Ncert Exercises & Solutions

During a total solar eclipse, the Moon appears to almost completely cover the Sun as seen from Earth. Given thatthe distance from the Earth to the Moon is approximately $3.84\times10^5~\text{km},$ the distance from the Earth to the Sun is approximately $1.5\times10^8~\text{km},$ and the Sun’s diameter is approximately $1.39\times10^6~\text{km}.$ Which of the following is the best estimate for the diameter of the Moon?
1. $3.5\times10^6~\text m$
2. $3.5\times10^6~\text {km}$
3. $3.5\times10^4~\text m$
4. $3.5\times10^4~\text{km}$

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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