def _normalized (self, value) :
if isinstance (value, (list, tuple)) :
result = Angle_D.normalized (* value)
elif not isinstance (value, (Angle_D, Angle_R)) :
result = Angle_D.normalized (value)
else :
result = value
return result
def mean_obliquity_ecliptic (self) :
"""Mean obliquity of the ecliptic (in degrees)."""
### see J. Meeus, p. 147, Eq. (22.2)
return \
( Angle_D (23, 26, 21.448)
- Angle_D (seconds = 46.815000) * self.t
- Angle_D (seconds = 0.000590) * self.t2
+ Angle_D (seconds = 0.001813) * self.t3
)
def __init__(self, ephs, loc, h0=Angle_D(-0.8333)):
self.__super.__init__(ephs, loc, h0)
vars = self.vars
vars["h0"] = Angle_D(-6.0)
self.civil_twilight_start = self._Event_(self.m1, **vars)
self.civil_twilight_finis = self._Event_(self.m2, **vars)
vars["h0"] = Angle_D(-12.0)
self.nautic_twilight_start = self._Event_(self.m1, **vars)
self.nautic_twilight_finis = self._Event_(self.m2, **vars)
vars["h0"] = Angle_D(-18.0)
self.astro_twilight_start = self._Event_(self.m1, **vars)
self.astro_twilight_finis = self._Event_(self.m2, **vars)
def nutation_obliquity (self) :
"""Nutation in obliquity (delta-epsilon)."""
### see J. Meeus, pp. 143–4
omega = self.longitude_ascending_node_moon
om_2 = omega * 2
ls_2 = self.geometric_mean_longitude_sun * 2
lm_2 = self.geometric_mean_longitude_moon * 2
result = \
( Angle_D (seconds = 9.20) * omega.cos
+ Angle_D (seconds = 0.57) * ls_2.cos
+ Angle_D (seconds = 0.10) * lm_2.cos
- Angle_D (seconds = 0.09) * om_2.cos
)
return result
def nutation_longitude (self) :
"""Nutation in longitude (delta-phi)."""
### see J. Meeus, pp. 143–4
omega = self.longitude_ascending_node_moon
om_2 = omega * 2
ls_2 = self.geometric_mean_longitude_sun * 2
lm_2 = self.geometric_mean_longitude_moon * 2
result = \
( Angle_D (seconds = -17.20) * omega.sin
- Angle_D (seconds = - 1.32) * ls_2.sin
- Angle_D (seconds = 0.23) * lm_2.sin
+ Angle_D (seconds = 0.21) * om_2.sin
)
return result
def local_hour_angle (self, h0, lat, delta) :
"""Local hour angle corresponding to the time of rise or set of a
celestial body.
"""
### J. Meeus, eq. (15.1), p. 102
cos_H0 = (h0.sin - lat.sin * delta.sin) / (lat.cos * delta.cos)
if abs (cos_H0) <= 1 :
return Angle_D.acos (cos_H0)
def local_hour_angle(self, h0, lat, delta):
"""Local hour angle corresponding to the time of rise or set of a
celestial body.
"""
### J. Meeus, eq. (15.1), p. 102
cos_H0 = (h0.sin - lat.sin * delta.sin) / (lat.cos * delta.cos)
if abs(cos_H0) <= 1:
return Angle_D.acos(cos_H0)
def sidereal_deg (self) :
"""Apparent sidereal time at `self.date` and `self.time` in degrees."""
### see J. Meeus, p. 95
result = \
( Angle_D.normalized (self.mean_sidereal_deg)
+ (self.nutation_longitude / 15) * self.obliquity_corrected.cos
)
return result
def azimuth (decl, ha, lat) :
"""Azimuth of a celestial body with declination `decl` and hour angle `ha`
for latitude `lat`.
Azimuth is measured eastward from the North.
"""
### J. Meeus, p. 93, Eq. (13.5)
tan_A = \
( ha.sin
/ (ha.cos * lat.sin - decl.tan * lat.cos)
)
result = Angle_D.normalized (Angle_R.atan (tan_A).degrees)
corr = 0
if ha < 0 and result > 180 :
corr = Angle_D (-180) ### ha < 0 --> E of meridian
elif ha > 0 and result < 180 :
corr = Angle_D (+180) ### ha > 0 --> W of meridian
result += corr
return Angle_D.normalized (result.degrees)
def azimuth (decl, ha, loc) :
"""Azimuth of a celestial body with declination `decl` and hour angle `ha`
for location `loc`.
Azimuth is measured eastward from the North.
"""
### J. Meeus, p. 93, Eq. (13.5)
lat = loc.latitude
tan_A = \
( ha.sin
/ (ha.cos * lat.sin - decl.tan * lat.cos)
)
result = Angle_D.normalized (Angle_R.atan (tan_A).degrees)
corr = 0
if ha < 0 and result > 180 :
corr = Angle_D (-180) ### ha < 0 --> E of meridian
elif ha > 0 and result < 180 :
corr = Angle_D (+180) ### ha > 0 --> W of meridian
result += corr
return Angle_D.normalized (result.degrees)
def __init__(self, ephs, loc, h0=Angle_D(-0.5667)):
"""Arguments:
* ephs : triple of positions for UT=0:0 for (day-1, day, day+1)
* loc : SKY.Location instance
* h0 : "standard" altitude, i.e., the geometric altitude of the
center of the body at the time of apparent rising or
setting
+ 0.5667 degrees for stars and planets
+ 0.8333 degrees for the sun
"""
rts = self
self.ephs = ephs
self.loc = loc
self.lat = lat = loc.latitude
self.lon = lon = loc.longitude_meuss
self.h0 = h0 = Angle(h0)
self.day = day = ephs[1].day
self.alpha = alpha = ephs[1].ra
self.delta = delta = ephs[1].decl
self.time = time = ephs[1].time
self.sid = sid = Angle_D.normalized(time.sidereal_deg)
### H0: local hour angle corresponding to the time of rise or set of a
### celestial body. J. Meeus, eq. (15.1), p. 102
self.H0 = H0 = self.local_hour_angle(h0, lat, delta)
self.vars = vars = locals()
### m0, m1, m2
### transit, rise, set times, on `day`, expressed as fractions of a day
### J. Meeus, eq. (15.2), p. 102
self.m0 = m0 = ((alpha + lon - sid).degrees / 360.) % 1.0
if H0 is not None:
self.m1 = m1 = (m0 - H0.degrees / 360.) % 1.0
self.m2 = m2 = (m0 + H0.degrees / 360.) % 1.0
self.rise = self._Rise_(m1, **vars)
self.set = self._Set_(m2, **vars)
self.transit = self._Transit_(m0, **vars)
def hour_angle (sid_UT, loc, ra) :
"""Hour angle for sidereal_time `sid_UT`, location `loc`, and
right ascension `ra`.
`sid_UT` and `ra` must be Angle_D/Angle_R instances.
"""
### J. Meeus, p. 92
lon = loc.longitude_meuss
ha = (sid_UT - lon - ra).degrees
if abs (ha) >= 360.0 :
ha = ha % 360.0
if ha > 180.0 :
ha -= 360.0
elif ha < -180.0 :
ha += 360.0
return Angle_D (ha)
def __init__ (self, ephs, lat, lon, h0 = Angle_D (-0.5667)) :
"""Arguments:
* ephs : triple of positions for UT=0:0 for (day-1, day, day+1)
* lat : latitude in degrees
+ positive in northern hemisphere
+ negative in southern hemisphere
* lon : longitude in degrees
+ positive W of Greenwich
+ negative E of Greenwich
* h0 : "standard" altitude, i.e., the geometric altitude of the
center of the body at the time of apparent rising or
setting
+ 0.5667 degrees for stars and planets
+ 0.8333 degrees for the sun
"""
rts = self
self.ephs = ephs
self.lat = lat = Angle_D (getattr (lat, "degrees", lat))
self.lon = lon = Angle_D (getattr (lon, "degrees", lon))
self.h0 = h0 = Angle_D (getattr (h0, "degrees", h0))
self.day = day = ephs [1].day
self.alpha = alpha = ephs [1].ra
self.delta = delta = ephs [1].decl
self.time = time = ephs [1].time
self.sid = sid = Angle_D.normalized (time.sidereal_deg)
### H0: local hour angle corresponding to the time of rise or set of a
### celestial body. J. Meeus, eq. (15.1), p. 102
self.H0 = H0 = self.local_hour_angle (h0, lat, delta)
self.vars = vars = locals ()
### m0, m1, m2
### transit, rise, set times, on `day`, expressed as fractions of a day
### J. Meeus, eq. (15.2), p. 102
self.m0 = m0 = ((alpha + lon - sid).degrees / 360.) % 1.0
if H0 is not None :
self.m1 = m1 = (m0 - H0.degrees / 360.) % 1.0
self.m2 = m2 = (m0 + H0.degrees / 360.) % 1.0
self.rise = self._Rise_ (m1, ** vars)
self.set = self._Set_ (m2, ** vars)
self.transit = self._Transit_ (m0, ** vars)
def air_mass (altitude) :
"""Air mass coefficient due to atmospheric extinction for `altitude`.
>>> for alt in (90, 30, 20, 15, 10, 5, 2, 0) :
... print ("z = %2d° --> AM = %4.1f" % (90-alt, air_mass (alt)))
z = 0° --> AM = 1.0
z = 60° --> AM = 2.0
z = 70° --> AM = 2.9
z = 75° --> AM = 3.8
z = 80° --> AM = 5.6
z = 85° --> AM = 10.3
z = 88° --> AM = 19.4
z = 90° --> AM = 37.9
https://en.wikipedia.org/wiki/Air_mass_(solar_energy), formula A.2
"""
z = Angle_D (90) - altitude
result = 1.0 / (z.cos + 0.50572 * ((96.07995 - z.degrees) ** -1.6364))
return result
lon -= 360.0
result = "%s %s, %s %s" % \
( abs (lon), "W" if lon.degrees < 0.0 else "E"
, abs (lat), "S" if lat.degrees < 0.0 else "N"
)
if self.height :
result = "%s, %2.0fm above sea level" % (result, self.height)
if self.name :
result = "%s [%s]" % (self.ui_name, result)
return result
# end def __str__
# end class Location
Location \
( Angle_D (48, 14)
, Angle_D (16, 22)
, "Vienna"
, 180
, tz_name = "Europe/Vienna"
)
Location \
( Angle_D (37, 51, 7)
, - Angle_D ( 8, 47, 31)
, "Porto Covo"
, 25
, tz_name = "Europe/Lisbon"
)
class _Location_Arg_ (TFL.CAO.Str) :
def decl (self) :
"""Apparent declination of the sun (in degrees)."""
### Eq. (25.7), for apparent position
o = self.time.obliquity_corrected
l = self.apparent_longitude
return Angle_D.asin (o.sin * l.sin)
def decl(self):
"""Apparent declination of the sun (in degrees)."""
### Eq. (25.7), for apparent position
o = self.time.obliquity_corrected
l = self.apparent_longitude
return Angle_D.asin(o.sin * l.sin)
def _scaled_phi(self, rhs):
result = self._phi
if rhs < 0:
result += Angle_D(180.0)
return result
def On_Day(cls, date, location, h0=Angle_D(-0.8333)):
s = Sun(date)
return cls((s - 1, s, s + 1), location, h0)
def __neg__(self):
return self.__class__(self._r, self._phi + Angle_D(180.0))