Question

The distance between the Sun and the Earth is \[1.496 \times 10{}^8\]km and the distance between the Earth and the Moon is \[3.84 \times 10{}^8\]m. During the solar eclipse the Moon comes in between the Earth and the Sun. What is the distance between the Moon and the Sun at a particular time?

Answer 1

Hint: Distance between the Sun and the Earth is already mentioned in the question above and by following these rules as mentioned in the above question we easily achieve to get the answer in no time. The distance between the earth and the Moon is\[ = 3.84 \times 10{}^8\].

Complete step-by-step solution:
 It is given that the distance between the Sun and the Earth is \[1.496 \times 10{}^8\]. Now, the distance between the sun and the Earth \[ = 1.496 \times 10{}^8\] \[ \times 1000\]m,
\[ = 1.496 \times 10{}^{11}\]m [since, \[1\]km=\[1000\]m]
And, the distance between the earth and the Moon is \[3.84 \times 10{}^8\]m. At the time of the solar eclipse the Earth, the moon and the Sun will be in a straight line and the Moon comes in between the Earth and the Sun. So,
distance between the Moon and the Sun \[ = \]Distance between the sun and the earth – Earth and Moon.
\[ = 1.496 \times 10{}^{11}\]m - \[3.84 \times 10{}^8\]m
\[ = 10{}^8\left( {1.496 \times 10{}^3} \right. - 3.8\left. 4 \right)\]m
\[ = 10{}^8\left( {1496 - 3.8\left. 4 \right)} \right.\]m
\[ = 10{}^8\left( {1492.1\left. 6 \right)} \right.\]m
\[ = 1.49216 \times 10{}^{11}\]m
At the time of solar eclipse, the distance between the Moon and the Sun is \[1.49216 \times 10{}^{11}\]m.

Note: By using the correct formula and the given circumstances the correct answer is \[1.49216 \times 10{}^{11}\] m. Distance between the Earth and the Moon \[ = 3.84 \times 10{}^8\]m. Now by using the formula, distance between the Moon and Sun= Distance between the earth and the moon, we got the right answer. As We know the moon revolves around the earth and earth revolves around the sun, the distance which we have found above is at the time when all these three were in a straight line otherwise we couldn’t find the distance.