Calculate the energy of the (i) Moon orbiting the Earth and (ii) Earth orbiting the Sun.

Explanation

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 Moon and the centre of the Earth
` R_(m ) 3.84 xx10^(6) km `
The distance between the Earth and the centre of the sun
`R_(e) = 150 xx10^(6) km`
(i) The energy of the Moon orbating 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