NCERT | Class 11 | Physics
From Kepler's laws of planetary motion to Einstein's curved spacetime — understand the fundamental force that governs every orbit, every tide, every falling apple.
Conceptual Framework
Quick Reference
| Quantity | Formula | Remarks |
|---|---|---|
| Gravitational Force | \(F = G\,\dfrac{m_1 m_2}{r^2}\) | \(G = 6.674\times10^{-11}\) N m² kg⁻² |
| Acceleration due to Gravity | \(g = \dfrac{GM}{R^2}\) | At Earth's surface |
| g at altitude h | \(g_h = g\!\left(1-\dfrac{2h}{R}\right)\) | For h ≪ R |
| g at depth d | \(g_d = g\!\left(1-\dfrac{d}{R}\right)\) | Uniform density assumed |
| Gravitational Potential | \(V = -\dfrac{GM}{r}\) | Scalar; negative at finite r |
| Gravitational PE | \(U = -\dfrac{GMm}{r}\) | Reference at infinity |
| Orbital Speed | \(v_o = \sqrt{\dfrac{GM}{r}}\) | Circular orbit at radius r |
| Escape Velocity | \(v_e = \sqrt{\dfrac{2GM}{R}} = v_o\sqrt{2}\) | ≈ 11.2 km s⁻¹ (Earth) |
| Time Period of Satellite | \(T = 2\pi\sqrt{\dfrac{r^3}{GM}}\) | Kepler's Third Law |
| Total Energy of Satellite | \(E = -\dfrac{GMm}{2r}\) | KE + PE; always negative |
Study Material
Exam-Ready Insights
G is a universal constant — its value \(6.674\times10^{-11}\) N m² kg⁻² is the same everywhere in the universe.
g decreases both on going up (above surface) and on going down (below surface) from Earth's surface. It is maximum at the surface.
At Earth's centre, \(g = 0\) — a body there is attracted equally in all directions, so the net gravitational force is zero.
Escape velocity is \(\sqrt{2}\) times the orbital velocity for the same radius. This factor of √2 appears frequently in exams.
Total mechanical energy of an orbiting satellite is always negative (bound system). KE = −E; PE = 2E.
Geostationary orbit has a radius ≈ 42,000 km from Earth's centre and time period exactly 24 hours, making it appear stationary.
Weightlessness in a satellite is due to free fall — both the astronaut and the spacecraft fall toward Earth at the same rate.
Kepler's Second Law (equal areas in equal times) is a consequence of conservation of angular momentum, not energy.
Gravitational potential is always negative or zero. It is maximum (zero) at infinity and decreases as you approach a massive body.
g due to rotation of Earth is minimum at the equator (due to maximum centrifugal effect) and maximum at the poles.
Competitive Exams
Gravitation is a high-weightage chapter across all major competitive examinations. Here are the most frequently tested topics:
Jump into the MCQ bank or take the True–False quiz to gauge how well you've understood Gravitation.