A Python library designed to provide solutions to Lambert's problem, a classical problem in astrodynamics that involves determining the orbit of a spacecraft given two points in space and the time of flight between them. The problem is essential for trajectory planning, particularly for interplanetary missions.

This library implements multiple algorithms, each named after its author and publication year, for solving different variations of Lambert's problem. These algorithms can handle different types of orbits, including multi-revolution paths and direct transfers.

Multiple installation methods are supported:

Logo	Platform	Command
	PyPI	python -m pip install lamberthub
	GitHub	python -m pip install https://github.com/jorgepiloto/lamberthub/archive/main.zip

Any Lambert's problem algorithm implemented in lamberthub is a Python function which accepts the following parameters:

from lamberthub import authorYYYY


v1, v2 = authorYYYY(
    mu, r1, r2, tof, M=0, is_prograde=True, is_low_path=True,  # Type of solution
    maxiter=35, atol=1e-5, rtol=1e-7, full_output=False  # Iteration config
)

where author is the name of the author which developed the solver and YYYY the year of publication. Any of the solvers hosted by the ALL_SOLVERS list.

Problem statement

Suppose you want to solve for the orbit of an interplanetary vehicle (that is Sun is the main attractor) form which you know that the initial and final positions are given by:

The time of flight is $\Delta t = 0.010794065$ years. The orbit is prograde and direct, thus $M=0$. Remember that when $M=0$, there is only one possible solution, so the is_low_path flag does not play any role in this problem.

Solution

For this problem, gooding1990 is used. Any other solver would work too. Next, the parameters of the problem are instantiated. Finally, the initial and final velocity vectors are computed.

from lamberthub import gooding1990
import numpy as np


mu_sun = 39.47692641
r1 = np.array([0.159321004, 0.579266185, 0.052359607])
r2 = np.array([0.057594337, 0.605750797, 0.068345246])
tof = 0.010794065

v1, v2 = gooding1990(mu_sun, r1, r2, tof, M=0, is_prograde=True)
print(f"Initial velocity: {v1} [AU / years]")
print(f"Final velocity:   {v2} [AU / years]")

Result

Initial velocity: [-9.303608  3.01862016  1.53636008] [AU / years]
Final velocity:   [-9.511186  1.88884006  1.42137810] [AU / years]

Directly taken from An Introduction to the Mathematics and Methods of Astrodynamics, revised edition, by R.H. Battin, problem 7-12.

Benchmarks run with pytest-benchmark. All Numba JIT functions are pre-compiled once before timing begins, compilation cost is never included in the measurements. Six test groups cover the main solver regimes:

This section is auto-generated from CI benchmark artifacts.

• Generated: 2026-06-14 15:44 UTC
• Commit: a3af78b1af9a
• Environment: Linux, Python 3.12.13, AMD EPYC 7763 64-Core Processor

Times are in microseconds (lower is better). Speedup is relative to the slowest solver for each case. All solvers are JIT-warmed before timing begins.