# 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:

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.