Final answer:
By rearranging and applying the formula for tangential speed in a circular orbit, we can use Earth's mass and the Moon's tangential speed to calculate the distance to the Moon. The mean distance has been known to be approximately 3.84 × 108 meters.
Step-by-step explanation:
To determine the distance between the Earth and its Moon, we can use the given Moon's tangential speed and apply Newton's law of universal gravitation. The tangential speed v of an object in a circular orbit is calculated using the formula v = √(GM/r), where G is the gravitational constant, M is the mass of the central object, and r is the radius of the object's circular orbit (the distance we want to find).
We are given Earth's mass (M) as 6.0 × 1024 kg. The moon's tangential speed (v) is 1,025 m/s. Rearranging the formula to solve for r, we get r = GM/v2.
Using the provided masses of the Earth and the Moon, and knowing the value of the gravitational constant G (6.674 × 10−12 N(m/kg)2), we can substitute into the formula:
r = (6.674 × 10−12 N(m/kg)2 × 6.0 × 1024 kg) / (1,025 m/s)2
This calculation gives us the mean distance from the Earth to the Moon, which as per known astronomical data, is approximately 3.84 × 108 meters (384,000 kilometers). The question likely intends for us to recognize this value as the approximate correct distance to the Moon.
Learn more about the Moon's Distance from Earth