A satellite of mass m revolving in a circular orbit of radius 3 R_Earound the earth (mass of earth is Me and radius is R_E ). How much excess energy be spent to bring it to orbit of radius 9 R_E ?

A satellite of mass m revolving in a circular orbit of radius 3 R_Earo

1.	A satellite of mass m revolving in a circular orbit of radius 3 R_Earound the earth (mass of earth is Me and radius is R_E ). How much excess energy be spent to bring it to orbit of radius 9 R_E ?
Answer» `(GM_Em)/(3R_E)` `(GM_Em)/(18R_E)` `(3GM_Em)/(2R_E)` `(GM_Em)/(9R_E)` Solution :`implies` Total energy of SATELLITE `\|E\| = (GM_Em)/R` `:.` Energy at `r = 3R_E` `\|E_1\|=(GM_Em)/(2(3R_E))=(GM_Em)/(6R_E)` and Energy at `r = 9R_E` `\|E_2\|=(GM_Em)/(2(9R_E))=(GM_Em)/(18R_E)` `:.` EXCESS energy from going `3R_E " to " 9R_E` `DeltaE=E_1 -E_2` `= (GM_Em)/(6R_E) - (GM_Em)/(18R_E)` `= (2GM_Em)/(18R_E)` `= (GM_Em)/(9R_E)`