Venus Transit and the
Astronomical Unit
Biman Basu
bimanbasu@gmail.com
Measuring the Universe

Our idea of the structure and size 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 large distances

Measuring the size of the Earth did not
involve measuring large distances.

But most astronomical distances are
quite large.

To measure them astronomers use a
method involving the measurement of
parallax - the apparent shift of a nearby
object in relation to more distant
objects.
5
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
three dimensions.

Astronomers use parallax to find distances of
astronomical objects.
6
Parallax due to position of the eyes
7
Measuring the distance of the Moon
using parallax

In 129 BC, the Greek astronomer
Hipparchus, used parallax of the Moon
during a total solar eclipse to calculate
the distance of the Moon from Earth.

He used the observation of the eclipse
from two different locations to
determine the parallax of the Moon.
8
Hipparchus's method
From Hellespont (Lat. 4020N) the total
eclipse could be seen, as the Moon fully covered
the Sun from there.
9
Hipparchus’s method-II
However, when viewed from Alexandria (Lat.
3120N), only a partial eclipse could be seen at
the same moment due to parallax of the Moon
relative to the Sun.
10
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
(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’s edge as seen from
A and B.
11
Hipparchus calculations-II
From this diagram we can see that AB is also equal to
(2R/360)×0.1, where R is the Earth-Moon 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.
12
Finding larger distances

After finding a method to determine the distance to
the Moon using parallax, the next step was to find
the distance to the Sun.

But determining the parallax of the Sun was difficult,
as the distant background stars cannot be seen
during daytime.

However, the parallax method could be used to
determine the distance of nearby stars.

The first star for which the distance was measured
using the parallax method was 61 Cygni in the
constellation of Cygnus.
13
Parallax of 61 Cygni
When 61 Cygni was photographed six months apart, it
appeared to shift slightly against the background stars
because of the shift in Earth's position. From the angle
of parallax P the distance d could be calculated.
14
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.
15
Earth’s orbit around the Sun
16
Kepler's third law and the AU

By 1619, German astronomer Johannes Kepler had
figured out the relative distances of all the planets
from the Sun.

For example, if the Earth's distance from the Sun is
one astronomical unit (AU), then Mercury’s distance
from Sun is 0.38 AU, Venus's is 0.72 AU, Mars's is 1.5
AU, Jupiter’s is 5.2 AU, and so on.

If two planets have orbital periods Pplanet and Pearth,
the ratio of their distances aplanet and aearth in AU
from the Sun can be worked out from the
relationship
17
Parallax and the AU

Kepler's third law 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.

However, to express the AU in kilometres we need some
sort of parallax - some difference in the observed position
of some object in the solar system, when seen from two
separated points, the distance between which (in
kilometres) is known.

The problem is, planetary objects are so enormously
distant, that the shift in their apparent position, when
viewed from two separated locations on Earth, is
extremely small.
18
Determining the Astronomical Unit

Nevertheless, astronomers have been
trying to determine the value of the AU
since Kepler’s time and various
techniques have been used.

One of the earliest efforts was made in
1672 when the Italian astronomer
Giovanni Cassini was able to measure
the distance to Mars using parallax when
the planet was in opposition; that is,
nearest to Earth.
19
Determining AU using Mars parallax
Cassini sent a colleague
to French Guiana while
he remained in Paris.
At an agreed time the
two measured the
position of Mars against
background stars.
By comparing the two
positions and they could
measure the tiny angle
of parallax.
Knowing this, and the straight distance between the
two locations, they could calculate the Earth-Mars
distance, which came out to be approx. 74,000,000 km.
20
Determining AU using Mars parallax-II
From Kepler's Third
Law it is known
that Sun-Mars
distance DM = 1.524
times DE (SunEarth distance)
So, 74,000,000 = DM
- DE = 1.524 DE - DE
or 74,000,000 =
0.524 DE
Finally, we get DE or AU = 74,000,000/0.524 =
141,000,000 km (compared to the modern value of
149,597,870 km); an error of approx. 6%.
21
Parallax and transits

Parallax of planetary transits can also
be used to determine the Sun-Earth
distance.

During a planetary transit, the
difference in position of the planet, as
seen in the background of the solar
disc, when observed from two widely
separate locations, can be used to
determine Earth's distance from the
Sun.
22
What are 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 and we have
a solar eclipse.
23
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 (about 1/30th).
To viewers on Earth, during such a passage
or transit the planet appears as a tiny black
dot moving across the solar disc.
24
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.

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.
25
Transits are rare

Mercury comes between the Sun and
the Earth every 116 days on average,
while Venus does so every 584 days on
average.

But transits do not occur as frequently.

On the average, there are 13 transits of
Mercury in 100 years compared to only
two transits of Venus during the same
period.
26
Transits of Mercury & Venus
Being more distant and smaller, Mercury (left)
appears much smaller than Venus (right)
during transit.
27
Why transits are so rare

Transits of Mercury and Venus are not quite
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.
28
Orbits of Mercury and Venus
29
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.
30
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.
31
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.
32
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.
33
Jeremiah Horrocks (1618-1641)
Jeremiah Horrocks observing the Venus
transit of 4 December 1639.
34
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)
35
Parallax of planetary transits

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.
36
Venus transit parallax
From two separate locations on
Earth the position of Venus on
the solar disc appears different
because of parallax.
37
Edmund Halley and the AU
Edmund Halley
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.
38
Transit of Venus and the AU

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.
39
Transit of Venus 1769

Halley died in 1742, but the transits of 1761 and
1769 were observed from many places around the
world and several expeditions were sent to observe
the transits.

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.
40
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.
41
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.
42
Stages in Venus transit 2012
43
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.
44
Black drop sequence
1
2
3
4
5
6
45
Transit timings in India
Location
Greatest
transit
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
07:02:22
28
10:03:47
69
10:21:16
73
Delhi
Sunrise
(IST)
04:51:00
Internal
egress
hms
(IST)
Sun
alt.

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.
46
View from India at sunrise
47
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!
48
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.
49
Locations for observing the transit
of Venus
50
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.
51
Displacement of the tracks of Venus
Path of Venus
as recorded
from
Australia,
India, and
the Canary
Islands
during the
2004 Venus
transit.
52
Geometry of Venus transit
s = Δ ((re / rv ) - 1)
53
Relevant websites
"How to measure the Earth-Sun
distance by studying the transit of
Venus"
http://skolor.nacka.se/samskolan/eaae/summer
schools/TOV2.html
“From Stargazers to Starships"
http://wwwspof.gsfc.nasa.gov/stargaze/Smap.htm
54
The main points so far

How ingenious techniques have been evolved to
measure the universe.

How the apparent shift in position of a nearby
object in the background of distant objects when
seen from two widely separated locations, called
parallax, can be used to measure distances.

What the Astronomical Unit is and why it is
difficult to measure.

What planetary transits are and why they are so
rare.

How measurement of parallax of planetary transits
can be used to compute the Astronomical Unit.
55
Modern techniques of measuring
AU

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 speed 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.
56
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.
AU = XY×cos (e)
57
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.

It presents an opportunity for everyone to try
out a unique technique of making
astronomical measurements.
58
REMEMBER!
This is last chance to watch and enjoy
a transit of Venus because the next
one will not be seen for the next
105½ 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!
59
I’m grateful to NCSTC and
Vigyan Prasar for giving me
this opportunity to share my
thoughts with you.
Thank you!
60