Friction is where energy hides

Why this rule exists

An orbiting body is in free fall — gravity is the only force, pulling it toward the center — yet it never arrives, because its sideways speed carries it past. The surface curves away exactly as fast as the body falls. This is Newton's cannonball: fire fast enough horizontally and the planet's curvature keeps pace with the fall, closing the path into a closed orbit.

In practice

For a circular orbit, set gravity equal to the centripetal requirement: gravity must supply exactly the v²/r needed to curve the path. Solve that single balance for orbital speed or radius. Remember that astronauts are weightless not because gravity is absent but because they and their craft are falling together at the same rate.

Example

Gravity supplies the centripetal force:

m*g = m*v²/r

The mass cancels:
v = sqrt(g*r)

Near Earth (g ≈ 9.8, r ≈ 6.4e6 m):
v ≈ 7900 m/s   (about 8 km/s)

When it doesn't apply

The simple balance assumes a two-body, inverse-square field. Add a third body, atmospheric drag, or general-relativistic curvature and orbits precess or decay — Mercury's perihelion shifts measurably, a discrepancy unexplained until Einstein.