If a vehicle circled Earth at a distance equal to the Earth-Moon distance, how long would it take to make a complete orbit?

What is the Moon's period?

To find out how long it would take for a vehicle to complete an orbit around the Earth at a distance equal to the Earth-Moon distance, you can use Kepler's Third Law of Planetary Motion. This law states that the square of the orbital period of a planet is directly proportional to the cube of its semi-major axis.

Here's how you can calculate the orbital period:

Step 1: Find the semi-major axis
The semi-major axis is the average distance between the Earth and the Moon, which is about 384,400 kilometers.

Step 2: Square the semi-major axis
384,400 km * 384,400 km = 147,585,760,000 km²

Step 3: Cube the result from Step 2
147,585,760,000 km² * 384,400 km = 56,699,423,718,400,000,000 km³

Step 4: Take the square root of the result from Step 3
√(56,699,423,718,400,000,000 km³) ≈ 7,527,739,398 km²

Step 5: Take the square root of Step 4 to determine the orbital period
√(7,527,739,398 km²) ≈ 2,745,709 seconds

So, a vehicle circling the Earth at a distance equal to the Earth-Moon distance would take approximately 2,745,709 seconds, or about 31 days, 17 hours, and 14 minutes, to complete one orbit.