Understanding the Formula
The force of gravity between two objects is calculated using Newton's Law of Universal Gravitation:
* F = G * (m1 * m2) / r²
Where:
* F is the force of gravity
* G is the gravitational constant (approximately 6.674 × 10⁻¹¹ N⋅m²/kg²)
* m1 is the mass of the first object (Earth in this case)
* m2 is the mass of the second object (1 kg in this case)
* r is the distance between the centers of the two objects (Earth's radius)
Calculations
1. Mass of Earth: m1 ≈ 5.972 × 10²⁴ kg
2. Mass of the body: m2 = 1 kg
3. Earth's radius: r ≈ 6.371 × 10⁶ m
Now, plug these values into the formula:
F = (6.674 × 10⁻¹¹ N⋅m²/kg²) * (5.972 × 10²⁴ kg * 1 kg) / (6.371 × 10⁶ m)²
Result
F ≈ 9.81 N
Therefore, the magnitude of the gravitational force between the Earth and a 1-kg body is approximately 9.81 Newtons. This is why we experience a gravitational acceleration of 9.81 m/s² near the Earth's surface.
