F = Gm₁m₂/r² Formula – Gravity Practice
F = Gm₁m₂/r² — Newton’s law of universal gravitation
The attractive force between two point masses is F = G m₁ m₂ / r². Separation is squared in the denominator — double r and force falls to one quarter.
Guide — how to use this formula
- 1. Use masses in kg and r in metres.
- 2. F = Gm₁m₂/r²; square r in the denominator.
- 3. G ≈ 6.67×10⁻¹¹ unless told otherwise.
- 4. Halving r multiplies F by 4.
Derivation
Newton’s inverse-square law for point masses:
- Force magnitude:
F = \frac{G m_1 m_2}{r^{2}} - Solve for separation:
r = \sqrt{\frac{G m_1 m_2}{F}}
Near Earth’s surface, W = mg is the practical shortcut; G ≈ 6.67×10⁻¹¹ N·m²/kg².
Examples
Example: 1 kg at 1 m
F = G ≈ 6.67×10⁻¹¹ N.
Example: double distance
2r → F/4.