The axis of the Earth precesses with a period of about...

The axis of the Earth precesses with a period of about 25,000 years. This is much like the precession of a top. Explain how the Earth's equatorial bulge gives rise to a torque exerted by the Sun and Moon on the Earth; see Fig. $11-29$, which is drawn for the winter solstice (December 21). About what axis would you expect the Earth's rotation axis to precess as a result of the torque due to the Sun? Does the torque exist three months later? Explain.

Key Concepts

Axial Precession Mechanics

The mechanics of axial precession involve the concept of angular momentum conservation in a rotating system subject to an external torque. Although the gravitational forces from the Sun and Moon are nearly constant in magnitude, the resulting torque acts perpendicular to Earth’s angular momentum. This causes the rotation axis to precess around the normal to the ecliptic plane. Importantly, while the orientation of the torque relative to Earth’s axis changes throughout the year (for example, differing between solstices), the torque itself persists continuously, ensuring that the precession continues regardless of the season.

Gravitational Torque

Gravitational torque arises when a non-spherical body is subjected to a gravitational field that does not act uniformly on all parts of the body. In Earth’s case, the Sun and Moon pull on the mass concentrated in the equatorial bulge, creating a torque. This torque does not significantly alter the speed of Earth’s rotation but continually changes the direction of its rotation axis, leading to the observed precession.

Precession

Precession refers to the slow, conical motion of the axis of a spinning object when exposed to an external torque. For Earth, this means that its rotation axis slowly traces a circle in space, similar to how the axis of a spinning top precesses under gravity. This gradual shift in the orientation of Earth’s axis over long time scales is a direct consequence of the torque exerted by external gravitational forces.

Equatorial Bulge

The equatorial bulge is the result of Earth’s rotation, which causes the planet to be slightly flattened at the poles and bulging at the equator. This non-spherical mass distribution is crucial because it makes Earth susceptible to gravitational torques applied by other celestial bodies, such as the Sun and Moon, which would not occur if the Earth were perfectly spherical.

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