Could anyone help with this problem?
On the unit sphere $S$ in 3-D space, we describe every point on $S$ by its spherical coordinates $(θ,φ)$ . Given a point $(θ_1,φ_1)$ on $S$ , and a nonzero vector $p$ on the tangent space to $S$ at $(θ_1,φ_1)$ , determine how to find analytically a geodesic on $S$ that passes through $(θ_1, φ_1)$ and has tangent vector equal to $p$.
Thank you