def gooding(k, r, v, tofs, numiter=150, rtol=1e-8):
"""Propagate the orbit using the Gooding method.
The Gooding method solves the Elliptic Kepler Equation with a cubic convergence,
and accuracy better than 10e-12 rad is normally achieved. It is not valid for
eccentricities equal or greater than 1.0.
Parameters
----------
k : ~astropy.units.Quantity
Standard gravitational parameter of the attractor.
r : ~astropy.units.Quantity
Position vector.
v : ~astropy.units.Quantity
Velocity vector.
tofs : ~astropy.units.Quantity
Array of times to propagate.
numiter : int
Maximum number of iterations for convergence.
rtol : float
This method does not require of tolerance since it is non iterative.
Returns
-------
rr : ~astropy.units.Quantity
Propagated position vectors.
vv : ~astropy.units.Quantity
Notes
-----
This method was developed by Gooding and Odell in their paper *The
hyperbolic Kepler equation (and the elliptic equation revisited)* with
DOI: https://doi.org/10.1007/BF01235540
"""
k = k.to_value(u.m**3 / u.s**2)
r0 = r.to_value(u.m)
v0 = v.to_value(u.m / u.s)
tofs = tofs.to_value(u.s)
results = np.array([
gooding_fast(k, r0, v0, tof, numiter=numiter, rtol=rtol)
for tof in tofs
])
return results[:, 0] << u.m, results[:, 1] << u.m / u.s
def gooding(k, r, v, tofs, numiter=150, rtol=1e-8):
"""Solves the Elliptic Kepler Equation with a cubic convergence and
accuracy better than 10e-12 rad is normally achieved. It is not valid for
eccentricities equal or greater than 1.0.
Parameters
----------
k : ~astropy.units.Quantity
Standard gravitational parameter of the attractor.
r : ~astropy.units.Quantity
Position vector.
v : ~astropy.units.Quantity
Velocity vector.
tofs : ~astropy.units.Quantity
Array of times to propagate.
rtol: float
This method does not require of tolerance since it is non iterative.
Returns
-------
rr : ~astropy.units.Quantity
Propagated position vectors.
vv : ~astropy.units.Quantity
Note
----
This method was developed by Gooding and Odell in their paper *The
hyperbolic Kepler equation (and the elliptic equation revisited)* with
DOI: https://doi.org/10.1007/BF01235540
"""
k = k.to(u.m**3 / u.s**2).value
r0 = r.to(u.m).value
v0 = v.to(u.m / u.s).value
tofs = tofs.to(u.s).value
results = [
gooding_fast(k, r0, v0, tof, numiter=numiter, rtol=rtol)
for tof in tofs
]
return (
[result[0] for result in results] * u.m,
[result[1] for result in results] * u.m / u.s,
)