Statement

Every particle of matter in the universe attracts every other particle with a gravitational force that is:

• Directly proportional to the product of their masses
• Inversely proportional to the square of the distance between them

Mathematical Form

The gravitational force F between masses m_{1} and m_{2} separated by distance r is:

F = G × m_{1} × m_{2} / $r^{2}$

Key Constants

• G = $6.674 \times 10^{-11}$ N $m^{2}$ $kg^{-2}$
• Dimensional formula of G: [$M^{-1}$ $L^{3}$ $T^{-2}$]
• G was first measured by Henry Cavendish (1798) using a torsion balance

Properties of Gravitational Force

• Always attractive (no repulsion possible)
• Acts along the line joining the two masses
• Obeys Newton's Third Law: $F_{12}$ = −$F_{21}$ (equal magnitude, opposite direction)
• Obeys superposition principle (vector addition of forces from multiple masses)
• Central force (acts along the radius vector) — conserves angular momentum
• Universal — applies to all masses everywhere in the universe
• Conservative — work done is path-independent

Cavendish Experiment

• Torsion balance with known masses
• Tiny angular twist measured by mirror-light lever
• This effectively "weighed the Earth" — once G known, M_Earth = $gR^{2}$/G

Surface Gravity

From Newton's Law, the gravitational acceleration at Earth's surface:

g = GM/$R^{2}$ ≈ 9.8 m $s^{-2}$

where M = Earth's mass = $5.97 \times 10^{24}$ kg, R = $6.4 \times 10^{6}$ m.