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Gravitation

NCERT Class 11 Physics Chapter 7

Gravitation for Class 11 Physics, JEE and NEET: Kepler’s laws, the law of gravitation, variation of g, potential energy, escape velocity and satellites.

9 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part I (Class 11), Chapter 7 “Gravitation”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.8 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Kepler’s laws

    The law of orbits, the law of areas and the law of periods, T ∝ a, with planetary data and solved examples.

    NCERT Section 7.2 12 min read 3 solved examples 6 practice questions

  2. Universal law of gravitation

    F = Gmm/r, the Moon test, vector form, superposition, the shell theorem and solved examples.

    NCERT Section 7.3 12 min read 3 solved examples 6 practice questions

  3. The gravitational constant

    Its value, unit and dimensions, and Cavendish’s torsion balance experiment, with solved examples.

    NCERT Section 7.4 10 min read 3 solved examples 6 practice questions

  4. Acceleration due to gravity

    The Earth as shells, g = GM/R, g from density and the mass of the Earth, with solved examples.

    NCERT Section 7.5 11 min read 3 solved examples 6 practice questions

  5. Variation of g with height and depth

    Exact and approximate g(h), g(d) = g(1 − d/R) for a uniform Earth, with solved examples.

    NCERT Section 7.6 10 min read 3 solved examples 6 practice questions

  6. Gravitational potential energy

    Mgh, U = −GMm/r and why it is negative, systems of particles, potential V = −GM/r, examples.

    NCERT Section 7.7 11 min read 3 solved examples 7 practice questions

  7. Escape speed

    Derived from energy, √(2GM/R) = √(2gR) ≈ 11.2 km/s, the Moon’s value and NCERT Example 7.4.

    NCERT Section 7.8 16 min read 4 solved examples 6 practice questions

  8. Earth satellites

    V = √(GM/r), the period and Kepler’s third law, the 85-minute orbit and geostationary orbits.

    NCERT Section 7.9 14 min read 4 solved examples 7 practice questions

  9. Energy of an orbiting satellite

    Kinetic, potential and total energy, E = −GMm/(2r), binding energy and changing orbits, with examples.

    NCERT Section 7.10 13 min read 3 solved examples 6 practice questions

Key formulas in this chapter

Kepler’s laws

  • a = (rP + rA)/2
  • dA/dt = L/(2m) (constant)
  • vP rP = vA rA
  • T ∝ a
  • T = (4π/GM) r (circular orbit)

Universal law of gravitation

  • F = Gmm/r (point masses or non-overlapping spherical bodies)
  • F = −G(mm/r) r̂ (vector form, force on m)
  • F = −F (as vectors)
  • am = 4π2Rm/T2 (the Moon)
  • g/am = Rm^2/RE^2 ≈ 3600

Gravitational constant

  • G = 6.67 × 10 N m kg
  • [G] = [M L T]
  • G(Mm/d) L = κθ (torsion balance)
  • G = κθd/(MmL)

Acceleration due to gravity

  • g = GME/RE^2 (surface)
  • g = (4/3)πGρRE
  • ME = gRE^2/G
  • F(r) = GmME r/RE^3 (inside a uniform Earth)
  • W = mg

Variation of g

  • g(h) = gRE^2/(RE + h)2 (exact)
  • g(h) ≈ g(1 − 2h/RE) (h ≪ RE)
  • g(d) = g(1 − d/RE) (uniform Earth)
  • g = 0 at the centre

Gravitational potential energy

  • U = −Gmm/r (zero at infinity)
  • U = −GME m/r (mass m outside the Earth)
  • ΔU = GME m(1/r1 − 1/r2) (from r1 to r2)
  • ΔU ≈ mgh (h ≪ RE)
  • V = −GME/r (potential)

Escape speed

  • ve = √(2GME/RE) = √(2gRE) ≈ 11.2 km/s
  • ve = √(2GME/(RE + h)) (from a height h)
  • vf^2 = v2 − ve^2 (speed left at infinity)
  • h = RE v2/(ve^2 − v2) (thrown straight up at v < ve)

Earth satellites

  • V = √(GME/(RE + h)) (orbital speed)
  • V0 = √(gRE) ≈ 7.9 km/s (just above the surface)
  • T = 2π(RE + h)/V, T2 = k(RE + h)3, k = 4π2/(GME)
  • T0 = 2π√(RE/g) ≈ 85 min
  • M ≈ 4πr/(GT) (circular orbit; negligible satellite mass)

Energy of an orbiting satellite

  • K = GME m/(2r)
  • U = −GME m/r
  • E = K + U = −GME m/(2r)
  • K = −E, U = 2E
  • ΔE = (GME m/2)(1/r1 − 1/r2) (between circular orbits)

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