Question

The angle subtended by the moon's diameter at a point on the earth is about ${0.50}^{\circ }$. Use this and the fact that the moon is about 384000 km away to find the approximately diameter of the moon.

• A. 192000 km
• B. 3350 km
• C. 1600 km
• D. 1920 km

Answer 1

The correct option is B 3350 km

For objects that subtend a relatively small angle we can use the following approximation:

$s=r\theta$

Where is the actual diameter of the object in question, r is the distance to the object, and θ is the angle subtended by the object in the sky in radians we must convert degrees to radians:

$0.5ºx\left(\pi /180º\right)=0.00873rad$

$s=\left(384000000\right)\left(0.00873\right)=3.35\times {10}^{6}m$

A diameter of the moon is $3.35\times {10}^{6}m$