Question

The following problem presents hypothetical values. In the diagram below, the synodic period (one lunar month) is given as 30 days. The measured time from 3rd to 1st Quarter is 14.9 days. Use the given values to find x. Show your work in the space below.

Answer 1

Answer:

x is approximately 95.495

Explanation:

The given information are;

One lunar month = 30 days

The measured time between the first and third quarters = 14.9 days

Therefore, the angle of rotation for 30 days = 360°

The angle of rotation for 14.9 days = 14.9×360/30 = 178.8°

Therefore, whereby 2·θ = 178.8°

θ = 178.8°/2 = 89.4°

Therefore, given that the angle at the tangent from Sun to the Moon = 90°, we have;

The angle between the line from the Sun to the Moon = 90° - 89.4° = 0.6°

From sine rule, we have;

1/(sin 0.6) = x/(sin 90°)

x = (sin 90°)/(sin 0.6°) ≈ 95.495

x = 95.495.