Physics XI - Chapter 08: Gravitation
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Quick Revision Box: Gravitation
- Newton's Law of Gravitation: F = G m₁m₂/r²; force between two point masses, always attractive.
- Universal Gravitational Constant (G): 6.67 × 10⁻¹¹ N m² kg⁻²; determined by Cavendish.
- Principle of Superposition: Net gravitational force on a particle is the vector sum of forces from all other particles.
- Gravitational Acceleration (g): g = GM/R² (at surface); acceleration due to gravity.
- Variation of 'g': Decreases with height (g' = g[1 - 2h/R]) and depth (g' = g[1 - d/R]).
- Gravitational Potential (V): V = -GM/r; work done to bring unit mass from infinity to a point.
- Gravitational Potential Energy (U): U = -G m₁m₂/r; for two point masses, zero at infinity.
- Escape Velocity (vesc): vesc = √(2GM/R); minimum speed to escape a planet's gravity.
- Orbital Velocity (vo): vo = √(GM/r); speed of a satellite in circular orbit.
- Time Period of Satellite: T = 2π√(r³/GM); Kepler's third law for circular orbits.
- Geostationary Satellite: Orbits in equatorial plane, T = 24 hours, fixed relative to Earth.
- Kepler's Laws: 1) Elliptical orbits, 2) Equal areas in equal times, 3) T² ∝ a³.
- Weightlessness: Experience of zero apparent weight in free-fall, like in an orbiting satellite.
- Gravitational Field (I): I = F/mo = -GM/r² (radially inward); force per unit mass.
- Relation between g and G: g = GM/R²; connects universal constant with local acceleration.
Basic Level Questions
Chapter Summary
This chapter introduces us to one of the most fundamental forces in the universe: Gravitation. We begin with Newton's Law of Universal Gravitation, which tells us that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This universal law, governed by the constant G, explains not only why we stay grounded on Earth but also the majestic motion of planets and galaxies.
We then explore the concepts of gravitational field, potential, and potential energy, which provide different perspectives for understanding gravitational interactions. A key application is understanding satellite motion, where we derive the orbital velocity that keeps a satellite in a stable circular path and the escape velocity required to break free from a celestial body's gravitational pull entirely. We also study the practical case of geostationary satellites, which remain fixed above a point on Earth, revolutionizing communication and weather monitoring.
The chapter beautifully connects back to Kepler's Laws of Planetary Motion, which were derived from meticulous astronomical observations. Newton's law provided the theoretical foundation for these empirical laws, particularly showing why the square of a planet's orbital period is proportional to the cube of its semi-major axis. From the apple falling to the planets orbiting, this chapter unveils the elegant unity of celestial and terrestrial mechanics governed by the same gravitational force.