Questions
5 questions per paper
Difficulty
Medium
Importance
High-yield core topic for JEE and NEET
Overview
Gravitation describes the fundamental attractive force between masses, governed by Newton's Law and Kepler's laws of planetary motion. Mastery of this topic is essential for competitive exams as it serves as a gateway to understanding field theories and energy conservation principles applied in mechanics.
Newton's Law and Field Theory
Gravitational force is a central, conservative force that acts along the line joining the centers of two point masses. In exams, you must be comfortable calculating net gravitational force and field intensity for symmetric distributions like rings, shells, and solid spheres.
- F = G(m1m2)/r^2
- Gravitational field E = GM/r^2
- Shell Theorem: Field inside a uniform shell is zero
- Field inside solid sphere: E = GMr/R^3
- Principle of Superposition for multiple masses
Gravitational Potential and Energy
Gravitational potential is the work done per unit mass in bringing a test mass from infinity to a point. Focus on the distinction between potential at the surface and interior points, and always account for the negative sign indicating a bound state.
- Potential V = -GM/r
- Potential Energy U = -G(m1m2)/r
- Work done to move mass: W = m(Vf - Vi)
- Potential inside solid sphere: V = -GM(3R^2 - r^2)/(2R^3)
- Gravitational potential is always negative
Satellites and Orbital Mechanics
Satellite motion is governed by the balance between gravitational force and centripetal acceleration. Problems often require analyzing changes in orbital radius, kinetic energy, and potential energy when a satellite shifts orbits.
- Orbital velocity v = sqrt(GM/r)
- Total Energy E = -GMm/2r
- Binding Energy = GMm/2r
- Kepler's Third Law: T^2 proportional to r^3
- Areal velocity remains constant
Escape Velocity and Earth's Variation
Escape velocity is the minimum launch speed required for an object to overcome the gravitational pull of a celestial body. Examiners frequently test the variation of 'g' due to altitude, depth, and the Earth's rotation (latitude).
- Escape velocity v_e = sqrt(2GM/R)
- Variation with height: g' = g(1 - 2h/R)
- Variation with depth: g' = g(1 - d/R)
- Variation with latitude: g' = g - omega^2 R cos^2(lambda)
- Escape velocity is independent of the mass of the projectile
Formula Sheet
F = G m1 m2 / r^2
g = GM / R^2
U = -G M m / r
T = 2 * pi * sqrt(r^3 / GM)
v_e = sqrt(2 g R)
Exam Tip
Always verify if the distance 'r' in your formulas is measured from the center of the planet or is just the height 'h' above the surface; this is the most common trap.
Common Mistakes
- Ignoring the negative sign in gravitational potential energy leading to incorrect work-done calculations.
- Confusing the depth and altitude formulas for the variation of acceleration due to gravity (g).
- Failing to add the radius of the Earth when calculating distances for satellites or objects above the surface.
More Revision Notes
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