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InterviewSolution
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A lauching vehicle carrying an artificial satellite of mass `m` is set for launch on the surface of the earth of mass `M` and radius `R`. If the satellite intended to move in a circular orbit of radius `7R`, the minimum energy required to be spent by the launching vehicle on the satellite is |
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Answer» Here `r=R+h=7R` Orbital velocity `V_(0)=sqrt((GM)/r)` `TE` of satellite in its orbit `=PE+KE` `=-(GMm)/r+1/2mV_(0)^(2)` `=-(GMm)/r+1/2m((GM)/r)` `=-(GMm)/(7R)+1/2m((GM)/(7R))=-(GMm)/(14R)` `TE` of satellite on the earth `=-(GMm)/R` If the minimum energy to launch the satellite in to its orbit is `E_(min)`, then, `-(GMm)/R+E_(min)=-(GMm)/(14R)rArr E_(min)=(13GMm)/(14R)` |
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