Gravitation

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Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

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Law of Orbits: All planets move in elliptical orbits with the Sun situated at one of the foci of the ellipse. Key points: - Planets follow elliptical paths, not circular ones - The Sun is located at

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Law of Areas: The line that joins any planet to the Sun sweeps equal areas in equal intervals of time. Why it occurs: - This law is a consequence of conservation of angular momentum - Gravitational f

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Law of Periods: The square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of the ellipse traced out by the planet. Mathematically: T² ∝ a³ Or: T² = (4

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Value: G = 6.67 × 10⁻¹¹ N m²/kg² First measured by: Henry Cavendish in 1798 Cavendish's experiment: - Used a torsion balance with lead spheres - Measured the tiny gravitational attraction between ma

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For a mass m on Earth's surface: - Gravitational force: F = GMₑm/Rₑ² - From Newton's second law: F = mg Therefore: mg = GMₑm/Rₑ² Canceling m: g = GMₑ/Rₑ² Where: - g = acceleration due to gravity (≈

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At height h above Earth's surface: g(h) = GMₑ/(Rₑ + h)² For small heights (h << Rₑ): g(h) ≈ g(1 - 2h/Rₑ) Key points: - Gravity decreases with height - For small heights, decrease is approximately l

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At depth d below Earth's surface: g(d) = g(1 - d/Rₑ) Key points: - Gravity decreases linearly with depth - At Earth's center (d = Rₑ), gravity becomes zero - Only the inner sphere of radius (Rₑ - d)