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Yuki888 [10]
3 years ago
12

To find some of the parameters characterizing an object moving in a circular orbit.The motivation for Isaac Newton to discover h

is laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit: a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass M.For all parts of this problem, where appropriate, use G for the universal gravitational constant.The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given byU=−GMmR.What is the kinetic energy K of the satellite?Find an expression for the square of the orbital period.Express your answer in terms of G, M, R, and π.
Physics
1 answer:
tamaranim1 [39]3 years ago
3 0

Answer:

K = \frac{GMm}{2r}

T^2 = 4\pi^2(\frac{r^3}{GM})

Explanation:

As we know that for a satellite the force of gravitation is equal to the centripetal force

so we will have

F = \frac{GMm}{r^2}

\frac{mv^2}{r} = \frac{GMm}{r^2}

so we know that kinetic energy is given as

K = \frac{1}{2}mv^2

so we have

K = \frac{GMm}{2r}

now for time period we know

T = \frac{2\pi r}{v}

from above expression of kinetic energy we have

v = \sqrt{\frac{GM}{r}}

so we have

T = \frac{2\pi r}{\sqrt{\frac{GM}{r}}}

so square of time period is given as

T^2 = 4\pi^2(\frac{r^3}{GM})

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