force of gravity

Meaning: Every pair of masses attracts each other with equal and opposite forces (Newton's third law), directed along the line joining their centers. Near Earth's surface the force on an object of mass m is its weight, mg, where g is about 9.8 m/s². Gravity depends on mass, not charge, and it is the dominant force between large bodies such as planets.

Equation: F = Gm₁m₂/r², where F is the force in N, G is the gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²), m₁ and m₂ are the masses in kg, and r is the center-to-center distance in m.

On the MCAT: Expect ratio questions: doubling one mass doubles F, and doubling r cuts F to one quarter. At height h above the surface, r = R + h, where R is the planet's radius. For a circular orbit, gravity supplies the centripetal force, so GMm/r² = mv²/r and v = √(GM/r), independent of the satellite's mass. The inverse-square form is often compared with Coulomb's law.

Common confusion: Students think heavier objects fall faster. The force is larger, but so is the inertia, so a = F/m = g for every mass when air resistance is negligible. Also, orbiting astronauts feel weightless because they are in free fall, not because gravity is absent.