Determine the ratio of the earth's angular momentum about its axis due to its spinning motion to its angular momentum about the sun due to its orbital motion. The radius of the earth is 6400 km and the radius of the earth's orbit around the sun is 1.5 10^8 km .

Step-by-step solution

The angular momentum of the earth about its own axis due to its spinning motion is given by L_s = I_s _s = 2 5 M R^2 ( 2 T_s ) where M is the mass of the earth, R is its radius, and T_s is the time period of its rotation ( 1 day ). The angular momentum of the earth about the sun due to its orbital motion is given by L_o = I_o _o = M r^2 ( 2 T_o ) where r is the radius of the earth's orbit and T_o is the time period of its revolution ( 365 days ). The ratio of the two angular momenta is L_s L_o = 2 5 M R^2 ( 2 T_s )