1.Consider a satellite of the earth in a circular orbit of radius R. Let M and...

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Physics

1.Consider a satellite of the earth in a circular orbit ofradius R. Let M and m be the mass of the earth and that of thesatellite, respectively. Show that the centripetal acceleration ofthe satellite is a_R =-(v^2/R)*(r/r) where v = |v| isthe magnitude of the velocity V andr/r is a unit vector in the radial direction.
2.Using Newton's second low of motion and the law of universalgravitation, determine the speed v=|V| and theangular speed w for the circular orbit.
3.For two satellites in two different circular orbits with radiiR1 and R2, respectively, prove kepler's second and third laws forthis special case.

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1The position of an object in a plane can be converted from polarto cartesian coordinates through the equationsExpressing as a function of time gives equations for thecartesian coordinates as a function of time in uniform See Answer

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