Practical Applications
The most typical use of this algorithm to solve Lambert's problem is certainly for the design of interplanetary missions. A spacecraft traveling from the Earth to for example Mars can in first approximation be considered to follow a heliocentric elliptic Kepler orbit from the position of the Earth at the time of launch to the position of Mars at the time of arrival. By comparing the initial and the final velocity vector of this heliocentric Kepler orbit with corresponding velocity vectors for the Earth and Mars a quite good estimate of the required launch energy and of the maneuvres needed for the capture at Mars can be obtained. This approach is often used in conjunction with the Patched Conic Approximation. This is also a method for Orbit determination. If two positions of a spacecraft at different times are known with good precision from for example a GPS fix the complete orbit can be derived with this algorithm, i.e an interpolation and an extrapolation of these two position fixes is obtained.
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