Series Reversion/Inversion of Lambert's Time Function
Abstract
The time of flight of a two-body 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 semi-major axis of the conic flight path. For mission planning purposes, it is often desirable to know the semi-major axis as a function of time, rather than the reverse. Normally, a root finding technique such as Newton-Raphson 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 semi-major axis. The expression for semi-major 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. Keywords: Theses numerical analysis; Fortran.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1989
- Accession Number
- ADA216243
Entities
People
- James D. Thorne
Organizations
- Air Force Institute of Technology