Example 4. It is known that there are two places $A$ and $B$ on the Earth's surface, located at latitudes $60^{\circ}$ N and $45^{\circ}$ N, respectively, with a longitudinal difference of $60^{\circ}$: Find the spherical distance between $A$ and $B$. (Figure 9)
Solve As shown in Figure 9, the essence of this problem is to find $\angle A O B$.
Let $\angle A O B=\theta, \angle A O N=\theta_{1}, \angle B O N=\theta_{2}$
$\alpha=$ dihedral angle $A-S N-B=60^{\circ}$.
We have $\cos \theta=\cos \theta_{1} \cos \theta_{2}$
$$
\begin{aligned}
& +\sin \theta_{1} \sin \theta_{2} \cos \alpha \\
= & \cos 30^{\circ} \cos 45^{\circ} \\
& +\sin 30^{\circ} \sin 45^{\circ} \cos 60^{\circ} \\
= & \frac{2 \sqrt{6}+\sqrt{2}}{8} .
\end{aligned}
$$
$$
\text { Therefore, } \theta=\arccos \left(\frac{2 \sqrt{6}+\sqrt{2}}{8}\right)
$$
(unit: radians).
Thus, the spherical distance between $A$ and $B$ is
$$
\arccos \left(\frac{2 \sqrt{6}+\sqrt{2}}{8}\right) R \text {. }
$$