Aristarchus of Samos
Born: about 310 BC in Greece
Died: about 230 BC in Greece
Died: about 230 BC in Greece
Hometown: Greece
He is a student of Strato of Lampsacus, head of Aristotle's Lyceum.
Achievements/Contributions:
· He is most celebrated as the first to propose a sun-centred universe.
· He is also famed for his pioneering attempt to determine the sizes and distances of the sun and moon.
· On the Sizes and Distances of the Sun and Moon provides the details of his remarkable geometric argument, based on observation, whereby he determined that the Sun was about 20 times as distant from the Earth as the Moon, and 20 times the Moon's size. Both these estimates were an order of magnitude too small, but the fault was in Aristarchus's lack of accurate instruments rather than in his correct method of reasoning.
The diagram shows an argument used by Aristarchus. He knew that the moon shines by reflected sunlight, so he argued, if one measured the angle between the moon and sun when the moon is exactly half illuminated then one could compute the ratio of their distances. Aristarchus estimated that the angle at the time of half illumination was 87° so the ratio of the distances is sin 3°.
· Aristarchus also figured out how to measure the size of the Moon. During a lunar eclipse, he measured the duration of time between the moment when the edge of the Moon first entered the umbra and the moment when the Moon was first totally obscured. He also measured the duration of totality. Because he found the two times to be the same, he concluded that the width of the Earth's shadow at the distance where the Moon crosses it must be twice the diameter of the Moon.
Therefore, the Moon must be about half as big as the Earth. Note that he already knew the approximate size of the Earth. Actually, the Moon is about 1/4 as big as the Earth.
· Aristarchus also reasoned that since the Sun and the Moon have the same angular size, but the Sun is 19 times further (or so he thought), then the Sun must be 19 times bigger than the Moon. 
· He invented a sundial in the shape of a hemispherical bowl with a pointer to cast shadows placed in the middle of the bowl.
· Aristarchus was also faced with calculating an approximation for what is in our notation sin 3°. He obtained the inequality
1/18 > sin 3° > 1/20
Reference:
Article by: J J O'Connor and E F Robertson
April 1999
MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Aristarchus.html]
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Aristarchus.html]
