Theory vs. practice

Orbital transfer, calculated with a solution of Lambert problem may seems an “ultimate weapon” for those who never applied it for real practice.

But those who did, knows that this opinion is a mistake.

Problem #1. Two-body approach.

Lambert transfer is, actually, still a “1st order approximation”, because it is based on conic sections and (relatively) simple geometry. That’s why, even in case it’s converged properly, in practice transfer may fail in precision, because of drift caused by atmospheric drag and gravitation pull of third-party objects. This may happens even if you are using sophisticated propagators (like Gauss-Jackson or Runge-Kutta-Nyström) and advanced physical models (for example, based on EGM gravity and Jacchia or MSIS-based atmospheric models).

Problem #2. Energy difference required.

Next, solving of Lambert problem wouldn’t allow you to calculate a transfer to an orbit have close or same mechanical energy and angular momentum as initial one. The reason of this is in the roots of solution of the problem. By sense, any solution is based on difference of energy between initial and final position, and oriented on search this difference (in a form of speed, required to change current energy to final). When this difference is negligible, Lambert solution will find correct answer for you… But this would be useless answer – because it will built an arc of humongous energy, useless in practice. That’s why it’s bad idea to use it for any phasing or drift correction maneuvers.

Problem #3. Convergence issues.

Next think to notice is convergence limits. Sometimes Lambert solver algorithms can not achieve convergence because of different reasons. But they will return you an answer even in that case, and it would be wrong. So when you implementing such algorithms, you need to add to your code checks about correct convergence and proper final position, just to avoid problems with maneuvers on practical application.

Problem #4. Input parameters sensitivity.

Last but not least is questions of time step and grid density on search of optimal maneuver within time period. Lambert solvers are sensitive for input parameters, so you may get, for example, different delta-v values depends on initial position of interceptor. This differences would be not too big… But you always have not too much delta-v, and this differences could be sensitive.

Summarizing

Finally, I may repeat words I already said: all your algorithms are not the “silver bullet” but just a tools in your pocket. You are astrogator, and in the end especially you (not your software) guide your spacecraft to its destination.

So, follow your knowledge and increase your practical experience. In critical conditions this – with a pinch of patience, common sense and courage – is will save your missions.