A Deduce that a satellite orbiting a planet of mass in a circular orbit of radius has…

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

1. a Deduce that a satellite orbiting a planet of mass MM in a circular orbit of radius rr has a period of revolution given by T=4π2r3GMT = \sqrt{\frac{4\pi^2 r^3}{GM}} . (a) Deduce that a satellite orbiting a planet of mass MM in a circular orbit of radius rr has a period of revolution given by T=4π2r3GMT = \sqrt{\frac{4\pi^2 r^3}{GM}} . (b) A grazing orbit is one in which the orbit radius is approximately equal to the radius RR of the planet. Deduce that the period of revolution in a grazing orbit is given by T=3πGρT = \sqrt{\frac{3\pi}{G\rho}} where ρ\rho is the density of the planet. (c) The period of a grazing orbit around the earth is 85 minutes, and around the planet Jupiter it is 169 minutes. Deduce the ratio ρearthρJupiter\frac{\rho_{\text{earth}}}{\rho_{\text{Jupiter}}} .

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