Ch 8 covers gravitation in depth — Kepler's laws, Newton's law with derivations, gravitational field, potential energy, escape and orbital velocities, and satellite mechanics.
Kepler's laws: (1) orbits are ellipses with Sun at one focus, (2) radius vector sweeps equal areas in equal time (areal velocity constant), (3) T² ∝ a³. Newton's law: F = GMm/r². Gravitational field g = GM/r² (at surface, g = GM/R²). Variation: with height g_h = g(1−2h/R) for h<<R; with depth g_d = g(1−d/R).
Gravitational PE: U = −GMm/r (zero at infinity). Total energy of satellite: E = −GMm/2r (negative → bound). Escape velocity: minimum speed to leave Earth's gravity = √(2gR) ≈ 11.2 km/s. Orbital velocity: v_o = √(GM/r) = √(gR) for near-surface orbit ≈ 7.9 km/s. Geostationary orbit: T = 24 h, r ≈ 42,000 km, above equator.
Download: https://ncert.nic.in/textbook/pdf/keph108.pdf | Part I: https://ncert.nic.in/textbook/pdf/keph1ps.zip
At exactly escape velocity (11.2 km/s for Earth), the projectile has just enough kinetic energy to overcome gravitational pull. Its total energy (KE + PE) equals zero. It will keep moving away, slowing down but never stopping or returning. At any speed less, it returns; at any speed more, it escapes with residual velocity.
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