Final answer:
Using Newton's Law of Universal Gravitation, the magnitude of the gravitational attraction between the Earth and the Moon, with given masses and distance, is calculated to be approximately 1.982 × 10^20 N.
Step-by-step explanation:
To calculate the magnitude of the gravitational attraction between the Earth and the Moon, we use Newton's Law of Universal Gravitation, which states that the force (F) between two masses (m1 and m2) is given by the equation:
F = G * (m1 * m2) / r^2
Where G is the gravitational constant (6.674 × 10^-11 N·m²/kg²), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
Given:
Earth's mass (m1) = 6 × 10^24 kg
Moon's mass (m2) = 7.35 × 10^22 kg
Distance (r) = 384,403 km = 384,403 × 10^3 m = 3.84 × 10^8 m
Plugging these values into the equation, we get:
F = (6.674 × 10^-11 N·m²/kg²) * (6 × 10^24 kg * 7.35 × 10^22 kg) / (3.84 × 10^8 m)^2
Performing the calculation yields:
F ≈ 1.982 × 10^20 N
Thus, the correct answer is A. 1.982 × 10^20 N, which is the magnitude of the gravitational force between the Earth and the Moon.