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A 400 kg satellite is in a circular orbit of radius 2R_(E) about the Earth. How much energy is required to transfer it to a circular orbit of radius 4R_(E) ?

Answer» <html><body><p></p>Solution :Initially `E_(i) = (-GM_(E)m)/(4R_(E))` <br/> while <a href="https://interviewquestions.tuteehub.com/tag/finally-461212" style="font-weight:bold;" target="_blank" title="Click to know more about FINALLY">FINALLY</a> `E_(<a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a>) = -(GM_(E)m)/(8R_(E))` <br/> The <a href="https://interviewquestions.tuteehub.com/tag/change-913808" style="font-weight:bold;" target="_blank" title="Click to know more about CHANGE">CHANGE</a> in the total energy is `Delta E = E_(f) - E_(i)` <br/> `= (GM_(E)m)/(8R_(R)) = ((GM_(E))/(R_(E)^(2)))(mR_(E))/(8)` <br/> `Delta E = (gm R_(E))/(8) = (<a href="https://interviewquestions.tuteehub.com/tag/9-340408" style="font-weight:bold;" target="_blank" title="Click to know more about 9">9</a>.81 <a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a> 400 xx 6.37 xx 10^(6))/(8)` <br/> `= 3.13 xx 10^(9)J` <br/> `T^(2) = (4pi^(2) R^(3))/(GM_(E)) M_(E) = (4pi^(2)R^(3))/(G T^(2))` <br/> `= (4 xx 3.14 xx 3.14 xx (3.84)^(3) xx 10^(24))/(6.67 xx 10^(-11) xx (27.3 xx 24 xx 60 xx 60)^(2))` <br/> `= 6.02 xx 10^(24) kg` <br/> Both methods yields almost the same answer, the difference between them being less than 1%.</body></html>


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