Derive an expression for the work required to move an earth satellite of mass m from a circular orbit or radius 2re to one of radius 3re. (use any variable or symbol stated above along with the following as necessary: g and me for the mass of the earth.)

W = 0.1667 (G mM / Re)

Explanation:

The work is defined as

     dW = F .ds

where F is the force and ds of the displacement difference, the point represents the scalar product

In this case the force is radial from the satellite to the center of the plant and the direction coincides with the direction of the radius of the spherical earth, so it is work remains

        dW = - F dr

The force is the gravitational force is

       ∫ dw = G m M   ∫ dr / r²

     W = G m M (-1 / r)

Let's evaluate at r = 2Re and r = 3Re

    W = - GmM (1 / 3Re - 1 / 2Re)

    W = - GmM / Re (1/3 - ½)

    W = G m M / Re (-0.16667)

    W = 0.1667 (G mM / Re)

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