Gravitation – Class 11 Physics Chapter 7 Notes & NCERT PDF

Introduction

The fact that all objects fall towards the earth has been known forever; the motion of planets was studied by Indian and Greek astronomers for centuries. Newton's genius was to see that the force that makes an apple fall is the same force that keeps the moon in orbit. This chapter covers Kepler's laws, Newton's universal law of gravitation, the variation of g, gravitational potential energy, escape speed and satellites.

Key Concepts

7.1–7.2 Kepler's Laws

Based on Tycho Brahe's careful observations, Johannes Kepler gave three laws:

7.3 Universal Law of Gravitation

Every body in the universe attracts every other body with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

F = G m₁m₂/r², directed along the line joining them. For extended bodies: a uniform spherical shell attracts an outside point mass as if all its mass were at its centre, and exerts zero force on a point mass inside it.

7.4 The Gravitational Constant

G was first measured by Henry Cavendish (1798) with a torsion balance. Accepted value: G = 6.67 × 10⁻¹¹ N m² kg⁻². Knowing G allowed "weighing the earth".

7.5 Acceleration due to Gravity on the Earth's Surface

g = G M_E/R_E². Because G and g are known, the earth's mass can be found.

7.6 Variation of g

So g decreases both above and below the surface.

7.7 Gravitational Potential Energy

For a mass m at distance r from the earth's centre, V(r) = −G M_E m/r (taking zero at infinity). Near the surface, the difference reduces to m g h. The gravitational potential is the potential energy per unit mass. The potential energy of a system of particles is the sum over all pairs.

7.8 Escape Speed

The minimum speed that lets a body escape the earth's gravity: ½ m v² = G M_E m/R_E ⇒ v_e = √(2 G M_E/R_E) = √(2 g R_E) ≈ 11.2 km s⁻¹. For the moon it is only about 2.3 km s⁻¹, about five times smaller, which is why the moon has no atmosphere.

7.9 Earth Satellites

A satellite in a circular orbit of radius R_E + h: gravity supplies the centripetal force ⇒ orbital speed v = √(G M_E/(R_E + h)) and period T = 2π √((R_E + h)³/(G M_E)), which is Kepler's third law. For a satellite close to the surface, T ≈ 85 minutes. The moon is a natural satellite; artificial satellites are used for communication, weather and remote sensing.

7.10 Energy of an Orbiting Satellite

KE = G M_E m/[2(R_E + h)], PE = −G M_E m/(R_E + h), so total E = −G M_E m/[2(R_E + h)]. The total energy is negative, meaning the satellite is bound; if E ≥ 0 it escapes.

Worked Examples

Formula / Key-Facts Sheet

Exam Focus

Frequent questions: statements and proofs of Kepler's second law (from angular momentum conservation), derivations of g(h) and g(d), escape speed, orbital velocity and period, energy of a satellite, and numericals like the mass of Mars and "weighing the earth".

Key Terms

Common Mistakes