# A new solution for Lambert's problem

- Paper ID
1968-AD101

- author
- company
Instrumentation laboratory, Massachusetts Institute of technology

- country
U.S.A.

- year
1968

- abstract
A new universal solution of Lambert's problem, encompassing elliptic, parabolic and hyperbolic orbits is presented in which the independent variable has an immediate physical interpretation. In terms of this new variable, the time of flight equation is the sum of two hyper geometric functions while the equations for the terminal velocity vectors are characterized by elegant simplicity. Although the hypergeometric functions are expressible in terms of elementary functions, the resulting forms are not computationally useful when the orbit is nearly parabolic. On the other hand, by means of power series and continued fraction expansions extremely useful algorithms for calculation of the time of flight, which are continuous through the parabolic case, are obtained. Another distinct advantage of this formulation is the lack of computational difficulty which usually accompanies the case for which the transfer angle is 180°.