Time Period Of A Satellite — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Time Period of a Satellite Strictly applicable to circular orbits. Can be approximated for elliptical orbits by replacing the orbital radius 'r' with the semi-major axis 'a'. Assumes the mass of the satellite is negligible compared to the central body. Equate Gravitational Force and Centripetal Force: G M m/r 2 = m v 2/r Solve for velocity v: v = sqrt(GM/r) Relate velocity to period for circular motion: v = 2 pi r / T Substitute v: 2 pi r / T = sqrt(GM/r) Isolate T: T = 2 pi r sqrt(r/GM) which simplifies to T = 2 pi sqrt(r 3/GM) r > Radius of Central Body (to avoid collision) M >> mass of satellite Confusing orbital radius (r) with altitude (h). r must include the planet's radius. Believing the period depends on the mass of the satellite (it cancels out). Forgetting to square the period or cube the radius when working with proportionalities.