Gravitation

One force, written in one line, that holds an apple to the ground and the Earth to the Sun. The chapter opens with Kepler's three laws — the empirical pattern in the planets' motion that Newton then explained — and shows that the law of areas is simply the conservation of angular momentum for a central force. It then states the universal law of gravitation, $F = G\frac{m_1 m_2}{r^2}$, adds the superposition principle and the two shell theorems that let an entire planet be treated as a point mass, and describes how Cavendish actually weighed $G$. From there everything follows: acceleration due to gravity, $g = \frac{G M_E}{R_E^2}$, which lets us weigh the Earth itself, and how $g$ varies with altitude, with depth, with latitude as the Earth spins, and with the planet's oblate shape. Then the energy picture — gravitational potential energy $U = -\frac{G M m}{r}$, why it is negative, the gravitational potential $V = -\frac{G M}{r}$ that belongs to the field alone, and the escape speed $v_e = \sqrt{2 g R_E} \approx 11.2$ km/s that follows from setting the total energy to zero. The chapter closes on satellites: orbital speed and period, the energy triple $K = -E$ and $U = 2E$ with the binding energy that would free a satellite, and the geostationary and polar orbits that carry our communications and weather instruments. Topics the rationalised syllabus trimmed — the latitude variation of $g$, geostationary and polar satellites, and weightlessness — are restored in full, because Boards, JEE Main and NEET ask about them every single year. Dedicated JEE and NEET Corners follow, each with a full-length exam-pattern practice drill.