Newton's Law of Gravitation — Two Asteroids (Worked Example)

Given

• m₁ = m₂ = 1.0 × 10¹² kg

• r = 500 m

• G = 6.674 × 10⁻¹¹ N·m²/kg²

Find

The mutual gravitational force F.

Principle

The same law governs asteroids and planets — only the masses and distances change. Both asteroids feel this identical force (Newton's third law).

Formula

Solution

1. Substitute: $F = \frac{(6.674 \times 10^{-11})(1.0 \times 10^{12})^2}{500^2}$

2. Numerator: $6.674 \times 10^{13}$; denominator: $2.5 \times 10^5$

3. Divide: $F = 2.67 \times 10^8\ \mathrm{N}$

Unit check

N·m²/kg² × kg² / m² = N — correct.

What this means physically

2.67 × 10⁸ N — enormous by everyday standards, yet between trillion-kilogram rocks it produces only a gentle drift together. Gravity is feeble unless masses are planetary.