The earth precesses once every 26000 years and spins on its axis once a day. Est

Question

The earth precesses once every 26000 years and spins on its axis once a day.

Estimate the magnitude of the torque that causes the precession of the earth, take M_E = 5.97 middot 10^24 kg and R_E = 6.39 middot 10^3 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 1/2 degree; this affects the calculated torque by about a factor of 2.

Explanation / Answer

here is what we can get:
1 day = 86,400s , 1yr = 3.156x107 s, earth mass,M, =5,97x1024 kg and R = 6.38x106 m

=I=(2 /5)MR2
solve for = 2 rad/ 86,400s
and = 2 rad / [(26,000 y)(3.156x107s/y)]
and mass and radius from Appendix F
=5.4 N*m

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