# Problem: Learning Goal:To teach you how to find the parameters characterizing an object in a circular orbit around a much heavier body like the earth.The motivation for Isaac Newton to discover his 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.Part AFind the orbital speed v for a satellite in a circular orbit of radius R.Express the orbital speed in terms of G, M, and R.Part BFind the kinetic energy K of a satellite with massm in a circular orbit with radius R.Express your answer in terms of m, M, G, and R.K =

###### FREE Expert Solution

Part A

The net centripetal force experienced by the satellite in the circular motion is:

$\begin{array}{rcl}{\mathbf{F}}_{\mathbf{c}}& \mathbf{=}& \frac{{\mathbf{M}}_{\mathbf{sat}}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{R}}\end{array}$

The distance from the center of the earth, R = RE + h

$\begin{array}{rcl}{\mathbf{F}}_{\mathbf{c}}& \mathbf{=}& \frac{{\mathbf{M}}_{\mathbf{sat}}{\mathbf{v}}^{\mathbf{2}}}{{\mathbf{R}}_{\mathbf{E}}\mathbf{+}\mathbf{h}}\end{array}$ ###### Problem Details

Learning Goal:
To teach you how to find the parameters characterizing an object in a circular orbit around a much heavier body like the earth.

The motivation for Isaac Newton to discover his 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.

Part A
Find the orbital speed v for a satellite in a circular orbit of radius R.
Express the orbital speed in terms of G, M, and R.
Part B
Find the kinetic energy K of a satellite with massm in a circular orbit with radius R.