AI Tutor
What keeps the Moon locked in orbit around Earth instead of drifting endlessly into deep space? In 1687, Isaac Newton realized that the exact same invisible pull causing an apple to drop from a branch also commands the orbits of moons and planets.
This revolutionary concept became Newton's Law of Universal Gravitation, which states that every single object with mass in the universe attracts every other object.
How do we quantify this invisible attraction between two bodies?

The Universal Equation

The gravitational force (FgF_g) between two objects depends directly on their masses and drops off with the distance separating their centers.
Mathematically, the law is written as Fg=Gm1m2r2F_g = G \frac{m_1 m_2}{r^2} where m1m_1 and m2m_2 are masses in kilograms, rr is the center-to-center distance in meters, and GG is the universal gravitational constant.
The constant GG equals 6.674×10−11 N⋅m2/kg26.674 \times 10^{-11} \text{ N}\cdot\text{m}^2/\text{kg}^2. Because GG is so unimaginably tiny, gravitational forces between everyday objects like chairs and laptops are far too small to feel.
What happens to the gravitational pull if we make one or both objects heavier?

Proportional to Mass

Gravitational force is directly proportional to the product of the two masses (Fg∝m1m2F_g \propto m_1 m_2).
If you double the mass of one object (2m12m_1), the gravitational pull doubles (2Fg2F_g). If you double both masses (2m12m_1 and 2m22m_2), the force becomes 2×2=42 \times 2 = 4 times stronger (4Fg4F_g).