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Obtain the conditions of the K's for stable circular orbits and the period of small oscillations about the stable circular orbit for the following central force fields: (a) f(r) = ²; (b) f(r) = −, a > 0; (c) ƒ (r) = (2) + (*).

Obtain the conditions of the K's for stable circular orbits and the period of small oscillations about the stable circular orbit for the following central force fields: (a) f(r) = ²; (b) f(r) = −, a > 0; (c) ƒ (r) = (2) + (*).

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Obtain the conditions of the K's for stable circular orbits and the period of small oscillations about the stable circular orbit for the following central force fields: (a) f(r) = kr²; (b) f(r) = − ª ‚ a > 0; (c) ƒ (r) = (²2) + (¹²²).
Transcribed Image Text:Obtain the conditions of the K's for stable circular orbits and the period of small oscillations about the stable circular orbit for the following central force fields: (a) f(r) = kr²; (b) f(r) = − ª ‚ a > 0; (c) ƒ (r) = (²2) + (¹²²).
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