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A 400 kg satellite is in a circular orbi...

A 400 kg satellite is in a circular orbit of radius `2R_(E)` about he Earth. How much energy is required to transfer it to a circular orbit of radius `rR_(E)`? What are the changes in the kinetic and potential energies?

Text Solution

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Initial total energy is - `(GMm)/(2r_(2)) =-(GMm)/(8R) =E_2`
Final total energy is `-(GMm)/(2r_(2))=-(GMm)/(8R)=E_2`
The change in the total energy is
`DeltaE=E_(2)-E_(1)=(GMm)/(8R) implies DeltaE=((GM)/R^2) (mR)/8`
`DeltaE=(gmR)/(8)=(9.8xx400xx6.37xx10^(6))/8 = 3.13 xx10^(9)J`
Change in Kinetic energy `=K_(2)-K_(1) =-3.13 xx10^(9)J`
Change in potential energy `=U_(2)-U_(1) =-6.25 xx10^(9)J`
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