Ncert Exercises & Solutions

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.

The position of the Sun, Moon, and Earth during a lunar eclipse is shown in the given figure.

Distance of the Moon from the Earth = 3.84 × $10^{8}$ m

Distance of the Sun from the Earth = 1.496 × $10^{11}$ m

Diameter of the Sun = 1.39 × $10^{9}$ m

It can be observed that ΔTRS and ΔTPQ are similar. Hence, it can be written as:

$\frac{P Q}{R S} = \frac{V T}{U T}$
$\Rightarrow \frac{1.39 \times 10^{9}}{R S} = \frac{1.496 \times 10^{11}}{3.84 \times 10^{8}}$
$\Rightarrow R S = 3.57 \times 10^{6} m$

Hence, the diameter of the Moon is 3.57× $10^{6}$ m.

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