strophysical background: The celestial equator and celestial pole are the line a

Question

strophysical background: The celestial equator and celestial pole are the line and points respectively in the sky above the Earth's equator and north and south poles. The ecliptic is the plane of Earth's orbit around the Sun.

(a) Model the Earth as a uniform sphere. Calculate the angular momentum of the Earth due to its spinning motion about its axis to three significant figures.

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

Explanation / Answer

Angualar moment L = Iw
a).For spinning earth
I = [2/5]mr^2 and w = 2*pie/T =[ 2Ï€/86400] rad/s
m = 5.978e24kg, r = 6.378e6m

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

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

b).For orbitting 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
w = 2pie/T = 2pie/T = 2pie/3.1536e+7s = 1.99e-7rad /s
.
L = Iw = 5.978e24*1.496e11*1.496e11*1.99e-7
.
L = 2.66e+40 kg.m^2S^-1.

c). angular momentum of the Earth due to its orbital motion about the Sun is larger.

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