Precession of the earth's axis

[Ulysees]

I remember an analogy with a child's spinning top, that does not rotate in a fixed axis but the axis makes a precessional movement.

But the spinning top is sitting on something, it's getting a force from below that's not aligned with its weight, so this force has a torque, etc etc (can't continue cause I don't really know how to )

But the Earth is not like this, there's no force from the bottom. Why does it have a precession then?

Would there be no precession without the moon?

 

[Janus]

Both the Sun and Moon contribute to the precession of the Earth.

The Earth is not an homogeneous sphere. It has an equatorial bulge. It is the Sun's and Moon's pull on this bulge that leads to precession.

 

[D H]

The reason a spinning top precesses is because gravity and the normal force collectively exert a torque on the top. The Sun and Moon similarly exert a torque on the Earth due to the non-spherical nature of the Earth. The result is the precession of the Equinoxes.

There are some smaller effects on top of this large precession. The Moon has an 18.6 year nodal precession, and this couples with the non-spherical nature of the Earth to create an 18.6 cycle equinoctial precession on top of the lunisolar precession. To confuse things, astronomers call this equinoctial precession on other planets but nutation on the Earth.

For any non-spherical object, the angular velocity vector cannot be constant in a torque-free situation unless the angular velocity is perfectly aligned with one of the object's eigenaxes. The Earth undergoes a very small precession, the Chandler wobble, as a result.

A detailed model of the Earth's rotational motion is necessarily numerical. The IERS uses a rather ad-hoc model with several fitted parameters to describe the orientation of the Earth to the milliarcsecond level.

 

[Ulysees]

The Sun and Moon similarly exert a torque on the Earth due to the non-spherical nature of the Earth. The result is the precession of the Equinoxes.

Now that I thought of it it has occurred to me that it is not the gravity that causes the torque but the gravity gradient. In other words, in a homogeneous field there would be no torque, no matter the shape of the earth. Presumably the gradient from the strongest to the weakest solar gravity, over the extent of the earth, is just sufficient to make the 25000 year cycle. And the moon adds a much weaker cycle on top of it, right? And the equinoctial precession adds an even weaker cycle on top, and the Chandler precession yet another, right?

If we imagine the sphere of "the heavens" with the Earth in the centre, does the axis trace a circle due to the sun, and another circle due to the moon, and another circle due to the equinoctial cycle, and another circle due to the Chandler wobble, so they all add up to make something wobbly? The cycle due to the sun probably dominates, tracing its circle?

Maybe we can compare the solar and lunar gradients to get a rough idea and confirm if the sun dominates the lunisolar cycle or not.