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The moon is observed from two diametrica...

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

Text Solution

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Distance between points of observation=Diameter of earth.
i.e., `b = 2rimplies b=2 xx 0.638 xx10^(7) = 1.276xx 10^(7)`m Angle subtended at moon `theta =1^(@)54^(1)= 1.9^(@)`
`implies theta=1.9 xx 1.745 xx 10^(-2) = 3.32 xx10^(-2)` rad Distance of moon, `D = (b)/(theta)implies D= (1.276 xx10^(7))/(3.32 xx10^(-2))= 3.84 xx10 ^(8)m`
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Knowledge Check

  • What is the approximate distance (in km) of the moon from Earth?

    A
    3,84,400
    B
    2,80,500
    C
    5,60,000
    D
    6,00,000

  • If the distance of the moon from earth is and the period of revolution is T_(m) ,then the mass of the earth is

    A
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    B
    `(4pi^(2)r_(m)^(3))/(GT_(m)^(2))`
    C
    `(4pi^(2)r_(m))/(GT_(m))`
    D
    `(4pi^(2)r_(m))/(GT_(m)^(2))`

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