Physics
Newton's Law of Universal Gravitation
Quick fact
The gravitational force between two 1-kilogram objects 1 meter apart is only about 6.67 × 10⁻¹¹ newtons—roughly the weight of a single bacterium.
Why this is interesting
You feel weight pushing you against the ground right now—but what invisible force reaches across empty space to keep the Moon circling Earth, or to hold planets in their orbits around the Sun?
Read the full explanation
Understanding Newton's Law of Universal Gravitation
Imagine holding a ball in your hand. When you let go, it falls straight down. Why? Because Earth's mass is pulling it. But here's a surprising idea: the ball also pulls on Earth with an equally strong force—it's just that Earth is so massive its motion is negligible. Now extend this thought: any two objects with mass attract each other. The strength of that pull depends on two things: how much mass they have (more mass → stronger pull) and how far apart they are (greater distance → weaker pull). Newton found that the force drops off as the square of the distance—if you double the distance, the force becomes only one-quarter as strong. This is the 'inverse-square law.' It works for apples, moons, and galaxies alike.
A deeper explanation
The law is expressed mathematically as F = G·(m₁·m₂)/r², where F is the gravitational force, m₁ and m₂ are the masses, r is the distance between their centers, and G is a tiny constant that makes the units work. Newton realized that the same force causing an apple to fall also keeps the Moon in its orbit. The Moon is essentially 'falling' toward Earth—but it moves so fast sideways that it keeps missing, creating a circular path. This insight unified terrestrial and celestial physics, overturning the ancient belief that heavens followed different rules. The inverse-square nature arises naturally from the geometry of a sphere: gravity spreads out uniformly from a point mass, and the intensity over a spherical surface decreases with area (4πr²). Understanding this law explains phenomena from planetary orbits to ocean tides (caused by the Moon's pull on Earth's water), and it laid the groundwork for modern spaceflight—every rocket trajectory is calculated using this same equation.