Gravitation

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Gravitation — Key Facts Newton’s Law: F = Gm₁m₂/r²; G = 6.67×10⁻¹¹ N·m²/kg² g = GM/r² (on Earth’s surface g ≈ 9.8 m/s²); g varies with altitude and latitude Orbital velocity: v = √(GM/r) = √(gr) for orbit near surface; v ≈ 7.9 km/s Escape velocity: v_e = √(2GM/r) = √(2gr) ≈ 11.2 km/s from Earth ⚡ Exam tip: satellite in circular orbit — centripetal force = gravitational force

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Gravitation — NEET/JEE Study Guide Gravitational field: g = F/m = GM/r²; points toward mass; superposition for multiple masses Gravitational potential: V = -GM/r (negative); equipotential surfaces are spherical Kepler’s Laws: (1) orbits are ellipses with Sun at focus, (2) equal areas in equal times (L = constant), (3) T² ∝ r³ Time period: T = 2π√(r³/GM); for near-surface orbit, T ≈ 84 min; geostationary orbit T = 24h Mass of Earth: M = gR²/G where R = Earth’s radius ≈ 6400 km

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Gravitation — Comprehensive Notes Gravitational potential energy: U = -GMm/r (from infinity to r); total mechanical energy E = KE + PE = -GMm/2r = -KE Black hole: Schwarzschild radius R_s = 2GM/c²; escape speed = c; event horizon at R_s Variation of g: with altitude g’ = g(R/(R+h))²; with depth g’ = g(1 - d/R); at equator g_min due to rotation Satellite: geostationary orbit (T=24h, h≈36,000km, equatorial), polar orbit (sun-synchronous) Inertial vs gravitational mass: experimentally equivalent to 1 part in 10¹²; foundation of equivalence principle Gravitational slingshot: Δv = 2v_planet in planet frame; used by spacecraft to gain/lose speed

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