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

Question

Pn Model the Earth as a uniform sphere. (a) Calculate the angular momentum of the Earth due to its spinning motion about its axis. Magnitude Your response differs significantly from the correct answer. Rework your solution from the beginning and Direction toward the north celestial pole (b) Calculate the angular momentum of the Earth due to its orbital motion about the Sun. Magnitude Your response differs significantly from the correct answer. Rework your solution from the beginning and Direction toward the north ecliptic pole (c) Explain why the answer in part (b) is larger than that in part (a) even though it takes significantly longer for the 7.07e-3 check each step carefully, kg m2/s 267e-40 check each step carefully. kg·m2/s Earth to go once around the Sun than to rotate once about its axis. This answer has not been graded yet

Explanation / Answer

We know that,

mE = 5.97 x 10^24 kg ; rE = 6.38 x 10^6 m

orbital radius = rO = 1.5 x 10^11 m

T = 24 hrs = 86400 s

for an year = 3.16 x 10^7 s

We know that the anglular momentum is given by:

L = I w

a)I = 2/5 M R^2

L = (2/5 M R^2)(2 pi/T)

L = (2 x 5.97 x 10^24 x (6.38 x 10^6)^2/5) (2 x 3.14/86400) = 7.06 x 10^33 kg-m^2/s

Hence, L = 7.06 x 10^33 kg-m^2/s

b)Now I = M r^2

L = I w

L = 5.97 x 10^27 x (1.5 x 10^11)^2(2 x 3.14/(3.16 x 10^7)) = 2.67 x 10^40 kg-m^2/s

Hence, L = 2.67 x 10^40 kg-m^2/s

c)Its larger because from sun frame of referance, earth is the point object with moment of inetrtia higher than that of a rotaing sphere about its won axis and the distance of this point abject from the axis of rotation is very high compared to that of the radius of earth.

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