Universal Gravitation Governs Every Orbit

Here is what Newton realized that changed everything: every object in the universe pulls on every other object with gravity. Not just Earth pulling you down — the Moon pulling Earth, Jupiter pulling its moons, even you pulling the Sun (a tiny bit!). Gravity always pulls objects toward each other — it is never repulsive. The law is written as F = Gm₁m₂/r², where F is the gravitational force in newtons, m₁ and m₂ are the masses of the two objects in kilograms, r is the center-to-center distance between them in meters, and G is the universal gravitational constant — 6.674 × 10⁻¹¹ N·m²/kg². Two things control how strong gravity is. First, mass: double either mass and the force doubles. Second — and this is the part that surprises most people — distance: double the separation and the force drops to one-quarter. Triple it and the force falls to one-ninth. That 1/r² pattern is called the inverse-square law, and it shows up in the brightness of starlight, sound intensity, and the intensity of electromagnetic radiation too. Let's try a ratio problem. Suppose a satellite orbits at distance r from Earth's center, producing force F. If you move it to distance 3r, how does the force change? The new force is F × (r/3r)² = F × (1/9). The satellite feels one-ninth the original force — no calculator needed, just the ratio. So how does this explain orbits? An orbit is not a special kind of motion — it is free-fall that keeps missing. A planet falls toward the Sun because of gravity, but it also moves sideways fast enough that the curved surface of its path matches the curve of its fall. Planets actually move faster when they are closer to the Sun and slower when farther away. Newton showed that an inverse-square force produces exactly the elliptical orbits Kepler had mapped decades earlier from data alone. Gravity unifies the falling apple and the orbiting Moon into a single law.