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) ?

A 400 kg satellite is in a circular orbit of radius 2R_(E) about the E

1.	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» Solution :Initially `E_(i) = (-GM_(E)m)/(4R_(E))` while FINALLY `E_(F) = -(GM_(E)m)/(8R_(E))` The CHANGE in the total energy is `Delta E = E_(f) - E_(i)` `= (GM_(E)m)/(8R_(R)) = ((GM_(E))/(R_(E)^(2)))(mR_(E))/(8)` `Delta E = (gm R_(E))/(8) = (9.81 XX 400 xx 6.37 xx 10^(6))/(8)` `= 3.13 xx 10^(9)J` `T^(2) = (4pi^(2) R^(3))/(GM_(E)) M_(E) = (4pi^(2)R^(3))/(G T^(2))` `= (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))` `= 6.02 xx 10^(24) kg` Both methods yields almost the same answer, the difference between them being less than 1%.