AristarchusAristarchus ≈ 250 BC, the size of the sun
| The sun and the moon appear to have the same size. |  |
 |
That observation was made by Aristarchus when he observed a solar eclipse. He also realized that they do not have to be equal in size if only the sun is further away than the moon. |
| Let d be the distance to the moon and D the distance to the sun. Let r be the radius of the moon and R the radius of the sun. If the angular sizes of the moon and the sun are equal, the triangles are similar. |  |
Aristarchus wanted to compare the radius of the sun to the radius of the earth.
Exercise 1
Find the ratio of R and r in terms of D and d!
Exercise 2
Aristarchus knew what the moon looked like when the angle β was 90°. (What does it look like?). He then estimated the angle α. Make a construction to illustrate his calculations. Insert a slider d and a slider α. Then place the point Earth. Insert the coordinates of the points Moon and Sun in the input bar. Drag the two sliders to check out the construction. |
 |
Exercise 3
Aristarchus estimated the angle α to 87°. During a lunar eclipse he estimated that the radius of the moon was about one third of the radius of the earth. Using these numbers, calculate the ratio of the radius of the sun and the radius of the earth! Using these numbers, how much larger is the sun than the earth (volume)?
Aristarchus then concluded:
the giant sun does not move around the tiny earth,
it is probably the
other way around! |
Exercise 4
Aristarchus' estimation of the angle α was not correct. It is not 87°, it is 89°50'. (89 + 50/60 degrees). Find the ratio D:d using the correct angle! What was his relative error when measuring the angles? What is the relative error in distances?
1 sun ≈ 1 300 000 earths
image from: NASA
