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  • During a total solar eclipse the moon almost entirely covers the sphere of the sun. Write the relation between the distances and sizes of the sun and moon.

During a total solar eclipse the moon almost entirely covers the sphere of the sun. Write the relation between the distances and sizes of the sun and moon.

Answers (1)

Thus, \Omega _{s}= \Omega _{m}

Thus, \frac{\pi (\frac{D_{s}}{2})^{2}}{r{_{s}}^{2}}= \frac{\pi (\frac{D_{m}}{2})^{2}}{r{_{m}}^{2}}

i.e., \frac{D_{s}^{2}}{4r_{s}^{2}}= \frac{D_{m}^{2}}{4r_{m}^{2}}

Thus, \frac{4R_{s}^{2}}{4r_{s}^{2}}= \frac{4R_{m}^{2}}{4r_{m}^{2}}

Taking square roots,

\frac{R_{s}}{r_{s}}=\frac{R_{m}}{r_{m}}

Or,

\frac{R_{s}}{R_{m}}=\frac{r_{s}}{r_{m}}

Therefore, the ratio of the size of the sun to the moon is equal to the distances from the sun to the moon from earth.

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