Question

It is a well known fact that during a total solar eclipse the disk of the moon almost completely covers the disk of the Sun. From this fact and from the information you can gather from examples 2.3 and 2.4, determine the approximate diameter of the moon.

Answer 1

In the following figure, the position of Sun, Moon and Earth during a solar eclipse is shown.

The distance of Moon from Earth is 3.844× 10 8  m, so PQ=3.844× 10 8  m.

Since the distance of Sun from Earth is 1.496× 10 11  m, so PR=1.496× 10 11  m.

Also the diameter of Sun is 1.39× 10 9  m, so BC=1.39× 10 9  m.

From the above figure, AD is the diameter of the Moon.

Since, triangles PQD and PRC are equilateral triangles, therefore

PQ PR = QD CR PQ PR = AD 2 BC 2 PQ PR = AD BC

Substitute the values in the above equation.

3.844× 10 8 1.496× 10 11 = x 1.39× 10 9 AD≈3581 km

Hence, the diameter of the Moon is 3581 km.