The Angular Diameter of a Spherical Object

What is the angular diameter to the nearest hundredth of a degree of a spherical object with a diameter of 16 m at a distance of 1338 m?

A. 0.09 degrees B. 6.28 degrees C. 0.21 degrees D. 1.24 degrees E. 0.69 degrees

Answer:

E. 0.69 degrees

When calculating the angular diameter of a spherical object with a given diameter and distance, we use the formula:

Angular Diameter = 2 * arcsin(d / 2D)

Where:

d = 16 m is the diameter of the object

D = 1338 m is the distance to the object

Plugging in the values into the formula:

Angular Diameter = 2 * arcsin(16 / (2*1338))

Angular Diameter ≈ 0.685 degrees ≈ 0.69 degrees

Therefore, the angular diameter of the spherical object with a diameter of 16 m at a distance of 1338 m is approximately 0.69 degrees to the nearest hundredth of a degree.