Force of gravity and weight of a body

The Earth attracts a body near its surface; this force is the force of gravity: F = mg, where g is the free-fall acceleration. From the law of universal gravitation g = GM/R², with M the Earth’s mass and R its radius (about 6400 km). The calculation gives g ≈ 9.8 m/s²; in problems g = 10 m/s² is often used. g is slightly larger at the poles (9.83 m/s²) and smaller at the equator (9.78 m/s²), because the Earth is flattened at the poles and rotates. g decreases with height above the surface. The force of gravity is proportional to the body’s mass, directed toward the Earth’s centre (vertically down) and applied at the body’s centre of mass.