On the Lambert problem with drag

TL;DR

This paper extends the classical Lambert problem by incorporating drag forces, analyzing the existence and uniqueness of solutions under bounded friction conditions in a gravitational setting.

Contribution

It provides a novel analysis of the Lambert problem with drag, establishing conditions for the number of solutions based on the position of points and friction bounds.

Findings

Exactly one rectilinear solution if points are on the same ray

At least two solutions in opposite directions otherwise

Conditions for solution existence under bounded friction

Abstract

The Lambert problem consists in connecting two given points in a given lapse of time under the gravitational influence of a fixed center. While this problem is very classical, we are concerned here with situations where friction forces act alongside the Newtonian attraction. Under some boundedness assumptions on the friction, there exists exactly one rectilinear solution if the two points lie on the same ray, and at least two solutions travelling in opposite directions otherwise.