To determine the distance to the Moon, you can use Kepler's third law of planetary motion, which states that the square of the period of revolution is proportional to the cube of the average distance from the center of revolution.
1. Start by converting the period of revolution, which is given as 27.3 days, into seconds. There are 24 hours in a day and 60 minutes in an hour, so multiply 27.3 by 24 and then by 60 to get the number of seconds in the period:
27.3 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 2,360,320 seconds.
2. Now, we need to find out the average distance of the Moon from the Earth (also called the semi-major axis of the Moon's orbit). Rearranging Kepler's third law formula, we can solve for the distance:
Distance³ = Period²
Distance = ∛(Period²)
Plugging in the value we found for the period (2,360,320 seconds), we get:
Distance = ∛(2,360,320²)
3. Calculate the cube of the period:
Distance = ∛(5,572,914,790,400)
4. Calculate the cube root:
Distance ≈ 238,855 miles
Therefore, the Moon is approximately 238,855 miles away from the Earth.