I What causes the precession of the equinox?

[Trying2Learn]

TL;DR Summary

How do the planets exert a moment on the earth?

I am reading an introductory undergraduate textbook problem in rigid body dynamics, about the precession of the equinox. I will quote the beginning of the problem:

All the other planets and the sun, exert a combined average moment, M, on the earth. This moment causes the axis of the Earth to precess about a precession axis that is perpendicular to the plane of the elliptic. This precession, called “the precession of the equinox” takes 25,800 years.

Once I accept that statement, I can being the problem: it is merely the gyroscopic effect, and is not the issue for me.

Rather, I am confused as to one issue: where does this moment come from?

The planets actually exert a force on the Earth and this force acts at the center of mass. In so doing, there cannot be a moment. So where does the moment come from? (Unless, of course -- I just thought of this -- the center of mass of the Earth is NOT at the geometric center of its form as an oblate spheroid).

Could someone advise me please?

 

[Ibix]

Rather, I am confused as to one issue: where does this moment come from?

Same place tides do - gravitational force varies slightly with distance, so you get a small difference in force on the near side and far side of Earth.

 

[Trying2Learn]

Same place tides do - gravitational force varies slightly with distance, so you get a small difference in force on the near side and far side of Earth.

OK, so I see that. But forces act at the Center of Mass. So are you essentially saying the CM of Earth is NOT at the geometric center? Is that it?

 

[Orodruin]

If the Earth (and the gravitating bodies) was a perfectly homogeneous sphere (or had perfect spherical symmetry) then there would be no torque. However, that is not the case.

 

[Hornbein]

If the Earth (and the gravitating bodies) was a perfectly homogeneous sphere (or had perfect spherical symmetry) then there would be no torque. However, that is not the case.

Right. The Earth is an oblate sphereoid, which means it "bulges" at the equator. This provides a lever that the tidal forces can act on.

As for orbital forces acting at the center of mass, it seems to me that this would only be true if the gravitational force is the same everywhere in the body. In the case of the Earth this would be quite close to being so.

I think the ancient Egyptians must have known about the precession of the equinoxes once they got a thousand years worth of observational data. It's pretty obvious then. In those days it was kept as a religious secret so they failed to publish.

 

[Janus]

OK, so I see that. But forces act at the Center of Mass. So are you essentially saying the CM of Earth is NOT at the geometric center? Is that it?

If you take into account all the gravitational forces acting on all points of the Earth, It averages out to to the center of the Earth for the Earth as a whole in terms of how they effect its orbit around the Sun. But this is not he case for the Earth's orientation. Since the gravitational forces acting from the other bodies act more or less along the same plane, and the Earth is an oblate spheroid, you end up with all those forces pulling on the different parts of the Earth trying to align the equatorial bulges along that plane.
Since the Earth is a rotating body and is rotating at an angle to this plane, this instead results in a precession.

 

[Trying2Learn]

Thank you, all.

 

[sophiecentaur]

But forces act at the Center of Mass.

That's an approximation that applies only in a uniform gravitational field. It works most of the time, such as seesaw experiments and chemical balances on Earth.

The departure from this is only small between astronomical objects but has very long term effects such as tidal locking and that precession.