Gravitational Fields & Orbital Mechanics

Kepler's laws, satellite orbits, and escape velocity

Gravity follows an inverse-square law (F ∝ 1/r²). The circular orbital velocity v = √(GM/r) is the exact speed for a stable circular orbit — faster means elliptical or escape, slower means the satellite falls. Kepler's 3 laws: (1) orbits are ellipses with the planet at one focus; (2) equal areas in equal times (conservation of angular momentum); (3) T² ∝ a³. Escape velocity is √2 times the circular orbital speed.