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The moon is observed from two diametric...

The moon is observed from two diametrically opposite points A and B on Earth. The angle `theta` subtended at the moon by the two directions of observation is `1^(@)54'` . Given the diameter of the Earth to be about `1.276xx10^(7)` , compute the distance of the moon from the Earth.

Text Solution

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We have `theta = 1^(@)54. =114. = (114xx60)"xx(4.85xx10^(-6))` rad
=`3.32xx10^(-2)` rad,
Since `1" = 4.85xx10^(-6)` rad,
Also b=AB=`1.276xx10^(7)m`
Hence from Eq. (2.1.) , we have the earth-moon distance.
D=b/`theta`
`=(1.276xx10^(7))/(3.32xx10^(-2))`
`=3.84xx10^(8)m`
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