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15 April, 00:08

Use the small-angle formula to calculate the angular diameter of Earth as seen from the Moon. (Note: The linear diameter of Earth is; the average distance between the Moon and Earth is; the small-angle formula is.)

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  1. 15 April, 01:00
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    Answer: 1.90°

    Explanation:

    The small angle formula is given as:

    tanθ = D/d

    Where

    θ = angular diameter;

    D = diameter of the earth;

    d = distance from moon to the earth.

    Therefore, angular diameter, θ, is:

    θ = tan⁻¹ (D/d)

    The (equatorial) diameter of the earth, D, is 12756.2km.

    The mean distance of the moon from the earth, d, is 384399km.

    Hence,

    θ = tan⁻¹ (12756.2/384399)

    θ = tan⁻¹ (0.03318478976272)

    θ = 1.90°

    Hence, the angular diameter of the earth, using the small angle formula, is 1.90°.
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