To find the angular diameter of the Moon at perigee, we can use the formula for angular diameter:
Angular Diameter (in degrees) = (Diameter of the object / Distance to the object) * (180 / π)
Given:
- Diameter of the Moon = 3,474 km
- Distance from the Earth to the Moon at perigee = 362,399 km
Let’s plug these values into the formula:
Angular Diameter = (3,474 km / 362,399 km) * (180 / π)
Now, calculating the values:
First, calculate the fraction:
- 3,474 / 362,399 = 0.009605
Then multiply by (180 / π):
- Angular Diameter ≈ 0.009605 * 57.2958 ≈ 0.5506 degrees
Next, to convert the decimal into degrees and arc minutes:
- 0.5506 degrees = 0 degrees and (0.5506 * 60) arc minutes
- 0.5506 * 60 ≈ 33.036 arc minutes
Therefore, the angular diameter of the Moon at perigee is approximately:
- 0 degrees and 33 arc minutes.