Astrophysical background: The celestial equator and celestial pole are the line

Question

Astrophysical 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.

Magnitude    Dimensionally incorrect. Please check the type or dimension of your unit. 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)

M = mass of earth = 5.98 x 1024 kg

R = radius of earth = 6.37 x 106 m

I = moment of inertia of earth = (0.4) MR2 = (0.4) (5.98 x 1024) (6.37 x 106)2 = 9.71 x 1037 kgm2

T = time period of rotation on its own axis = 24 hours = 24 x 3600 sec

W = angular velocity = 2pi/T = 2 x 3.14 /( 24 x 3600 ) = 7.3 x 10-5 rad/s

angular momentum is given as

L = I w

L = (9.71 x 1037) (7.3 x 10-5)

L = 7.1 x 1033 kgm2/s

b)

r = distance of earth from sun = 1.5 x 1011 m

moment of inertia of earth around sun is given as

I = M r2

I = (5.98 x 1024) (1.5 x 1011)2 =1.35 x 1047 kgm2

T = time period of orbit around sun = 365 days = 365 x 24 hours = 365 x 24 x 3600 sec

W = angular velocity = 2pi/T = 2 x 3.14 /( 365 x 24 x 3600 ) = 2 x 10-7 rad/s

angular momentum is given as

L = I w

L = (1.35 x 1047 ) (2 x 10-7)

L = 2.7 x 1040

c)

Lorbital is larger

factor = (2.7 x 1040 )/(7.1 x 1033) = 3.8 x 106

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