Model the Earth as a uniform sphere. (a) Calculate the angular momentum of the E

Question

Model the Earth as a uniform sphere.

(a) Calculate the angular momentum of the Earth due to its spinning motion about its axis.

(b) Calculate the angular momentum of the Earth due to its orbital motion about the Sun.

(c) Explain why the answer in part (b) is larger than that in part (a) even though it takes significantly longer for the Earth to go once around the Sun than to rotate once about its axis.

Magnitude kg · m2/s Direction ---Select--- toward the north ecliptic pole toward the north celestial pole toward the south celestial pole toward the south ecliptic pole

Explanation / Answer

a) Angular moment L = I .
For spinning earth
I = [2/5]mr^2 and = 2/T =[ 2/86400] rad/s
m = 5.978e24 kg, r = 6.378e6 m

L = [2/5]*5.978e24* 6.378e6*6.378e6*[ 2/86400]

L = 7.074e+33 kg.m^2S^-1.

b) For orbiting earth
I = [2/5] mr^2 + m R^2 where R is the orbital radius.
R =1.496e11m
R/r = 1.496e11/ 6.378e6 = 23455.
Hence the term 2/5 mr^2 can be ignored as small.
I = m R^2
.
T = 1 year = 3.1536e+7 s
= 2/T = 2/T = 2/3.1536e+7s = 1.99e-7rad /s
.
L = I . = 5.978e24*1.496e11*1.496e11*1.99e-7
.
L = 2.66e+40 kg.m^2S^-1.

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