Series reversion/inversion of Lambert's time function
Abstract
The time of flight of a twobody orbit may be determined by integrating the radial velocity equation for a conic section. The resulting expression is sometimes called Lambert's time function, which depends on the gravitational constant, two position vectors, and the semimajor axis of the conic flight path. For mission planning purposes, it is often desirable to know the semimajor axis as a function of time, rather than the reverse. Normally, a root finding technique such as NewtonRaphson is employed to find the value of a characteristic orbital parameter which matches a given time of flight. Alternatively, Lambert's time function may be expanded as a power series involving the inverse semimajor axis. The expression for semimajor axis is then determined through series reversion and inversion of the resulting series. A simplified method of obtaining the series coefficients is given, as well as a numerical study of convergence properties.
 Publication:

Astrodynamics 1989
 Pub Date:
 1990
 Bibcode:
 1990asdy.conf...45T
 Keywords:

 Astrodynamics;
 Flight Paths;
 Flight Time;
 Orbital Elements;
 Radial Velocity;
 Time Functions;
 Bouguer Law;
 Gravitational Constant;
 Orbital Mechanics;
 Power Series;
 Two Body Problem;
 Astrodynamics