Orbital Motion, Gravity & Planets: JEE Main Guide

Gravitation is one of the most concept-rich chapters in JEE Main Physics, contributing three to four marks every year. Unlike Electrostatics, where you can lean on formulaic pattern recognition, Gravitation demands a clear mental picture: why satellites stay in orbit, why escape velocity is independent of mass, and how Kepler's laws encode centuries of astronomical observation into three elegant statements. This guide covers every corner of Gravitation that JEE Main actually tests.

Newton's Law of Gravitation and the Gravitational Field

The gravitational force between two masses m₁ and m₂ separated by distance r is F = Gm₁m₂/r². The gravitational field g = GM/r² is the force per unit mass — it depends only on the source, not the test mass. Inside a solid uniform sphere, g decreases linearly with r (g ∝ r); outside it falls as 1/r². At depth d below the surface, g_depth = g₀(1 − d/R); at height h above, g_height = g₀/(1 + h/R)². The difference between these two expressions trips up students every year — memorise both and know when each applies.

Gravitational potential V = −GM/r (negative because gravity is attractive and we take the reference at infinity). Potential energy U = mV = −GMm/r. The escape velocity v_e = √(2GM/R) = √(2gR) emerges from setting kinetic energy equal to the magnitude of potential energy at the surface. For Earth, v_e ≈ 11.2 km/s. The fact that escape velocity is mass-independent is a conceptual JEE favourite. Test your Gravitation speed with a free mock before moving on.

Kepler's Laws and Orbital Mechanics

Kepler's three laws are: (1) planets move in ellipses with the Sun at one focus; (2) the line joining Sun and planet sweeps equal areas in equal times (conservation of angular momentum); (3) T² ∝ a³ where a is the semi-major axis. For circular orbits, T² = 4π²r³/GM, giving T ∝ r^(3/2). JEE uses the third law extensively — given one planet's orbit, find another's period. The derivation uses F_gravity = F_centripetal: GM/r² = ω²r, giving ω = √(GM/r³) and v_orbital = √(GM/r).

Note that v_orbital decreases as r increases (higher orbits are slower), while T increases. Geostationary orbits have T = 24 hours and are at r ≈ 42,000 km from Earth's centre. Energy of a circular orbit: E = −GMm/2r (negative, meaning bound). The total energy is half the potential energy — the Virial theorem result that JEE tests in integer-type questions. For related orbital energy ideas, see our complete gravitation guide and mechanics master guide.

Satellites, Weightlessness and Binding Energy

Orbital speed v₀ = √(GM/r) = √(gR²/r). At the surface approximation (r = R), v₀ = √(gR) ≈ 7.9 km/s for Earth. Weightlessness in a satellite is not because gravity is zero — it is because both the satellite and the astronaut are in free fall together. Gravitational acceleration at orbital altitude is still significant (about 8.7 m/s² at ISS altitude). Understanding this distinction earns you marks in reasoning questions.

Binding energy = −E = GMm/2r. To move a satellite from radius r₁ to r₂ > r₁ requires doing positive work (more binding energy is lost than kinetic energy gained, and the orbit slows down — a counterintuitive result). Atmospheric drag on low-Earth satellites decreases r, which paradoxically speeds them up. JEE sometimes probes this speed-up-when-decelerating idea as a conceptual question.

Exam Strategy for Gravitation

The chapter has roughly six question archetypes: orbital speed derivation, Kepler's third law ratio, gravitational field inside/outside/at-surface comparisons, escape velocity variants, potential and potential energy calculations, and geostationary orbit properties. Solve ten previous-year questions from each type and you will recognise the next JEE question instantly. For the broader Physics scoring framework, revisit our Physics 100+ strategy guide.