The Moon's period of revolution around the Earth is 27.3 d. How far away is the moon?

You need to know the mass of the earth (M) to answer that question. You can look it up or use the relation

g = G M/r^2,

where g is the universal constant of gravity, r is the Earth's radius and g is the acceleration of gravity at the Earth's surface.

To get the radius R of the moon's orbit, use Kepler's third law.

G M/R^2 = V^2/R = [(2 pi R)/P]^2/R
which rearranges to
R^3/P^2 = M G/(4 pi^2)
where P is the period in seconds.

For another explanation see
http://www-istp.gsfc.nasa.gov/stargaze/Skepl3rd.htm

Well, let me tell you a little secret. The moon is actually a master at hide and seek. It's been playing this game with Earth for billions of years. Sometimes it hides behind clouds or trees and other times it's just chilling in the sky, like "Hey, I'm here, can you spot me?" So, the moon is actually about 384,400 kilometers away from Earth on average. But don't feel bad if you can't find it, it's a pro at this game!

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.

To calculate the distance to the moon, we need to use the period of revolution and some information about Earth's orbit around the Sun.

Step 1: Find Earth's orbital period
Earth's orbital period around the Sun is approximately 365.25 days. This value takes into account the extra quarter day in a leap year.

Step 2: Calculate the average distance from Earth to the Sun
This distance is known as an astronomical unit (AU). On average, Earth is about 1 AU away from the Sun.

Step 3: Determine the Moon's average speed
The Moon completes one revolution around the Earth in 27.3 days. So, we can calculate its average speed using the equation:
Speed = Distance / Time

The distance traveled by the Moon in one revolution is the circumference of its orbit. This can be expressed as:
Distance = 2πr
where r is the radius of the Moon's orbit.

The time taken for one revolution is 27.3 days.

By substituting these values into the speed equation, we get:
Speed = 2πr / 27.3

Step 4: Calculate the Moon's distance from Earth
We know that the Moon's average speed is approximately 1 km/s (kilometer per second). We can solve the speed equation for r:
1 km/s = 2πr / 27.3

By rearranging the equation, we find:
r = (1 km/s) * 27.3 / 2π

Evaluating this expression will give us the Moon's distance from Earth.

The calculated average distance between the Moon and Earth is approximately 384,400 km.