To calculate the gravitational force between the Earth and the Moon, we can use Newton's law of universal gravitation, which is given by:
F = (G * m1 * m2) / r²
Where F is the force of gravity, G is the gravitational constant (6.674 x 10⁻¹¹ N·(m/kg)²), m1 and m2 are the masses of the two objects (Earth and Moon), and r is the distance between the centers of the two objects.
In this case, m1 (Earth's mass) = 6 x 10²⁴ kg, m2 (Moon's mass) = 7.35 x 10²² kg, and r (distance between the Earth and the Moon) = 3.84 x 10¹¹ m.
Plugging these values into the formula, we get:
F = (6.674 x 10⁻¹¹ N·(m/kg)²) * (6 x 10²⁴ kg) * (7.35 x 10²² kg) / (3.84 x 10¹¹ m)²
Now, calculate the force:
F ≈ 1.9821 x 10²⁰ N·m²/kg² / 1.4756 x 10²³ m²
F ≈ 1.3426 x 10²⁷ N·m² / 1.4756 x 10²³ m²
F ≈ 9.09 x 10²³ N
The gravitational force between the Earth and the Moon is approximately 9.09 x 10²³ N.