Measuring the diameter of the Sun

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Measuring the diameter of the Sun

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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.

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• 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

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• 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.

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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)

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Activity Measure the diameter of the Sun

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• 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.

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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.
•  

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Length of tube / mm Diameter of hole /mm
600 1.1
800 1.3
1000 1.4
1200 1.5
1400 1.7
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• 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.

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• 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)

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• Using this method, we should get a value for the
  diameter of the Sun which is the right order of
  magnitude (700,000 km).

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• 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