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Calculate the energy of the (i) Moon orbiting the Earth and (ii) Earth orbiting the Sun. |
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Answer» SOLUTION :Gravitational CONSTANT`G = 6.67 xx10^(11) "Nm"^(2)kg^(-2)` Mass of the Monn `M_(m) = 7.35 xx10^(22)` kg Mass of the Sun `M_(5) = 2xx10^(30) kg` The distance between the Moonand the centre of the Earth ` R_(m ) 3.84 xx10^(6) km ` The distance betweenthe Earth and thecentre of the sun `R_(e) = 150 xx10^(6) km` (i) The energy of the Moonorbating the Earth `E_(m) = -(GM_(E )M_(m))/(2R_(m))` ` = (-6.67 xx10^(11) xx 6.02 xx10^(24) xx 7.35 xx10^(22))/(2xx3.84 xx10^(5) xx10^(3))` ` = (-295.1275)/(7.68) xx 10^(-9) xx10^(46)` `E_(m) = - 38.42 xx10^(27) ` Joule `E_(m) = -3.842 xx10^(28)` joule (or) J (ii) The energy of the Earth orbiting the Sun ` E_(m) = (-GM_(s) M_(E))/(2R_(E))` `= (-6.67 xx10^(-11) xx 2xx 10^(30) xx 6.02 xx10^(-24))/(2xx150 xx10^(6))` ` = (-80.3068 xx10^(43))/(3xx10^(8)) = - 26.7689 xx10^(35)` `E_(E ) = - 26.77 xx10^(35)` joule `E_(E ) = - 2.677 xx10^(36) ` joule (or) J |
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