Estimate the magnitude of the torque that causes the precession of the earth, ta

Question

Estimate the magnitude of the torque that causes the precession of the earth, take ME=5.97?1024kg and RE=6.39?103km. Make the estimate by assuming (i) the earth is a uniform sphere and (ii) the precession of the earth is like that of the gyroscope. In this model, the precession axis and rotation axis are perpendicular. Actually, the angle between these two axes for the earth is only 2312?; this affects the calculated torque by about a factor of 2.

I have two different answers for this question 5.4 Nm and the other was   5.39*10^22 I want to Know which is the correct one? plese solve it step by step. thanks!

Part A Estimate the magnitude of the torque that causes the precession of the earth, take Mh 24 kg and RE 6.39.10 km. Make the estimate by assuming (i) the earth is a uniform sphere and (ii) the precession of the earth is like that of the gyroscope. In this model, the precession axis and rotation axis are perpendicular. Actually, the angle between these two axes for the earth is only 23 2 this affects the calculated torque by about a factor of 2. Submit My Answers Give U

Explanation / Answer

It is the later one. 5.4 Nm is too small for big bodies like sun, earth, moon etc.

Angular momentum of earth L = i w

= [2/5*5.97e24*6.39e6^2]*[2pi/(24*60*60)]

= 7.091e33 kgm^2/s

torque due to precession = L* W where W is precession rate of earth

= 7.091e33*7.6e-12

= 5.4*10^22 Nm

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