Propagating long times does not converge

🐞 Problem

Propagating long times fails in different ways:

In [5]: iss.propagate(100 * u.year)
---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-27-503eb53e62e7> in <module>()
----> 1 iss.propagate(100 * u.year)

~/Personal/poliastro/poliastro-library/src/poliastro/twobody/orbit.py in propagate(self, epoch_or_duration, rtol)
    245             time_of_flight = time.TimeDelta(epoch_or_duration)
    246 
--> 247         return propagate(self, time_of_flight, rtol=rtol)
    248 
    249     def sample(self, *, num_points=None, time_values=None):

~/Personal/poliastro/poliastro-library/src/poliastro/twobody/propagation.py in propagate(orbit, time_of_flight, method, rtol, **kwargs)
    156                   time_of_flight.to(u.s).value,
    157                   rtol=rtol,
--> 158                   **kwargs)
    159     return orbit.from_vectors(orbit.attractor, r * u.km, v * u.km / u.s, orbit.epoch + time_of_flight)
    160 

~/Personal/poliastro/poliastro-library/src/poliastro/twobody/propagation.py in kepler(k, r0, v0, tof, rtol, numiter)
    139     f, g, fdot, gdot = _kepler(k, r0, v0, tof, numiter, rtol)
    140 
--> 141     assert np.abs(f * gdot - fdot * g - 1) < 1e-5  # Fixed tolerance
    142 
    143     # Return position and velocity vectors

AssertionError: 

In [6]: halleys[0].propagate(73 * u.year)
---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
<ipython-input-26-9dcacad8e904> in <module>()
----> 1 halleys[0].propagate(73 * u.year)

~/Personal/poliastro/poliastro-library/src/poliastro/twobody/orbit.py in propagate(self, epoch_or_duration, rtol)
    245             time_of_flight = time.TimeDelta(epoch_or_duration)
    246 
--> 247         return propagate(self, time_of_flight, rtol=rtol)
    248 
    249     def sample(self, *, num_points=None, time_values=None):

~/Personal/poliastro/poliastro-library/src/poliastro/twobody/propagation.py in propagate(orbit, time_of_flight, method, rtol, **kwargs)
    156                   time_of_flight.to(u.s).value,
    157                   rtol=rtol,
--> 158                   **kwargs)
    159     return orbit.from_vectors(orbit.attractor, r * u.km, v * u.km / u.s, orbit.epoch + time_of_flight)
    160 

~/Personal/poliastro/poliastro-library/src/poliastro/twobody/propagation.py in kepler(k, r0, v0, tof, rtol, numiter)
    137     """
    138     # Compute Lagrange coefficients
--> 139     f, g, fdot, gdot = _kepler(k, r0, v0, tof, numiter, rtol)
    140 
    141     assert np.abs(f * gdot - fdot * g - 1) < 1e-5  # Fixed tolerance

RuntimeError: Maximum number of iterations reached

🎯 Goal

One thing is that the long term errors of propagation are big. But nonetheless, the propagator should always give an answer, instead of an internal error (at least for a full period, see the failure of the Halley’s comet). I wonder if this is possible at all?

💡 Possible solutions

The propagator of poliastro uses the universal variables approach, which is popular but has several limitations. Perhaps for long propagation times it should be replaced with a Newton-Raphson iteration and a good starting point as suggested by http://dx.doi.org/10.1007/s10569-013-9476-9.

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[nikita-astronaut]

Well, I realized there is no need to find the pericenter passage time. The rv2coe gives current true anomaly $\nu(t_0)$, which can be recalculated into current mean anomaly $M(t_0)$. Then, I recall that mean anomaly grows linearly with time, which gives me mean anomaly at the time $t_0 + \Deltat$: $M(t_0 + \Delta t) = M(t_0) + \sqrt{\mu (1 - e)^3 / q^3} \Delta t$. As I have $M(t_0 + \Delta t)$, I iteratively solve $E - e \sin E = M$, get $\nu$ (this is actually already implemented within M_to_nu) and thus new r, v.

I think I’ll do it this way.

[astrojuanlu]

Notice that the original convergence issues of kepler were addressed in #362.