Gravitational PE (Near Earth)
U = mgh — drop a ball from height h and watch PE convert to KE.
Key Notes
Gravitational potential energy U of mass m at distance r from M: U = −GMm/r. Always negative (taking U → 0 at infinity).
Near Earth's surface (h ≪ R): U ≈ mgh + constant. Linear approximation; offset reference is arbitrary.
Work done by gravity = −ΔU. Falling object loses PE, gains KE.
Energy required to ESCAPE from surface = |U_surface| = GMm/R. This gives escape velocity (½mv² = GMm/R).
Orbiting body: total energy E = ½mv² + U = −GMm/(2r) (for circular orbit). Negative total energy = bound.
PE is a SCALAR. PE differences are physically meaningful; absolute PE has an arbitrary zero.
PE of a two-body system depends only on separation, not on individual positions.
Tidal forces arise from gradients in gravitational PE — different parts of an extended body sit at different U.
Formulas
Gravitational PE (point masses)
Reference: U(∞) = 0.
Near-surface approximation
Valid for h ≪ R; U is taken relative to surface (an arbitrary zero).
Total orbital energy
For circular orbit; negative ⇒ bound system.
Work-energy in gravity
Gravity is conservative — total energy conserved if only gravity acts.
Important Points
Gravitational PE is most negative when bodies are close — they have 'farther to fall' (in a sense, the energy radiated escaping is now stored as negative PE).
Near Earth's surface, U = mgh is the LINEAR approximation to the −GMm/r formula. Both are valid in their range.
The negative sign of U is a CONVENTION (V_∞ = 0). Physically only differences matter.
Energy required to escape from Earth's surface to infinity: GMm/R = mgR ≈ 6.25 × 10⁷ J per kg.
Bound systems have NEGATIVE total mechanical energy; unbound have ≥ 0.
For multi-body systems: U = Σ (−Gm_i m_j/r_ij), sum over all pairs (not ordered).
Gravitational PE (Near Earth) notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.