SERIES REVERSION INVERSION OF LAMBERT TIME FUNCTION

The time of flight of a two-body orbit may be determined by integratin g the radial velocity equation for a conic section. The resulting expr ession is sometimes called Lambert's Time Function, which depends on t he gravitational constant, two position vectors, and the semi-major ax is of the conic flight path. For mission planning purposes, it is ofte n desirable to know the semi-major axis as a function of time, rather than the reverse. Normally, a root finding technique such as Newton-Ra phson is employed to find the value of a characteristic orbital parame ter which matches a given time of flight. Alternatively, Lambert's Tim e Function may be expanded as a power series involving the inverse sem imajor axis. The expression for semi-major axis is then determined thr ough series reversion and inversion of the resulting series. A simplif ied method of obtaining the series coefficients is given, as well as a numerical study of convergence properties.