Elliptical orbit can't compute true anomaly consistently

[translunar]

Bug report

Describe the bug

Can't compute true anomaly for an elliptical orbit consistently (or, consequently, get Cartesian coordinates at various times)

To Reproduce

def make_elliptical_orbit(
        direction: str = 'north',
        epoch: anise.time.Epoch = anise.time.Epoch.system_now(),
        true_anomaly: float = 0.0) -> anise.astro.Orbit:
    """Generate a northern or southern elliptical orbit (12 hour period).

    From Table 9.
    """
    almanac = spice_transforms.almanac
    mj2k = Frames.MOON_J2000
    loaded_mj2k = almanac.frame_info(mj2k)

    if direction == 'north':
        asc_node_d = 270.0
        aop_d = 270.0
    elif direction == 'south':
        asc_node_d = 0.0
        aop_d = 90.0
    else:
        raise ValueError(f"expected north or south, got {direction}")
    return anise.astro.Orbit.from_keplerian(
        sma=6142.400,  # sma
        ecc=0.6,  # ecc
        inc=57.7,  # inc
        aop=aop_d,  # argument of periselene
        raan=asc_node_d,  # ascending node
        ta=true_anomaly,
        epoch=epoch,
        frame=loaded_mj2k)

orbit = make_elliptical_orbit('north')
rs = []

for t in range(0, 12 * 60 * 60, dt_s):
    # Get PV throughout the orbit
    delta = Unit.Second * t
    print(t)
    x = orbit.at_epoch(orbit.epoch + delta)
    rs.append(np.array([x.x_km, x.y_km, x.z_km]))

I get the following output:

(Pdb) c
0
60
120
180
240
300
360
420
480
540
600
660
720
780
840
900
960
1020
1080
1140
1200
1260
1320
1380
1440
1500
1560
Traceback (most recent call last):
    x = orbit.at_epoch(orbit.epoch + delta)
Exception: max iterations reached (1001) when computing the true anomaly from the mean anomaly

Expected behavior

It should be really easy to output the Cartesian coordinates of this elliptical orbit for various epochs.

Code to reproduce the issue

See above.

Platform

Linux, Anise 0.4.4

Additional context

Add any other context about the problem here.

[ChristopherRabotin]

Thanks for the report. The function that computes the true anomaly from the mean anomaly loops until the difference between two consecutive true anomaly computations is less than 1e-16 radians:

anise/anise/src/astro/utils.rs

Line 71 in 4c2a01f

break;

. This check is too strict. An MA_EPSILON of 1e-10 is probably sufficient.

[ChristopherRabotin]

I was able to reproduce your bug, and fix it by changing that precision to 1e-12 degrees (from 1e-16). I was just about to release 0.4.5, so the fix will be in that version tomorrow morning.