Lambert’s problem involves solving the orbits connecting two position vectors with a given flight time. When introducing variations to the input of this problem (that is, terminal positions and the flight time), the output terminal velocities vary in response. The higher-order Lambert problem pursues a higher-order Taylor approximation of the output with respect to the input. Instead of finding a real number root, Householder methods are adapted to find a Taylor series solution of the transfer-time equation. By using explicit derivatives of the transfer-time equation, the newly implemented Householder methods converge faster than the general partial inversion method. In applications such as pork-chop plots and orbital admittance maps that require solving a large number of Lambert’s problems, a higher-order Lambert solution can reduce the running time by more than 80% when compared to solving the original Lambert problems one by one. Furthermore, the investigation of the parameter space of Lambert’s problem yields useful insights to the selection of higher-order expansion points.

兰伯特的问题涉及解决在给定飞行时间下连接两个位置矢量的轨道。当对该问题的输入（即终端位置和飞行时间）引入变化时，输出终端速度会相应变化。高阶兰伯特问题追求输出相对于输入的高阶泰勒近似。Householder 方法不是寻找实数根，而是适用于寻找转移时间方程的泰勒级数解。通过使用传递时间方程的显式导数，新实现的 Householder 方法比一般的部分反演方法收敛得更快。在需要解决大量兰伯特问题的猪排图和轨道导纳图等应用中，与一一解决原始 Lambert 问题相比，高阶 Lambert 解决方案可以减少 80% 以上的运行时间。此外，对兰伯特问题的参数空间的研究为高阶展开点的选择提供了有用的见解。