Gravitational Force Calculator

F = Gm₁m₂/r² describes gravitational attraction between any two masses. Every object with mass attracts every other object. The force is proportional to both masses and inversely proportional to distance squared. Discovered by Newton in 1687, it explained planetary motion and unified celestial and terrestrial mechanics.

G is the universal gravitational constant: 6.674×10⁻¹¹ N·m²/kg². It's extremely small, which is why gravity only matters for large masses (planets, stars). G is universal - same everywhere in the universe. Measured by Henry Cavendish in 1798 using a torsion balance experiment.

Gravity is the weakest fundamental force. The electrical force between two protons is 10³⁶ times stronger! Yet gravity dominates at large scales because: 1) it's always attractive (charges can cancel), 2) it has infinite range, and 3) astronomical objects are electrically neutral but have huge masses.

Force follows inverse square law: doubling distance quarters the force (2² = 4). Tripling distance reduces it to 1/9th. This explains why gravity weakens rapidly with distance. Earth's gravity at twice the radius (2× Earth's radius from center) is 1/4th surface gravity.

G is the universal constant (6.674×10⁻¹¹). g is local gravitational acceleration (9.8 m/s² on Earth's surface), calculated as g = GM/r². G is the same everywhere; g varies by location. On the Moon, g ≈ 1.6 m/s²; on Jupiter, g ≈ 25 m/s².

Extremely accurate for most situations (spacecraft, satellites, planets). However, Einstein's General Relativity is needed for extreme conditions: very strong gravity (black holes), very precise measurements (GPS satellites), or very high speeds. For everyday astronomy, Newton's law works perfectly.