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The moon is at a distance of 3.84xx10^8 ...

The moon is at a distance of `3.84xx10^8` m from the Earth. If viewed from two diametrically opposite points on the Earth, the angle subtended at the moon is `1^@ 54`'. What is the diameter of the Earth?

Text Solution

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Angle subtended
`theta =1^@ 54. = 114. = 114 xx 2.91 xx 10^(-4) rad`
` = 3.317 xx 10^(-2) rad`
Diameter of the Earth `=- theta xx `distance to the moon from the Earth
` = 3.317 xx 10^(-2) xx 3.84 xx 10^8 m`
` = 1.274 xx 10^7 m`
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