UNIVERSAL LAW OF GRAVITATION (Newton):
  F = G × m₁ × m₂ / r²
  G = 6.674 × 10⁻¹¹ N·m²/kg² (universal gravitational constant)
  F is attractive, acts along line joining the two masses
  
  Vector form: F = -G m₁ m₂ r̂ / r² (negative = attractive direction)

GRAVITATIONAL FIELD:
  g = GM/r² (gravitational field intensity)
  At Earth's surface: g = 9.8 m/s² = GM_E/R_E²
  
  Variation of g:
    Altitude h: g_h = g(1 - 2h/R) for h << R; exact: g_h = gR²/(R+h)²
    Depth d: g_d = g(1 - d/R) → g = 0 at centre of Earth
    Latitude φ: g_φ = g - ω²R cos²φ (Earth rotation effect)
      g minimum at equator | g maximum at poles
    Shape: Earth is oblate spheroid → g greater at poles than equator

GRAVITATIONAL POTENTIAL:
  V = -GM/r (potential at distance r from mass M)
  Negative sign: work done TO bring mass from infinity to that point
  Potential energy: U = -GMm/r (for mass m in field of M)
  
  At Earth's surface: V = -gR = -6.25 × 10⁷ J/kg

ESCAPE VELOCITY:
  Minimum velocity to escape gravitational pull
  v_e = √(2GM/R) = √(2gR)
  Earth: v_e = √(2 × 9.8 × 6.4×10⁶) = 11.2 km/s
  Moon: 2.4 km/s (lower → no atmosphere, gas molecules escape)
  
ORBITAL VELOCITY:
  For circular orbit at radius r from centre: v_o = √(GM/r)
  At Earth's surface (r = R): v_o = √(gR) ≈ 7.9 km/s
  Relationship: v_e = √2 × v_o

KEPLER'S LAWS:
  1st (Ellipse): planets orbit Sun in ellipses with Sun at one focus
  2nd (Area): equal areas swept in equal times (angular momentum conserved)
  3rd (Period): T² ∝ r³ → T₁²/T₂² = r₁³/r₂³
    For Earth around Sun: T = 1 year, r = 1 AU (defining values)

GEOSTATIONARY SATELLITE:
  Orbit: equatorial, circular, at 36,000 km altitude
  Period: 24 hours (same as Earth's rotation → appears stationary)
  Orbital velocity: 3.1 km/s
  Use: TV, communication, weather satellites

ORBITAL ENERGY:
  KE = GMm/2r = ½mv²
  PE = -GMm/r
  Total E = KE + PE = -GMm/2r (negative = bound system)
  
  Adding energy → orbit goes higher → velocity decreases (counterintuitive!)
  Energy to escape orbit: +GMm/2r (make total E = 0)

WEIGHTLESSNESS IN ORBIT:
  Not true weightlessness (gravity still acts)
  Apparent weightlessness: astronaut and spacecraft in free fall together
  Normal reaction N = m(g - a_centripetal) = 0 when in orbit (g = v²/r)

COMMON NEET QUESTIONS:
  Calculate escape velocity for Moon or other planet
  Find orbital velocity at given altitude
  Apply Kepler's third law to compare planetary orbits
  Variation of g with altitude, depth, latitude
  Energy of satellite, binding energy

FORMULA SUMMARY:
  F = Gm₁m₂/r² | g = GM/R² | v_o = √(GM/r) | v_e = √(2GM/R) = √2 × v_o
  T² = 4π²r³/GM (Kepler's 3rd) | E_satellite = -GMm/2r | g_h = gR²/(R+h)²

CONSTANTS:
  G = 6.67×10⁻¹¹ N·m²/kg² | M_E = 6×10²⁴ kg | R_E = 6.4×10⁶ m | g = 9.8 m/s²