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Part of JME-05 — Gravitation

Kepler's Laws

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First Law (Orbits): Every planet moves in an ellipse with the Sun at one focus. The closest point to the Sun is the perihelion, the farthest is the aphelion.

Second Law (Areas): The line joining the planet and Sun sweeps equal areas in equal times. dA/dt = L/(2m) = constant. This is equivalent to conservation of angular momentum. At perihelion, v is maximum; at aphelion, v is minimum.

Third Law (Periods): T^2 = (4*pi^2/(GM))*a^3, where a is the semi-major axis. For circular orbits: a = r. This means T^2/a^3 is the same for all planets orbiting the same star.

JEE Application: Usually tested as T1^2/T2^2 = r1^3/r2^3 for two satellites around the same planet.

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