মহাকর্ষ ও গ্রহের গতি
Kepler's laws, universal gravitation, variation of g with height/depth, gravitational potential, escape and orbital speeds.
Kepler's first law of elliptical orbits, second law of constant areal velocity and angular momentum conservation, and third harmonic law of orbital periods.
Fundamental inverse-square gravitational law, 3D vector formulation, action-reaction symmetry, experimental determination and dimensions of G, and multi-mass superposition.
Concept of gravitational field intensity vector E_g, field lines, Newton's shell theorems for thin spherical shells, and integration over continuous mass geometries.
Surface gravity g = GM/R^2, relation to Earth's mean density, exact and binomial variations with altitude, linear variation with depth, and variations due to shape and diurnal rotation.
Gravitational potential as line integral of field, conservative field properties, potential functions for shells and solid spheres, discrete potential energy, and gravitational self-energy.
Energetic derivation of escape velocity from planetary surfaces, altitudes, depths, and multi-body configurations, alongside statistical thermodynamics comparison with gas thermal rms speeds.
Orbital mechanics of circular satellite trajectories: orbital velocity, orbital period, energy partition (Virial theorem), binding energy, and operational classification of Geostationary and Polar satellites.
Advanced celestial dynamics: central force properties, planar orbit invariance, conic trajectory classifications by total energy, Hohmann transfer orbits, and weightlessness in orbiting frames.