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.

Fig. The Total Solar Eclipse.

Given, from examples 2.3 and 2.4 we have,

Distance between the Sun and the Earth = 1.496×10¹¹ m

Distance between the Moon and the Earth = 3.84×10⁸ m

Diameter of the Sun = 1.39×10⁹ m

Fig. Schematic diagram of positions of Sun, Moon and Earth during Total Solar Eclipse.

From the above figure,

Δ PQT and Δ RST are similar. Thus,

=

Where,

PQ = Diameter of the Sun

RS = Diameter of the Moon

VT = Distance between the Sun and the Earth

UT = Distance between the Moon and the Earth

∴ =

⇒ RS = ×10⁶ m = 3.57×10⁶ m

Hence, The diameter of the Moon = RS = 3.57×10³ km.