Measuring the diameter of
the Sun
Aristarchus
Aristarchus (310 B.C. - 230
B.C.) was a Greek
astronomer and
mathematician who was
the first to propose a
heliocentric model of the
solar system placing the
Sun and not the Earth at
the centre of the universe.
Aristarchus also
calculated the size of the
Moon and the size of and
distance to the Sun.
• Consider the previous diagram which
represents the relative positions of the
Sun, Moon and Earth during a first
quarter moon. Aristarchus reasoned
that during a first (or third) quarter
moon, the angle between the Sun and
Earth at the Moon is a right angle
or900.
•
• If you can then measure the angle
between the Sun and the Moon, as
shown in the previous diagram, it is
possible to calculate the distance
between the Earth and the Sun
What difficulties do you think Aristarchus
encountered when working out his
calculation ?
• The measurement of the angle between
the Sun and the Moon during first quarter
phase was difficult when Aristarchus was
alive due to the fact that the Sun is very
far away and the angle between the Sun
and the Moon is therefore very close to
900. In addition, it is very hard to
determine when the Moon is in exactly
quarter phase.
Activity: to measure the distance to the Sun:
• Use a value of 89.8530 as the angle between
the Sun and Moon. Call this angle .
• Use 384,403 km for the distance from the Earth
to the Moon
• Calculate the distance to the Sun
cosine() = (distance to moon)/(distance to Sun)
Activity – Measure the diameter
of the Sun
• In order to complete this activity we will
construct a device called a “pinhole viewer”
which is basically a pinhole camera without
the photographic film.
Method
1) Find a suitable tube at least 600 mm in length
2) Place a piece of tin foil over one end and tape it in
place over the edges
3) Using a pin or another sharp point, puncture the tin
foil to produce a small hole. The maximum diameter
of the hole depends on the tube length
4) Now tape some greaseproof paper on the other
end of the tube. This will act as a screen.
Length of tube / mm
Diameter of hole /mm
600
1.1
800
1.3
1000
1.4
1200
1.5
1400
1.7
• For this method to work, light from the Sun
must pass through the pinhole and fall on the
greaseproof paper forming an image.
• The measurements to be taken are
1) the diameter of the image of the Sun on
the paper and
2) the distance from the pinhole to the paper,
which is the length of the tube.
Calculate the diameter of the Sun using a value
of 149,600,000 km for the Earth-Sun distance.
Use the following formula:
(Sun image diameter)/(Tube length) =
(Actual Sun diameter)/(Actual Earth-Sun
distance)
Using this method, we should get a value
for the diameter of the Sun which is the
right order of magnitude (~700,000 km).
• This method can also be used to calculate
the diameter of the Moon.
• The Moon-Earth distance is 384,000 km.
• Useful website:
http://www.astro.washington.edu/labs/eratosthenes/index.html