def test_raan_from_ltan_sentinel5p():
# SENTINEL-5P LTAN: 13:30
# LTAN from https://sentinels.copernicus.eu/web/sentinel/missions/sentinel-5p/geographical-coverage
# 1 42969U 17064A 20049.78099017 -.00000032 00000-0 54746-5 0 9991
# 2 42969 98.7249 350.5997 0001077 82.0109 278.1189 14.19549365121775
ltan = (13 + (30 / 60)) * u.hourangle
epoch = astropy.time.Time(
astropy.time.Time("2020-01-01 00:00").to_value("mjd") + 49.78099017 - 1,
format="mjd",
)
expected_raan = 350.5997 * u.deg
raan = angles.raan_from_ltan(epoch, ltan)
assert_allclose(raan.wrap_at(360 * u.deg).to(u.deg), expected_raan, atol=0.3)
def test_raan_from_ltan_metopb():
# MetOp-B LTAN: 21:31:45
# LTAN from https://www.ospo.noaa.gov/Operations/METOP/status.html
# METOP-B
# 1 38771U 12049A 20049.95408566 -.00000014 00000-0 13607-4 0 9997
# 2 38771 98.7092 110.9899 0001263 48.5458 295.8781 14.21485930385043
ltan = (21 + ((31 + 45 / 60) / 60)) * u.hourangle
epoch = astropy.time.Time(
astropy.time.Time("2020-01-01 00:00").to_value("mjd") + 49.95408566 - 1,
format="mjd",
)
expected_raan = 110.9899 * u.deg
raan = angles.raan_from_ltan(epoch, ltan)
assert_allclose(raan.wrap_at(360 * u.deg).to(u.deg), expected_raan, atol=0.3)
def heliosynchronous(
cls,
attractor,
a=None,
ecc=None,
inc=None,
ltan=10.0 * u.hourangle,
argp=0 * u.deg,
nu=0 * u.deg,
epoch=J2000,
plane=Planes.EARTH_EQUATOR,
):
r""" Solves for a Sun-Synchronous orbit. These orbits make use of the J2
perturbation to precess in order to be always towards Sun. At least
two parameters of the set {a, ecc, inc} are needed in order to solve
for these kind of orbits. Relationships among them are given by:
.. math::
\begin{align}
a &= \left (\frac{-3R_{\bigoplus}J_{2}\sqrt{\mu}\cos(i)}{2\dot{\Omega}(1-e^2)^2} \right ) ^ {\frac{2}{7}}\\
e &= \sqrt{1 - \sqrt{\frac{-3R_{\bigoplus}J_{2}\sqrt{\mu}cos(i)}{2a^{\frac{7}{2}}\dot{\Omega}}}}\\
i &= \arccos{\left ( \frac{-2a^{\frac{7}{2}}\dot{\Omega}(1-e^2)^2}{3R_{\bigoplus}J_{2}\sqrt{\mu}} \right )}\\
\end{align}
Parameters
----------
a: ~astropy.units.Quantity
Semi-major axis.
ecc: ~astropy.units.Quantity
Eccentricity.
inc: ~astropy.units.Quantity
Inclination.
ltan: ~astropy.units.Quantity
Local time of the ascending node which will be translated to the Right ascension of the ascending node.
argp : ~astropy.units.Quantity
Argument of the pericenter.
nu : ~astropy.units.Quantity
True anomaly.
epoch : ~astropy.time.Time, optional
Epoch, default to J2000.
plane : ~poliastro.frames.Planes
Fundamental plane of the frame.
"""
mean_elements = get_mean_elements(attractor)
n_sunsync = (
np.sqrt(mean_elements.attractor.k / abs(mean_elements.a**3)) *
u.one).decompose()
R_SSO = attractor.R
k_SSO = attractor.k
J2_SSO = attractor.J2
try:
with np.errstate(invalid="raise"):
if (a is None) and (ecc is None) and (inc is None):
# We check sufficient number of parameters
raise ValueError(
"At least two parameters of the set {a, ecc, inc} are required."
)
elif a is None and (ecc is not None) and (inc is not None):
# Semi-major axis is the unknown variable
a = (-3 * R_SSO**2 * J2_SSO * np.sqrt(k_SSO) /
(2 * n_sunsync * (1 - ecc**2)**2) * np.cos(inc))**(2 /
7)
elif ecc is None and (a is not None) and (inc is not None):
# Eccentricity is the unknown variable
_ecc_0 = np.sqrt(-3 * R_SSO**2 * J2_SSO * np.sqrt(k_SSO) *
np.cos(inc.to(u.rad)) /
(2 * a**(7 / 2) * n_sunsync))
ecc = np.sqrt(1 - _ecc_0)
elif inc is None and (ecc is not None) and (a is not None):
# Inclination is the unknown variable
inc = np.arccos(-2 * a**(7 / 2) * n_sunsync *
(1 - ecc**2)**2 /
(3 * R_SSO**2 * J2_SSO * np.sqrt(k_SSO)))
except FloatingPointError:
raise ValueError(
"No SSO orbit with given parameters can be found.")
# Temporary fix: raan_from_ltan works only for Earth
if attractor.name.lower() != "earth":
raise NotImplementedError(
"Attractors other than Earth not supported yet")
raan = raan_from_ltan(epoch, ltan)
ss = cls.from_classical(attractor,
a,
ecc,
inc,
raan,
argp,
nu,
epoch=epoch.tdb,
plane=plane)
return ss