def sample_closed(min_nu, ecc, max_nu=None, num_values=100):
"""Sample a closed orbit
If ``max_nu`` is given, the sampling interval will go
from the minimum to the maximum true anomaly in the direction of the orbit.
If not given, it will do a full revolution starting in the minimum true anomaly.
Notes
-----
First sample the eccentric anomaly uniformly,
then transform into true anomaly
to minimize error in the apocenter,
see https://apps.dtic.mil/dtic/tr/fulltext/u2/a605040.pdf
"""
# Because how nu_to_E works, we don't need to wrap the angle here!
# It will do the right thing
min_E = nu_to_E(min_nu, ecc)
# This linspace will always increase positively,
# even though it might contain out of range values
E_values = alinspace(min_E,
nu_to_E(max_nu, ecc) if max_nu is not None else None,
num=num_values)
# Because how E_to_nu works, we don't need to wrap the angles here!
# It will do the right thing
nu_values = E_to_nu(E_values, ecc)
# We wrap the angles on return
return (nu_values + np.pi * u.rad) % (2 * np.pi * u.rad) - np.pi * u.rad
def sample(self, values=None, function=propagate):
"""Samples an orbit to some specified time values.
.. versionadded:: 0.8.0
Parameters
----------
values : Multiple options
Number of interval points (default to 100),
True anomaly values,
Time values.
Returns
-------
(Time, CartesianRepresentation)
A tuple containing Time and Position vector in each
given value.
Notes
-----
When specifying a number of points, the initial and final
position is present twice inside the result (first and
last row). This is more useful for plotting.
Examples
--------
>>> from astropy import units as u
>>> from poliastro.examples import iss
>>> iss.sample()
>>> iss.sample(10)
>>> iss.sample([0, 180] * u.deg)
>>> iss.sample([0, 10, 20] * u.minute)
>>> iss.sample([iss.epoch + iss.period / 2])
"""
if values is None:
return self.sample(100, function)
elif isinstance(values, int):
if self.ecc < 1:
# first sample eccentric anomaly, then transform into true anomaly
# why sampling eccentric anomaly uniformly to minimize error in the apocenter, see
# http://www.dtic.mil/dtic/tr/fulltext/u2/a605040.pdf
E_values = np.linspace(0, 2 * np.pi, values) * u.rad
nu_values = E_to_nu(E_values, self.ecc)
else:
# Select a sensible limiting value for non-closed orbits
# This corresponds to r = 3p
nu_limit = np.arccos(-(1 - 1 / 3.) / self.ecc)
nu_values = np.linspace(-nu_limit, nu_limit, values)
nu_values = np.insert(nu_values, 0, self.ecc)
return self.sample(nu_values, function)
elif hasattr(values, "unit") and values.unit in ('rad', 'deg'):
values = self._generate_time_values(values)
return (values, self._sample(values, function))
def test_mean_to_true():
for row in ELLIPTIC_ANGLES_DATA:
ecc, M, expected_nu = row
ecc = ecc * u.one
M = M * u.deg
expected_nu = expected_nu * u.deg
nu = E_to_nu(M_to_E(M, ecc), ecc)
assert_quantity_allclose(nu, expected_nu, rtol=1e-4)
def sample(self, values=100, method=mean_motion):
"""Samples an orbit to some specified time values.
.. versionadded:: 0.8.0
Parameters
----------
values : int
Number of interval points (default to 100).
method : function, optional
Method used for propagation
Returns
-------
positions: ~astropy.coordinates.BaseCoordinateFrame
Array of x, y, z positions, with proper times as the frame attributes if supported.
Notes
-----
When specifying a number of points, the initial and final
position is present twice inside the result (first and
last row). This is more useful for plotting.
Examples
--------
>>> from astropy import units as u
>>> from poliastro.examples import iss
>>> iss.sample() # doctest: +ELLIPSIS
<GCRS Coordinate ...>
>>> iss.sample(10) # doctest: +ELLIPSIS
<GCRS Coordinate ...>
"""
if self.ecc < 1:
# first sample eccentric anomaly, then transform into true anomaly
# why sampling eccentric anomaly uniformly to minimize error in the apocenter, see
# http://www.dtic.mil/dtic/tr/fulltext/u2/a605040.pdf
# Start from pericenter
E_values = np.linspace(0, 2 * np.pi, values) * u.rad
nu_values = E_to_nu(E_values, self.ecc)
else:
# Select a sensible limiting value for non-closed orbits
# This corresponds to max(r = 3p, r = self.r)
# We have to wrap nu in [-180, 180) to compare it with the output of
# the arc cosine, which is in the range [0, 180)
# Start from -nu_limit
wrapped_nu = self.nu if self.nu < 180 * u.deg else self.nu - 360 * u.deg
nu_limit = max(np.arccos(-(1 - 1 / 3.0) / self.ecc),
abs(wrapped_nu))
nu_values = np.linspace(-nu_limit, nu_limit, values)
time_values = self._generate_time_values(nu_values)
return propagate(self, time_values, method=method)
def _sample_closed(self, values, min_anomaly, max_anomaly):
limits = [
min_anomaly.to(u.rad).value if min_anomaly is not None else 0,
max_anomaly.to(u.rad).value if max_anomaly is not None else 2 * np.pi,
] * u.rad
# First sample eccentric anomaly, then transform into true anomaly
# to minimize error in the apocenter, see
# http://www.dtic.mil/dtic/tr/fulltext/u2/a605040.pdf
# Start from pericenter
E_values = np.linspace(*limits, values)
nu_values = E_to_nu(E_values, self.ecc)
return nu_values
def orbit_from_sbdb(name, **kwargs):
obj = SBDB.query(name, full_precision=True, **kwargs)
if "count" in obj:
# No error till now ---> more than one object has been found
# Contains all the name of the objects
objects_name = obj["list"]["name"]
objects_name_in_str = "" # Used to store them in string form each in new line
for i in objects_name:
objects_name_in_str += i + "\n"
raise ValueError(
str(obj["count"]) + " different objects found: \n" +
objects_name_in_str)
if "object" not in obj.keys():
raise ValueError(f"Object {name} not found")
a = obj["orbit"]["elements"]["a"]
ecc = float(obj["orbit"]["elements"]["e"]) * u.one
inc = obj["orbit"]["elements"]["i"]
raan = obj["orbit"]["elements"]["om"]
argp = obj["orbit"]["elements"]["w"]
# Since JPL provides Mean Anomaly (M) we need to make
# the conversion to the true anomaly (nu)
M = obj["orbit"]["elements"]["ma"].to(u.rad)
# NOTE: It is unclear how this conversion should happen,
# see https://ssd-api.jpl.nasa.gov/doc/sbdb.html
if ecc < 1:
M = (M + np.pi * u.rad) % (2 * np.pi * u.rad) - np.pi * u.rad
nu = E_to_nu(M_to_E(M, ecc), ecc)
elif ecc == 1:
nu = D_to_nu(M_to_D(M))
else:
nu = F_to_nu(M_to_F(M, ecc), ecc)
epoch = Time(obj["orbit"]["epoch"].to(u.d), format="jd")
return Orbit.from_classical(
attractor=Sun,
a=a,
ecc=ecc,
inc=inc,
raan=raan,
argp=argp,
nu=nu,
epoch=epoch.tdb,
plane=Planes.EARTH_ECLIPTIC,
)
def orbit_from_record(record):
"""Return :py:class:`~poliastro.twobody.orbit.Orbit` given a record.
Retrieve info from JPL DASTCOM5 database.
Parameters
----------
record : int
Object record.
Returns
-------
orbit : ~poliastro.twobody.orbit.Orbit
NEO orbit.
"""
body_data = read_record(record)
a = body_data["A"].item() * u.au
ecc = body_data["EC"].item() * u.one
inc = body_data["IN"].item() * u.deg
raan = body_data["OM"].item() * u.deg
argp = body_data["W"].item() * u.deg
M = body_data["MA"].item() * u.deg
epoch = Time(body_data["EPOCH"].item(), format="jd", scale="tdb")
# NOTE: It is unclear how this conversion should happen,
# see https://ssd-api.jpl.nasa.gov/doc/sbdb.html
if ecc < 1:
M = (M + np.pi * u.rad) % (2 * np.pi * u.rad) - np.pi * u.rad
nu = E_to_nu(M_to_E(M, ecc), ecc)
elif ecc == 1:
nu = D_to_nu(M_to_D(M))
else:
nu = F_to_nu(M_to_F(M, ecc), ecc)
orbit = Orbit.from_classical(Sun, a, ecc, inc, raan, argp, nu, epoch)
orbit._frame = HeliocentricEclipticJ2000(obstime=epoch)
return orbit
def newton(func, x0, ecc, M, fprime=None, maxiter=50):
EFD = 1.0 * x0
delta = 1e-2
nu_prev = 1e+10
converged = False
# Newton-Rapheson method
with u.set_enabled_equivalencies(u.dimensionless_angles()):
for iter in range(maxiter):
if ecc < 1.0 - delta:
nu = E_to_nu(EFD, ecc)
E_plus = nu_to_E(nu + variation, ecc)
E_minus = nu_to_E(nu - variation, ecc)
M_actual = _kepler_equation(EFD, M, ecc, count=False)
M_plus = _kepler_equation(E_plus, M, ecc, count=False)
M_minus = _kepler_equation(E_minus, M, ecc, count=False)
elif ecc > 1.0 + delta:
nu = F_to_nu(EFD, ecc)
F_plus = nu_to_F(nu + variation, ecc)
F_minus = nu_to_F(nu - variation, ecc)
M_actual = _kepler_equation_hyper(EFD, M, ecc, count=False)
M_plus = _kepler_equation_hyper(F_plus, M, ecc, count=False)
M_minus = _kepler_equation_hyper(F_minus, M, ecc, count=False)
else:
nu = D_to_nu(EFD, ecc)
D_plus = nu_to_D(nu + variation, ecc)
D_minus = nu_to_D(nu - variation, ecc)
M_actual = _kepler_equation_parabolic(EFD, M, ecc, count=False)
M_plus = _kepler_equation_parabolic(D_plus, M, ecc, count=False)
M_minus = _kepler_equation_parabolic(D_minus, M, ecc, count=False)
converged = (np.abs(nu_prev - nu) < variation) and (M_actual * M_plus <= 0 or M_minus * M_actual <= 0)
nu_prev = nu
EFD_new = EFD - func(EFD, M, ecc) / fprime(EFD, M, ecc)
if converged:
return EFD_new
EFD = EFD_new
print(ecc, "fail")
return -1
def test_eccentric_to_true_range(E, ecc):
nu = E_to_nu(E, ecc)
E_result = nu_to_E(nu, ecc)
assert_quantity_allclose(E_result, E, rtol=1e-8)
def from_sbdb(cls, name, **kwargs):
"""Return osculating `Orbit` by using `SBDB` from Astroquery.
Parameters
----------
name: str
Name of the body to make the request.
Returns
-------
ss: poliastro.twobody.orbit.Orbit
Orbit corresponding to body_name
Examples
--------
>>> from poliastro.twobody.orbit import Orbit
>>> apophis_orbit = Orbit.from_sbdb('apophis') # doctest: +REMOTE_DATA
"""
from poliastro.bodies import Sun
obj = SBDB.query(name, full_precision=True, **kwargs)
if "count" in obj:
# No error till now ---> more than one object has been found
# Contains all the name of the objects
objects_name = obj["list"]["name"]
objects_name_in_str = (
"" # Used to store them in string form each in new line
)
for i in objects_name:
objects_name_in_str += i + "\n"
raise ValueError(
str(obj["count"]) + " different objects found: \n" + objects_name_in_str
)
if "object" not in obj.keys():
raise ValueError(f"Object {name} not found")
a = obj["orbit"]["elements"]["a"]
ecc = float(obj["orbit"]["elements"]["e"]) * u.one
inc = obj["orbit"]["elements"]["i"]
raan = obj["orbit"]["elements"]["om"]
argp = obj["orbit"]["elements"]["w"]
# Since JPL provides Mean Anomaly (M) we need to make
# the conversion to the true anomaly (nu)
M = obj["orbit"]["elements"]["ma"].to(u.rad)
# NOTE: It is unclear how this conversion should happen,
# see https://ssd-api.jpl.nasa.gov/doc/sbdb.html
if ecc < 1:
M = (M + np.pi * u.rad) % (2 * np.pi * u.rad) - np.pi * u.rad
nu = E_to_nu(M_to_E(M, ecc), ecc)
elif ecc == 1:
nu = D_to_nu(M_to_D(M))
else:
nu = F_to_nu(M_to_F(M, ecc), ecc)
epoch = time.Time(obj["orbit"]["epoch"].to(u.d), format="jd")
ss = cls.from_classical(
Sun,
a,
ecc,
inc,
raan,
argp,
nu,
epoch=epoch.tdb,
plane=Planes.EARTH_ECLIPTIC,
)
return ss
