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max0005

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## Homework Statement

A satellite of mass m kg is sent into orbit at a distance of 5R, where R is the radius of the earth. Write down an expression for:

a) The potential energy of the satellite in orbit.

b) The kinetic energy of the satellite in orbit.

c) The minimum work needed to sent the satellite from rest on earth in orbit.

## Homework Equations

[tex]GPE = \frac{MmG}{R^2}[/tex]

M = Mass of Earth

[tex] Kinetic Energy = \frac{1}{2}mv^2[/tex]

[tex] Work = F*D[/tex]

## The Attempt at a Solution

a) Rewrite the formula for GPE.

b)Kinetic = -1/2Potential, rewrite formula for Gpe adding a division by -2.

c)[tex]W = FD[/tex]

[tex]W = F5R[/tex]

The force is the sum of the force needed to reach escape velocity on earth and that needed to keep the satellite in orbit.

The potential energy at rest of earth's surface is given by [tex]-\frac{MmG}{R}[/tex]

As the kinetic energy has to be equal to reach escape velocity: [tex]\frac{1}{2}mv^2 = -\frac{MmG}{R}[/tex]

How do I calculate the energy needed to keep it in orbit?