Lambert’s Problem – A Geometric Approach

A fundamental problem in spacecraft mission design is to find a free flight path from one place to another in a chosen travel time. Lambert studied this problem for free flight in an inverse square central force field, and Lagrange produced a solution in 1778. Although this is an old problem, a new approach may be of some value. There are two steps to the new solution. First, find every ellipse with focus at the origin that intersects two circles both centered at the origin. Then select only those ellipses that have a specified angle between the intersection points of the ellipse with the inner and outer circles. Second, find the travel times between intersections for each ellipse. These are all the possible travel times from which one may choose. Standard solutions to Lambert’s problem can be found in references [1-4].