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The energy required to move a satellite ...

The energy required to move a satellite of mass m from an orbit of radius 2R to 3R is (where M is the mass of the earth and R is the radius of the earth)

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The centre of mass of semicircular disc `= r_(cm)= int ydm// int dm` where `y_(cm)=2y//pi=C.M.` of the semicircular ring of radius y.
& `dm = {(M)/(pi r^(2)//2)}{pi ydy}=(2M)/(r^(2))ydy`
`r_(cm)=(int_(0)^(r )((2y)/(pi))((2M)/(r^(2))ydy))/(M)=(4r)/(3pi)` along y - axis
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