Lambert's Problem

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The classical boundary-value problem in orbital mechanics: given the initial position, final position, and time of flight in a central gravitational field, solve for the required instantaneous velocity. Named after Johann Heinrich Lambert (1728-1777), it forms the mathematical basis of Lambert guidance. Related to but distinct from the two-point boundary value problem: Lambert's problem specifically refers to the analytical solution framework in two-body gravitational fields, while the two-point boundary value problem is a more general numerical solution approach.

Application Value

In orbital design and transfer missions, this orbital type can be used to optimize fuel consumption and flight time. In practical missions, appropriate analysis methods should be selected based on specific application scenarios and constraint conditions.

  • On-Board Software
  • Barycentric Coordinate Time (TCB)
  • Horizontal Coordinate System

References

  • Burns and Scherock - 2004
  • Bucchioni and Innocenti - 2021
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Contributors: ouyangjiahong, Ou Yang Jiahong