7. GRAVITATION
Gravitation explains the attractive force between masses, a crucial concept in understanding celestial mechanics and planetary motion. The chapter discusses the historical development of gravitational theory from Galileo to Newton, including Kepler's laws of planetary motion and the universal law of gravitation. Essential properties like gravitational potential energy, escape velocity, and orbital mechanics of satellites are also covered.
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What we have learnt
- Newton's law of universal gravitation governs the force between two masses.
- Kepler's laws describe the motion of planets around the sun in elliptical orbits.
- The acceleration due to earth's gravity varies with altitude and depth.
Key Concepts
- -- Universal Law of Gravitation
- Every body in the universe attracts every other body with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
- -- Kepler's Laws
- Three laws that describe the motion of planets: they move in elliptical orbits, sweep equal areas in equal times, and have periods proportional to the cube of the semi-major axis.
- -- Gravitational Potential Energy
- The energy stored in a body due to its position in a gravitational field, given by the formula U = -G(m1*m2)/r.
- -- Escape Speed
- The minimum speed needed for an object to break free from a celestial body's gravitational influence, calculated as V_escape = sqrt(2gr_E).
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