Gravitation notes

Gravitation explains the attractive force between any two masses in the universe. Newton’s universal law gives this force as proportional to the product of masses and inversely proportional to the square of separation. This chapter connects falling bodies, planetary motion, satellites, tides, weightlessness and escape from planets. Kepler’s laws describe planetary orbits and are explained by Newton’s law. Acceleration due to gravity, g, changes with altitude, depth and Earth’s rotation. Gravitational potential and potential energy help solve energy-based problems, while escape velocity and orbital velocity explain rockets and satellites. For NEET, this chapter is highly scoring because formulas are direct and concepts are repeatedly tested in numerical and assertion-type questions.

Newton’s universal law of gravitation states that every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The force acts along the line joining the two masses and is always attractive. The proportionality constant G is called the universal gravitational constant and has the same value everywhere in the universe. Gravitation is a long-range central force and obeys the inverse square law. When many masses are present, the net gravitational force is found by vector addition using the superposition principle. This topic is a frequent source of NEET ratio-based questions.

Kepler’s laws describe how planets move around the Sun. The first law states that planets move in elliptical orbits with the Sun at one focus, not at the centre. The second law says the line joining the planet and Sun sweeps equal areas in equal intervals of time; this means a planet moves faster near the Sun and slower when far away. The third law states that the square of orbital period is proportional to the cube of semi-major axis: T² ∝ a³. Newton later explained these laws using universal gravitation and centripetal force. NEET commonly asks statements, area law interpretation and period-radius comparison.

Acceleration due to gravity, g, is the acceleration acquired by a body falling freely under Earth’s gravitational pull. At Earth’s surface, it is obtained by equating weight mg with gravitational force GMm/R², giving g = GM/R². Unlike G, g is not universal; it changes with altitude, depth, latitude and Earth’s rotation. At height above Earth, g decreases according to inverse square law. Inside Earth, assuming uniform density, g decreases linearly with depth and becomes zero at the centre. Earth’s rotation reduces effective gravity, most at the equator and least at the poles. Weightlessness occurs when normal reaction becomes zero, such as in free fall or orbiting satellites.

Gravitational potential at a point is the work done per unit mass by an external agent in bringing a small test mass from infinity to that point without changing kinetic energy. Taking potential zero at infinity, potential due to a mass M is V = -GM/r. Gravitational potential energy of mass m is U = mV = -GMm/r. The negative sign means the mass is bound to the gravitational field and energy must be supplied to take it to infinity. Gravitational field is related to potential by g = -dV/dr. Equipotential surfaces have the same potential everywhere, so no work is done in moving a mass along them. Potentials due to multiple bodies add algebraically.

Escape velocity is the minimum speed with which a body must be projected from the surface of a planet so that it can reach infinity with zero speed, without further propulsion. It is derived using conservation of mechanical energy: the initial kinetic energy must equal the energy needed to overcome gravitational binding. Thus, v_e = √(2GM/R) = √(2gR). Escape velocity depends on the mass and radius of the planet, but not on the mass of the escaping object or the direction of projection if air resistance and rotation are ignored. It is related to orbital velocity near the planet by v_e = √2 v_o. NEET often asks comparisons between planets.

A satellite is a body revolving around a planet under gravitational attraction. In a circular orbit, gravity provides the required centripetal force, so GMm/r² = mv²/r. This gives orbital velocity v = √(GM/r), where r is distance from the planet’s centre. The orbital period is T = 2π√(r³/GM). Artificial satellites are launched for communication, weather monitoring, navigation, defence and scientific observation. A geostationary satellite has a 24-hour period, moves in the equatorial plane in the same direction as Earth’s rotation and appears fixed over one point. Polar satellites pass over poles and scan the entire Earth. Satellites and astronauts feel weightless because they are in continuous free fall.