Newtonian Gravity Explorer

The 1/r² dependence is not an arbitrary choice — it emerges from geometry. Gravity spreads like light from a point source: the same total flux passes through any sphere surrounding the mass, so intensity falls as 1/(4πr²). This is why all fields that spread isotropically in three dimensions share the same 1/r² profile. The law holds everywhere Newton tested it — planets, pendulums, tides — but breaks down in strong-field regimes. Mercury's perihelion advances 43 arcseconds per century more than Newtonian gravity predicts. General relativity replaces the instantaneous force with the curvature of spacetime: mass tells space how to curve, and curved space tells mass how to move. For most engineering and solar-system work, the Newtonian formula is accurate to better than one part in a million.

The formula F = G·m₁·m₂/r² treats both masses the same, so the force Earth exerts on you is exactly the force you exert on Earth — equal and opposite, as Newton's third law demands. You don't fly toward nearby objects because acceleration is force divided by mass: Earth's enormous mass barely twitches. The constant G ≈ 6.674 × 10⁻¹¹ is so tiny that gravity only becomes noticeable once at least one mass is astronomically large.

Of nature's four fundamental forces, gravity is by far the feeblest. Compare two protons: their electric repulsion outmuscles their gravitational attraction by a factor of roughly 10³⁶. That is why a coin-sized magnet lifts a paperclip against the pull of the entire planet. Gravity only rules the cosmos because mass, unlike electric charge, never cancels out — it only ever adds up.