# The Lambert's problem The Lambert's problem is the boundary value problem of the two-body problem under the framework of astrodynamics. ## Problem statement The goal is to solve for the orbit of a body being known two of its position vectors $\vec{r_1}$ and $\vec{r_2}$, and the time it takes to travel between those, usually denoted by $\Delta t$. The geometry of the problem is shown in the figure below: ```{figure} ../_static/lamberts_problem_geometry.png --- width: 350px align: center --- ``` Because the problem states to find an orbit, it is usually included within the *Initial Orbit Determination* subject. Nevertheless, Lambert's problem solution has applications in the field of interplanetary maneuvers and orbital rendezvous too.