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| Kepler's Laws of Planetary Motion |
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| Kepler's first law |
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| The path of each planet around the sun is an ellipse with the sun at one focus. |
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| If F1 and F2 are the two foci, P is the planet and S is the sun: |
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| F1P + F2P = constant. |
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| Kepler's second law |
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| A line joining the sun to the planet sweeps out equal areas in equal intervals of time. |
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| If the time taken by a planet to travel from P1 to Q1 is equal to the time taken to travel from P2 to Q2, the areas covered are equal (shaded region). |
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| A planet moves around the sun in such a way that the square of its time period is proportional to the cube of the semi-major axis of its elliptical orbit. |
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| If T is the time period of revolution and 'a' the semi-major axis then, |
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| for circular orbits a = r (radius) |
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| Let m be the mass of a body in an orbit of radius r, velocity v and angular velocity 'w'. the centripetal force |
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| If T is the time period then, |
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| According to Kepler's third law, |
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| If M is the mass of the sun and the body of mass m is revolving around the sun, then the constant of proportionality is assumed to be GM, where G is a constant. |
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| which is Newton's law of gravitation. |
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