Final answer:
The magnitude of the gravitational force between the Earth and the Moon is determined using Newton's law of universal gravitation with the known values of the masses of the Earth and Moon and the distance between them.
Step-by-step explanation:
To calculate the magnitude of the gravitational force acting between the Earth and the Moon, we use Newton's law of universal gravitation:
F = G × (me × mm) / r²
where:
- F is the magnitude of the gravitational force between two masses,
- G is the gravitational constant (6.67 × 10-11 N·m²/kg²),
- me is the mass of the Earth (5.97 × 10²⁴ kg),
- mm is the mass of the Moon (7.35 × 10²² kg), and
- r is the distance between the centers of the two masses (3.93 × 10¸ meters).
Plugging in the values, we get:
F = (6.67 × 10^-11) × (5.97 × 10²⁴ × 7.35 × 10²²) / (3.93 × 10¸)²
After calculating this expression, you will get the magnitude of the gravitational force between the Earth and the Moon.