It is a well known fact that during a total solar eclipse the dis… - Vidyadip

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

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 $=3.84 \times 10^8 \mathrm{~m}$ Distance of the Sun from the Earth $=1.496 \times 10^{11} \mathrm{~m}$ Diameter of the Sun $=1.39 \times 10^9 \mathrm{~m}$ It can be observed that $\Delta \mathrm{TRS}$ and $\Delta \mathrm{TPQ}$ are similar. Hence, it can be written as: $\mathrm{PQ} / \mathrm{RS}=$ VT/UT $1.39 \times 10^9 /$ RS $=1.496 \times 10^{11} / 3.84 \times 10^8 \mathrm{RS}=(1.39 \times 3.84 / 1.496) \times 10^6=3.57 \times 10^6 \mathrm{~m}$ Hence, the diameter of the Moon is $3.57 \times 10^6 \mathrm{~m}$

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