vallado.lambert fails for long way transfers

When trying to set up poliastro.iod.vallado.lambert, I receive the following error when I set short=False (long path transfer):

Traceback (most recent call last):
  File "C:/Users/pawit/.PyCharmCE2019.3/config/scratches/scratch_4.py", line 11, in <module>
    v = lambert_v(k, r0, rf, tof, short=short, numiter=numiter, rtol=rtol).__next__()
  File "C:\Users\pawit\Documents\research_env\lib\site-packages\poliastro\iod\vallado.py", line 48, in lambert
    v0, v = vallado_fast(k_, r0_, r_, tof_, short, numiter, rtol)
  File "C:\Users\pawit\Documents\research_env\lib\site-packages\poliastro\core\iod.py", line 151, in vallado
    raise RuntimeError("Maximum number of iterations reached")
RuntimeError: Maximum number of iterations reached

Here is my minimal (non)working example:

from astropy import units as u, constants as c
from poliastro.iod.vallado import lambert as lambert_v

k = c.GM_earth.to(u.km ** 3/ u.s ** 2)
r0 = [10000., 0, 0] * u.km
rf = [8000., -5000, 0] * u.km
tof = (2 * u.hour).to(u.s)
short = False
numiter = 1000
rtol = 1e-6
v = lambert_v(k, r0, rf, tof, short=short, numiter=numiter, rtol=rtol).__next__()

print('v1 = ')
print(v[0])
print('v2 = ')
print(v[1])

It has worked for all of the tests I gave it when short=True, and failed every time short=False.

[jorgepiloto]

Origin of this algorithm and possible errata ⚠️

This routine is based on “Algorithm 58” from “Fundamentals of Astrodynamics” book. After comparing poliastro’s implementation of the algorithm and the one stated in the book, I noticed there is a difference in the values for psi_up and psi_low:

• poliastro: psi_up = 4.0 * pi and psi_low = -4.0 * pi
• vallado58: psi_up = 4.0 * pi ** 2 and psi_low = -4.0 * pi ** 2 (refer to the algorithm script since it seems to be an errata in the book between de values)

Proposed solution

By correcting the actual values for psiof our vallado implementation, it was possible to run the original issue code without any problem. Tests were also passing, thought an increase of iterations was required in one of them.

Regarding the pull request #845, if a numiter argument is passed, the exception for reached maximum number of iterations should be kept. Code modifications do not affect code workflow but force it to return the last value. I will let a review in the pull request.

[astrojuanlu]

Fixed in #845! @paul-witsberger if you want to test with master you’re welcome to do so 😃 And if the issue was still not fixed, please comment here.