Gravitation

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Newton's Universal Law of Gravitation: Every particle of matter attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square

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Kepler's First Law (Law of Orbit): All planets move in elliptical orbits around the Sun with the Sun at one of the foci of the ellipse. Key Terms: - Perihelion: Closest point to the Sun - Aphelion: F

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Kepler's Second Law (Law of Areas): The line joining a planet and the Sun sweeps equal areas in equal intervals of time. Physical Significance: - Planets move faster when closer to the Sun - Planets

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Kepler's Third Law (Law of Periods): The square of the period of revolution is proportional to the cube of the semi-major axis. T² ∝ r³ or T²/r³ = constant Solution: Given: T₁ = 1 year, r₂ = 4r₁ Us

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Acceleration due to gravity (g): The acceleration experienced by a freely falling body near Earth's surface due to gravitational attraction. Derivation: For a body of mass m at Earth's surface: Gravi

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Variation with Altitude: At height h above Earth's surface: gh = GM/(R+h)² Relation with surface gravity: gh/g = R²/(R+h)² Therefore: gh = g[R²/(R+h)²] For small heights (h << R): gh ≈ g(1 - 2h/R)

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Given: - h = 320 km = 3.2×10⁵ m - R = 6400 km = 6.4×10⁶ m - g = 9.8 m/s² Since h << R, we can use: gh = g(1 - 2h/R) Substituting values: gh = 9.8(1 - 2×320/6400) gh = 9.8(1 - 640/6400) gh = 9.8(1 -

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Variation with Depth: At depth d below Earth's surface: gd = g(1 - d/R) Derivation: - Only the inner sphere of radius (R-d) contributes to gravity - Outer spherical shell has no net effect - Mass of