Question

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 .)

Answer 1

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°.