Variation Of Acceleration Due To Gravity With Altitude

Variation Of Acceleration Due To Gravity With Altitude — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.

Variation of Acceleration due to Gravity with Altitude Valid for points exterior to the spherically symmetric mass distribution (h >= 0). Start with Newton's Law of Universal Gravitation: F = GMm/r 2 Define weight at surface: mg = GMm/R 2 implies g = GM/R 2 Define weight at altitude h: mg h = GMm/(R+h) 2 implies g h = GM/(R+h) 2 Divide g h by g: g h/g = R 2 / (R+h) 2 Rearrange to solve for g h h >= 0 Planet is modeled as a uniform sphere Using the approximation formula g h = g(1 - 2h/R) for large altitudes (only valid when h << R) Assuming gravity becomes zero immediately upon leaving the atmosphere Confusing altitude (h) with distance from center (r = R + h)