Gravitation
What this domain tests
Gravitation tests Newton's law of gravitation, variation of g with altitude and depth, gravitational potential and potential energy, escape speed, orbital motion and Kepler's laws.
Core rules
- F = Gm₁m₂/r², directed along the line joining the masses.
- g = GM/R² at Earth's surface; at height h, g_h ≈ g(1 − 2h/R) for h << R; at depth d, g_d = g(1 − d/R).
- Gravitational potential V = −GM/r; potential energy U = −GMm/r.
- Orbital speed v_o = √(GM/r); escape speed v_e = √(2GM/R) = √(2gR).
- Kepler's third law: T² ∝ r³ for orbits around the same central body.
Worked example
For Earth, take g = 9.8 m/s² and R = 6.4 × 10⁶ m. Escape speed v_e = √(2gR) = √(2 × 9.8 × 6.4 × 10⁶) ≈ √(1.25 × 10⁸) ≈ 1.12 × 10⁴ m/s, about 11.2 km/s. The mass of the escaping body cancels, so a satellite and a cricket ball need the same speed in principle.
Traps
Using surface g for a satellite far above Earth; thinking escape speed depends on the mass or launch angle; mixing up orbital speed and escape speed (v_e = √2 v_o at the same radius); applying Kepler's third law across different central bodies without accounting for their masses; dropping the negative sign in gravitational potential energy.