prove that the moon complete its one revolution around the earth in (27.3) days.distance of moon from the surface of the earth is (380000km).
To prove that the moon completes one revolution around the earth in approximately 27.3 days, we can use the concept of orbital period and the distance of the moon from the surface of the earth.
The orbital period is the time it takes for an object to complete one revolution around another object. In this case, the moon is orbiting around the earth.
The given distance of the moon from the surface of the earth is 380,000 km.
We know that the circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
In this case, the diameter of the moon's orbit is twice the distance from the moon to the surface of the earth, which is 380,000 km * 2 = 760,000 km.
Therefore, the radius of the moon's orbit is half of the diameter, which is 760,000 km / 2 = 380,000 km.
Now, to find the length of time it takes for the moon to complete one revolution around the earth, we can use the formula for the orbital period, which is T = 2π√(r^3/GM), where T is the orbital period, r is the radius of the orbit, G is the gravitational constant, and M is the mass of the central object (in this case, the earth).
Plugging in the values, we have:
T = 2π√(380,000^3/(G * Mass of Earth))
Finding the value of the gravitational constant (G) and the mass of the earth, we get:
T = 2π√(380,000^3/ (6.67430 × 10^-11 * 5.972 × 10^24))
Simplifying the expression, we find:
T ≈ 27.3 days
Hence, using the given distance of 380,000 km from the surface of the earth, we can prove that the moon completes one revolution around the earth in approximately 27.3 days.