
Transit of Venus and the A.U.

Halley’s method involved observing
and timing a transit from widely
spaced latitudes.

Although the method gave the first
reasonable value for the Sun's distance
from Earth, his method proved
somewhat impractical since contact
timings of the required accuracy are
difficult to make.
32
Transit of Venus 1769

Halley died in 1742, but the transits of 1761 and
1769 were observed from many places around the
world.

The transit of 1769 was one of the most
extensively observed transits of Venus of that
time.

In 1771, French astronomer Jerome Lalande was
able to use the combined measurements taken in
1761 and 1769 to determine the average Earth-Sun
distance to be 153 ( 1) million km, as against the
currently accepted value of 149.60 million km.
33
The effect of parallax on transit
observation

Parallax causes a planetary transit to
look slightly different for two observers
at different latitudes on Earth.

Venus does not appear to enter or leave
the Sun’s disc simultaneously from two
widely different locations, and,
observed at the same moment, Venus’
position on the disc of the Sun also
differs slightly.
34
Determining the Sun’s distance

The parallax effect gives rise to two ways of
obtaining the Sun’s distance from
observations of the transit of Venus.
i. Timing the start and end of the transit
from two stations - Halley’s original 1716
method.
ii. Photographing the Sun at the same
moment from two stations and measure the
northward or southward displacement of
Venus due to parallax.
35
Determining the Sun’s distance
From the time difference between T1 and T2
and the distance between A and B the distance
between the Sun and Earth can be calculated.
36
Transit paths of 2004 and 2012
The transits of 1874 and 1882 occurred during ascending
nodes, while the transits of 2004 and 2012 occur during
the descending node.
37
Stages in Venus transit 2012
38
Timing the transit
A transit of Venus across
the Sun takes about 7
hours, but this time has to
be measured to a precision
of a few seconds to be of
any use.
To be useful, the most critical times are the
first, second, third, and fourth contact.
Unfortunately, an optical phenomenon called
the ‘black drop’ effect makes it difficult to time
the second and third contacts precisely.
39
Transit timings in India
Location
Sun
alt.

Internal
egress
hms
(IST)
Sun
alt.

05:24:00 07:02:19
20
10:04:57
59
10:22:25
63
Mumbai 06:00:00 07:02:50
13
10:05:10
54
10:22:39
58
Kolkata
28
10:03:47
69
10:21:16
73
Delhi
Sunrise
(IST)
Greatest
transit
hms
(IST)
04:51:00 07:02:22
External
egress
hms
(IST)
Sun
alt.

The transit of Venus on 6 June 2012 will start long
before Sunrise in India and hence the timing of the
1st and 2nd contacts will not be visible.
However, it may be possible to determine the
apparent displacement of the position of Venus on
the solar disc if observed from two distant latitudes.
40
View from India at sunrise
41
Recording position of Venus during
transit
The best way for amateur astronomers to record the
position of Venus during transit would be to project the
image of the Sun on a white card using a small telescope.
CAUTION: NEVER LOOK AT THE SUN DIRECTLY!
42
Measuring Venus parallax

For measuring the parallax it is necessary
to have at least two simultaneous
observations at precisely the same instant
from two locations in different latitudes
along the same meridian.

Kanyakumari (8.06N, 77.30E) and New
Delhi (28.40N, 77.12E) are good
examples.

From Kanyakumari, Venus will appear a
little northward on the solar disc than
from New Delhi.
43
Locations for observing the transit
of Venus
44
Recording Venus position on solar
disc
The positions
can be recorded
on identical Sun
templates on
cards with
sketch pen, at
30-minute
intervals,
beginning at a
predetermined
time, from both
locations.
45
Displacement of the tracks of Venus
Path of Venus
as recorded
from
Australia,
India, and
the Canary
Islands
during the
2004 Venus
transit.
46
Geometry of Venus transit
s = Δ ((re / rv ) - 1)
[Can look up http://skolor.nacka.se/samskolan
/eaae/summerschools/TOV2.html for details.]
47
Modern techniques of measuring
A.U.

One of the modern methods for deriving
the absolute value of the Astronomical
Unit uses radar in combination with
triangulation.

In this technique, the distance of Venus at
its greatest elongation is measured using
radar.

From the known velocity of radio waves of
300,000 km/s and the time taken for the
signal to return, the distance of Venus can
be determined with high accuracy.
48
Use of radar to measure A.U.
Once the Earth-Venus distance is known
accurately, the Earth-Sun distance or
Astronomical Unit can be computed using
simple triangulation.
49
Why the transit of Venus is
important

Historically, the observation of the transit of
Venus has been the most valuable technique
for measuring the distance from the Earth to
the Sun, or the Astronomical Unit.

Even today, the observation of a transit and
using it to determine the value of the AU can
be an enjoyable activity for anyone.

But it would need collaboration between
groups located at widely separated places for
getting reasonably accurate results.
50
REMEMBER!
This is last chance to watch and enjoy
a transit of Venus because the next
one will not be seen for the next 105
years!
So go out and enjoy this rare celestial
event on 6 June 2012!
But one word of caution:
NEVER LOOK AT THE SUN
WITHOUT ADEQUATE EYE
PROTECTION!
51
I’m grateful to NCSTC and
PSCST for giving me this
opportunity to share my
thoughts with you.
Thank you!
52