The angular momentum vector of a precessing gyroscope sweeps out a cone as shown in Figure $P 10.58 .$ The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by $\omega_{p}=\tau / L$ where $\tau$ is the magnitude of the torque on the gyroscope and $L$ is the magnitude of its angular momentum. In the motion called precession of the equinoxes, the Earth's axis of rotation precesses about the perpendicular to its orbital plane with a period of $2.58 \times 10^{4}$ yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession.