In certain cases, using both the momentum principle and energy principle to anal

Question

In certain cases, using both the momentum principle and energy principle to analyze a system is useful, as they each can reveal different information. You will use the both momentum principle and the energy principle in this problem.

A satellite of mass 8500 kg orbits the Earth in a circular orbit of radius of 8.8 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 1024 kg.
What is the magnitude of the gravitational force on the satellite due to the earth?
F =( )N

Using the momentum principle, find the speed of the satellite in orbit. (HINT: Think about the components of parallel and perpendicular to .)
v =( )m/s

Using the energy principle, find the minimum amount of work needed to move the satellite from this orbit to a location very far away from the Earth. (You can think of this energy as being supplied by work due to something outside of the system of the Earth and the satellite.)
work =( )J

Explanation / Answer

The centripetal force is provided by the force of gravity. Fg = Fc GMm/r² = m4pi²r/T² GM/r² = 4pi²r/T² M = 4pi²(r^3)/(T²G) = 4pi²x [this is the mass of the planet] The gravitational force, Fg, is also equal to m*a. To find the acceleration, ma=GMm/r² a=GM/r² At the surface of the planet, a=y N/kg So, Fg=mg=z N make calculations

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