Lambert Transfer Ellipse Construction
The transfer ellipse between two points given the length of its semi-major axis a can be constructed geometrically. The process of determining the length of the semi-major axis given a desired time of flight is called Lambert's problem. Lambert's problem can be solved using the bisection algorithm.
The geometric construction of Lambert's problem uses the fact, that an ellipse has a constant distance between the two focal points and any point on the ellipse. This constant distance is equal to 2a.