Newton's Law of Universal Gravitation
Calculate the gravitational force between any two masses.
The formula that explains orbits, tides, and falling objects.
The Formula
F = G × (m₁ × m₂) / r²
Every object with mass attracts every other object with mass. The force is proportional to both masses and inversely proportional to the square of the distance between them.
Variables
| Symbol | Meaning |
|---|---|
| F | Gravitational force (Newtons) |
| G | Gravitational constant (6.674 × 10⁻¹¹ N⋅m²/kg²) |
| m₁, m₂ | Masses of the two objects (kg) |
| r | Distance between the centers of the two masses (meters) |
Example 1
Find the gravitational force between Earth and the Moon
m₁ = 5.972 × 10²⁴ kg (Earth), m₂ = 7.342 × 10²² kg (Moon)
r = 3.844 × 10⁸ m
F = 6.674 × 10⁻¹¹ × (5.972 × 10²⁴ × 7.342 × 10²²) / (3.844 × 10⁸)²
F ≈ 1.98 × 10²⁰ N
Example 2
Two 1,000 kg satellites are 10 m apart in space
F = 6.674 × 10⁻¹¹ × (1000 × 1000) / 10²
F = 6.674 × 10⁻¹¹ × 10⁶ / 100
F ≈ 6.674 × 10⁻⁷ N (extremely small — gravity is a weak force)
When to Use It
Use Newton's law of gravitation when:
- Calculating the force of gravity between celestial bodies
- Understanding why objects orbit planets and stars
- Comparing gravitational forces at different distances
- Determining the gravitational field strength on other planets