Question
Consider the earth-sun system. The earthcompletes one rotation about its axis of rotation passing thoughits center in 24 hours. At the same time the earth rotates aroundthe sun and takes 365 days to complete one rotation. The radius ofthe earth is ????=6.38×106 ?? and the distance from the earth to the sun is??????=1.496×1011 ??.
b) Determine ????????, the angular momentum ofthe earth about the sun. You can treat the earth as a point objectfor this part of the problem. (3)
c) Determine the total rotationalkinetic energy of the earth. (4)
Explanation / Answer
Given : . Radiusof Earth (R) = 6.38 * 106 m . Distance from Earth to Sun is (d) = 1.496 *1011 m . (a) We know that : . Angular moment is: L = I = I ( 2 /T ) . For a solid sphere : I = 2 mR2 / 5 . Hence L = ( 2 m R2 / 5 ) * (2 / T ) ; Here m = Mass of Earth . = ( 4 m R2 / 5 T) = ( 4 * 3.14 * 5.973 * 1024 *( 6.38 * 106 )2 ) / ( 5 *365 *24 *60 *60 s) . = --------- . (b) As the Earth is treated as object : . Hence L = ( 2 m d2 / 5 ) * ( 2 / T ) ; Here m = Mass of Sun . = ( 4 m d2 / 5 T) = ( 4 * 3.14 * 2 * 1030 *( 1.496 * 1011 )2 ) /( 5 * 365 *24 *60 *60 s) . = --------- . (c) Rotational K.E of Earth is : . K.E = (1/2 ) I 2 . = 0.5 * ( 2 m R2 / 5 ) * ( 2/ T)2 . = --------- J . Plug the values and solve. . Hope this helps u! . = ( 4 m d2 / 5 T) = ( 4 * 3.14 * 2 * 1030 *( 1.496 * 1011 )2 ) /( 5 * 365 *24 *60 *60 s) . = --------- . (c) Rotational K.E of Earth is : . K.E = (1/2 ) I 2 . = 0.5 * ( 2 m R2 / 5 ) * ( 2/ T)2 . = --------- J . Plug the values and solve. . Hope this helps u!