Optimal Two-Impulse Rendezvous Using Multiple-Revolution Lambert Solutions
نویسندگان
چکیده
Theminimum-¢V, xed-time, two-impulse rendezvousbetween two spacecraft orbitingalong two coplanarunidirectional circular orbits (moving-target rendezvous) is studied. To reach this goal, the minimum-¢V, xed-time, two-impulse transfer problem between two xed points on two circular orbits is rst solved. This xed-endpoint transfer is related to the moving-target rendezvous problemby a simple transformation.The xed-endpoint transfer problem is solved using the solution to the multiple-revolution Lambert problem. A solution procedure is proposed based on the study of an auxiliary transfer problem. When this procedure is used, the minimum¢V of the moving-target rendezvous problem without initial and terminal coasting periods is obtained for a range of separation angles and times of ight. Thus, a contour plot of the cost vs separation angle and transfer time is obtained. This contour plot, alongwith a sliding rule, facilitates the task of nding the optimal initial and terminal coasting periods and, hence, obtaining the globally optimal solution for the moving-target rendezvous problem. Numerical examples demonstrate the application of the methodology to multiple rendezvous of satellite constellations on circular orbits.
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