2. The Earth is both rotating around the Sun and rotating around its axis of rot

Question

2. The Earth is both rotating around the Sun and rotating around its axis of rotation (which is a line from the south pole to the north pole), thus is has two types of angular momentum, which are called spin angular momentum and orbital angular momentum. Both types of angular momentum point in the same direction. The Earth has a mass of 5.972 × 1024 kg, a mean radius of 6370 km, and an average distance from the Sun of 1.5 × 1011 m. Does the Earth have more spin angular momentum or orbital angular momentum?

Explanation / Answer

given
Me = 5.972*10^24 kg
Re = 6370,000 m
Rs = 1.5*10^11 m

hence
spin angular momentum = 2MeRe^2*w/5
here w = 2*pi/24*60*60
hence
Ls = 7.048955*10^33 kg m^2/s

similiarly
angular momentum, L = Me*Rs^2*w'
w' = 2*pi/365*24*60*60
hence
L = 2.677*10^40 kg m^2/s

hence earth has more orbital angular momentum than spin angular momentum

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