Newton's Law of Gravitation
F = Gm₁m₂/r² — inverse-square force between two masses.
Key Notes
Newton's law of universal gravitation (1687): every two point masses attract along the line joining them with F = Gm₁m₂/r².
G = 6.674 × 10⁻¹¹ N·m²/kg² — the universal gravitational constant.
Force is always ATTRACTIVE, inverse-square in distance, proportional to product of masses.
Gravity acts equally on both bodies (Newton's third law): each pulls the other with the same magnitude F.
For spherically symmetric mass distributions, you can replace the sphere by a point mass at its centre (shell theorem).
Inside a uniform shell: gravitational field is ZERO. Inside a solid sphere of uniform density: F ∝ r (linear).
Cavendish (1798) measured G using a torsion balance — first laboratory test of gravity.
Universal: same law works between two atoms, Earth-Moon, Sun-Planets, galaxy-galaxy. Galileo's free-fall, Kepler's orbits, and tides all follow from this single equation.
Formulas
Newton's universal law
G = 6.674 × 10⁻¹¹ N·m²/kg².
Vector form
Force on 1 due to 2 points from 1 toward 2.
Gravitational field
Field strength from mass M at distance r.
Inside uniform sphere
Linear with r for r < R; zero at center.
Important Points
F is ALWAYS attractive (no repulsive gravity). Different from electric force.
F is INVERSE-SQUARE in distance — same as Coulomb. Doubling r quarters F.
Independent of intervening medium — gravity reaches everywhere.
Tiny but cumulative. Two 1-kg masses 1 m apart: F = 6.67 × 10⁻¹¹ N — undetectable. Earth-apple: 1 N — easily noticed.
G's smallness makes precision measurement very hard. Best modern value still has ~50 ppm uncertainty.
Newton's gravity is superseded by Einstein's General Relativity for strong fields / high speeds, but excellent at low-energy/everyday scales.
Newton's Law of Gravitation notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.