def mean_longitude_perigee(self, jd):
"""Return mean longitude of lunar perigee
"""
T = jd_to_jcent(jd)
X = polynomial(
(d_to_r(83.3532465), d_to_r(4069.0137287), d_to_r(-0.0103200),
d_to_r(-1. / 80053), d_to_r(1. / 18999000)), T)
return modpi2(X)
def mean_longitude_perigee(self, jd):
"""Return mean longitude of lunar perigee
"""
T = jd_to_jcent(jd)
X = polynomial(
(d_to_r(83.3532465),
d_to_r(4069.0137287),
d_to_r(-0.0103200),
d_to_r(-1./80053),
d_to_r(1./18999000)
),
T)
return modpi2(X)
def nutation_in_obliquity(jd):
"""Return the nutation in obliquity.
High precision. [Meeus-1998: pg 144]
Arguments:
- `jd` : Julian Day in dynamical time
Returns:
- nutation in obliquity, in radians
"""
#
# Future optimization: factor the /1e5 and /1e6 adjustments into the table.
#
# Could turn the loop into a generator expression. Too messy?
#
T = jd_to_jcent(jd)
D, M, M1, F, omega = _constants(T)
deltaEps = 0.0
for tD, tM, tM1, tF, tomega, tpsiK, tpsiT, tepsK, tepsT in _tbl:
arg = D*tD + M*tM + M1*tM1 + F*tF + omega*tomega
deltaEps = deltaEps + (tepsK/10000.0 +
tepsT/100000.0 * T) * np.cos(arg)
deltaEps = deltaEps / 3600
deltaEps = d_to_r(deltaEps)
return deltaEps
def equinox_approx(yr, season):
"""Returns the approximate time of a solstice or equinox event.
The year must be in the range -1000...3000. Within that range the
the error from the precise instant is at most 2.16 minutes.
Parameters:
yr : year
season : one of ("spring", "summer", "autumn", "winter")
Returns:
Julian Day of the event in dynamical time
"""
if not (-1000 <= yr <= 3000):
raise Error, "year is out of range"
if season not in astronomia.globals.season_names:
raise Error, "unknown season =" + season
yr = int(yr)
if -1000 <= yr <= 1000:
Y = yr / 1000.0
tbl = _approx_1000
else:
Y = (yr - 2000) / 1000.0
tbl = _approx_3000
jd = polynomial(tbl[season], Y)
T = jd_to_jcent(jd)
W = d_to_r(35999.373 * T - 2.47)
delta_lambda = 1 + 0.0334 * cos(W) + 0.0007 * cos(2 * W)
jd += 0.00001 * sum([A * cos(B + C * T) for A, B, C in _terms]) / delta_lambda
return jd
def _latitude(self, jd):
"""Return the geocentric ecliptic latitude in radians.
A subset of the logic in dimension3()
"""
T = jd_to_jcent(jd)
L1, D, M, M1, F, A1, A2, A3, E, E2 = _constants(T)
bsum = 0.0
for tD, tM, tM1, tF, tb in _tblB:
arg = tD * D + tM * M + tM1 * M1 + tF * F
if abs(tM) == 1:
tb *= E
elif abs(tM) == 2:
tb *= E2
bsum += tb * sin(arg)
bsum += -2235 * sin(L1) + \
382 * sin(A3) + \
175 * sin(A1 - F) + \
175 * sin(A1 + F) + \
127 * sin(L1 - M1) - \
115 * sin(L1 + M1)
latitude = d_to_r(bsum / 1000000)
return latitude
def nut_in_lon(jd):
"""Return the nutation in longitude.
High precision. [Meeus-1998: pg 144]
Parameters:
jd : Julian Day in dynamical time
Returns:
nutation in longitude, in radians
"""
#
# Future optimization: factor the /1e5 and /1e6 adjustments into the table.
#
# Could turn the loop into a generator expression. Too messy?
#
T = jd_to_jcent(jd)
D, M, M1, F, omega = _constants(T)
deltaPsi = 0.0
for tD, tM, tM1, tF, tomega, tpsiK, tpsiT, tepsK, tepsT in _tbl:
arg = D*tD + M*tM + M1*tM1 + F*tF + omega*tomega
deltaPsi += (tpsiK/10000.0 + tpsiT/100000.0 * T) * sin(arg)
deltaPsi /= 3600
deltaPsi = d_to_r(deltaPsi)
return deltaPsi
def nutation_in_longitude(jd):
"""Return the nutation in longitude.
High precision. [Meeus-1998: pg 144]
Arguments:
- `jd` : Julian Day in dynamical time
Returns:
- nutation in longitude, in radians
"""
#
# Future optimization: factor the /1e5 and /1e6 adjustments into the table.
#
# Could turn the loop into a generator expression. Too messy?
#
T = jd_to_jcent(jd)
D, M, M1, F, omega = _constants(T)
deltaPsi = 0.0
for tD, tM, tM1, tF, tomega, tpsiK, tpsiT, tepsK, tepsT in _tbl:
arg = D * tD + M * tM + M1 * tM1 + F * tF + omega * tomega
deltaPsi += (tpsiK / 10000.0 + tpsiT / 100000.0 * T) * np.sin(arg)
deltaPsi /= 3600
deltaPsi = d_to_r(deltaPsi)
return deltaPsi
def nut_in_obl(jd):
"""Return the nutation in obliquity.
High precision. [Meeus-1998: pg 144]
Parameters:
jd : Julian Day in dynamical time
Returns:
nutation in obliquity, in radians
"""
#
# Future optimization: factor the /1e5 and /1e6 adjustments into the table.
#
# Could turn the loop into a generator expression. Too messy?
#
T = jd_to_jcent(jd)
D, M, M1, F, omega = _constants(T)
deltaEps = 0.0;
for tD, tM, tM1, tF, tomega, tpsiK, tpsiT, tepsK, tepsT in _tbl:
arg = D*tD + M*tM + M1*tM1 + F*tF + omega*tomega
deltaEps = deltaEps + (tepsK/10000.0 + tepsT/100000.0 * T) * cos(arg)
deltaEps = deltaEps / 3600
deltaEps = d_to_r(deltaEps)
return deltaEps
def _latitude(self, jd):
"""Return the geocentric ecliptic latitude in radians.
A subset of the logic in dimension3()
"""
T = jd_to_jcent(jd)
L1, D, M, M1, F, A1, A2, A3, E, E2 = _constants(T)
bsum = 0.0
for tD, tM, tM1, tF, tb in _tblB:
arg = tD * D + tM * M + tM1 * M1 + tF * F
if abs(tM) == 1:
tb *= E
elif abs(tM) == 2:
tb *= E2
bsum += tb * sin(arg)
bsum += -2235 * sin(L1) + \
382 * sin(A3) + \
175 * sin(A1 - F) + \
175 * sin(A1 + F) + \
127 * sin(L1 - M1) - \
115 * sin(L1 + M1)
latitude = d_to_r(bsum / 1000000)
return latitude
def mean_longitude_ascending_node(self, jd):
"""Return mean longitude of ascending node
Another equation from:
* This routine is part of the International Astronomical Union's
* SOFA (Standards of Fundamental Astronomy) software collection.
* Fundamental (Delaunay) arguments from Simon et al. (1994)
* Arcseconds to radians
DOUBLE PRECISION DAS2R
PARAMETER ( DAS2R = 4.848136811095359935899141D-6 )
* Milliarcseconds to radians
DOUBLE PRECISION DMAS2R
PARAMETER ( DMAS2R = DAS2R / 1D3 )
* Arc seconds in a full circle
DOUBLE PRECISION TURNAS
PARAMETER ( TURNAS = 1296000D0 )
* Mean longitude of the ascending node of the Moon.
OM = MOD ( 450160.398036D0 -6962890.5431D0*T, TURNAS ) * DAS2R
Current implemention in astronomia is from:
PJ Naughter (Web: www.naughter.com, Email: [email protected])
Look in nutation.py for calculation of omega
_ko = (d_to_r(125.04452), d_to_r( -1934.136261), d_to_r( 0.0020708), d_to_r( 1.0/450000))
Though the last term was left off...
Will have to incorporate better...
"""
T = jd_to_jcent(jd)
X = polynomial(
(d_to_r(125.0445479),
d_to_r(-1934.1362891),
d_to_r(0.0020754),
d_to_r(1.0/467441.0),
d_to_r(1.0/60616000.0)
),
T)
return modpi2(X)
def mean_longitude(self, jd):
"""Return mean longitude.
Parameters:
jd : Julian Day in dynamical time
Returns:
Longitude in radians
"""
T = jd_to_jcent(jd)
# From astrolabe
#X = polynomial((d_to_r(100.466457), d_to_r(36000.7698278), d_to_r(0.00030322), d_to_r(0.000000020)), T)
# From AA, Naughter
# Takes T/10.0
X = polynomial((d_to_r(100.4664567), d_to_r(360007.6982779), d_to_r(0.03032028), d_to_r(1.0/49931), d_to_r(-1.0/15300), d_to_r(-1.0/2000000)), T/10.0)
X = modpi2(X + pi)
return X
def mean_longitude(self, jd):
"""Return mean longitude.
Arguments:
- `jd` : Julian Day in dynamical time
Returns:
- Longitude in radians
"""
jd = np.atleast_1d(jd)
T = jd_to_jcent(jd)
# From astrolabe
#X = polynomial((d_to_r(100.466457),
# d_to_r(36000.7698278),
# d_to_r(0.00030322),
# d_to_r(0.000000020)), T)
# From AA, Naughter
# Takes T/10.0
X = polynomial(
(d_to_r(100.4664567), d_to_r(360007.6982779), d_to_r(0.03032028),
d_to_r(1.0 / 49931), d_to_r(-1.0 / 15300), d_to_r(
-1.0 / 2000000)), T / 10.0)
X = modpi2(X + np.pi)
return _scalar_if_one(X)
def mean_longitude(self, jd):
"""Return mean longitude.
Arguments:
- `jd` : Julian Day in dynamical time
Returns:
- Longitude in radians
"""
jd = np.atleast_1d(jd)
T = jd_to_jcent(jd)
# From astrolabe
#X = polynomial((d_to_r(100.466457),
# d_to_r(36000.7698278),
# d_to_r(0.00030322),
# d_to_r(0.000000020)), T)
# From AA, Naughter
# Takes T/10.0
X = polynomial((d_to_r(100.4664567),
d_to_r(360007.6982779),
d_to_r(0.03032028),
d_to_r(1.0/49931),
d_to_r(-1.0/15300),
d_to_r(-1.0/2000000)), T/10.0)
X = modpi2(X + np.pi)
return _scalar_if_one(X)
def mean_longitude_ascending_node(self, jd):
"""Return mean longitude of ascending node
Another equation from:
* This routine is part of the International Astronomical Union's
* SOFA (Standards of Fundamental Astronomy) software collection.
* Fundamental (Delaunay) arguments from Simon et al. (1994)
* Arcseconds to radians
DOUBLE PRECISION DAS2R
PARAMETER ( DAS2R = 4.848136811095359935899141D-6 )
* Milliarcseconds to radians
DOUBLE PRECISION DMAS2R
PARAMETER ( DMAS2R = DAS2R / 1D3 )
* Arc seconds in a full circle
DOUBLE PRECISION TURNAS
PARAMETER ( TURNAS = 1296000D0 )
* Mean longitude of the ascending node of the Moon.
OM = MOD ( 450160.398036D0 -6962890.5431D0*T, TURNAS ) * DAS2R
Current implemention in astronomia is from:
PJ Naughter (Web: www.naughter.com, Email: [email protected])
Look in nutation.py for calculation of omega
_ko = (d_to_r(125.04452), d_to_r( -1934.136261), d_to_r( 0.0020708), d_to_r( 1.0/450000))
Though the last term was left off...
Will have to incorporate better...
"""
T = jd_to_jcent(jd)
X = polynomial(
(d_to_r(125.0445479), d_to_r(-1934.1362891), d_to_r(0.0020754),
d_to_r(1.0 / 467441.0), d_to_r(1.0 / 60616000.0)), T)
return modpi2(X)
def mean_longitude_perigee(self, jd):
"""Return mean longitude of solar perigee.
Parameters:
jd : Julian Day in dynamical time
Returns:
Longitude of solar perigee in radians
"""
T = jd_to_jcent(jd)
X = polynomial((1012395.0, 6189.03, 1.63, 0.012), (T + 1)) / 3600.0
X = d_to_r(X)
X = modpi2(X)
return X
def sidereal_time_greenwich(jd):
"""Return the mean sidereal time at Greenwich.
The Julian Day number must represent Universal Time.
Parameters:
jd : Julian Day number
Return:
sidereal time in radians (2pi radians = 24 hrs)
"""
T = jd_to_jcent(jd)
T2 = T * T
T3 = T2 * T
theta0 = 280.46061837 + 360.98564736629*(jd - 2451545.0) + 0.000387933*T2 - T3/38710000
result = d_to_r(theta0)
return modpi2(result)
def sidereal_time_greenwich(julian_day):
"""Return the mean sidereal time at Greenwich.
The Julian Day number must represent Universal Time.
Arguments:
- `julian_day` : (int) Julian Day number
Returns:
- sidereal time in radians : (float) 2pi radians = 24 hours
"""
T = jd_to_jcent(julian_day)
T2 = T * T
T3 = T2 * T
theta0 = 280.46061837 + 360.98564736629 * (julian_day - 2451545.0) + 0.000387933 * T2 - T3 / 38710000
result = d_to_r(theta0)
return modpi2(result)
def mean_longitude_perigee(self, jd):
"""Return mean longitude of solar perigee.
Arguments:
- `jd` : Julian Day in dynamical time
Returns:
- Longitude of solar perigee in radians
"""
jd = np.atleast_1d(jd)
T = jd_to_jcent(jd)
X = polynomial((1012395.0, 6189.03, 1.63, 0.012), (T + 1)) / 3600.0
X = d_to_r(X)
X = modpi2(X)
return _scalar_if_one(X)
def sidereal_time_greenwich(jd):
"""Return the mean sidereal time at Greenwich.
The Julian Day number must represent Universal Time.
Parameters:
jd : Julian Day number
Return:
sidereal time in radians (2pi radians = 24 hrs)
"""
T = jd_to_jcent(jd)
T2 = T * T
T3 = T2 * T
theta0 = 280.46061837 + 360.98564736629 * (
jd - 2451545.0) + 0.000387933 * T2 - T3 / 38710000
result = d_to_r(theta0)
return modpi2(result)
def mean_longitude_perigee(self, jd):
"""Return mean longitude of solar perigee.
Arguments:
- `jd` : Julian Day in dynamical time
Returns:
- Longitude of solar perigee in radians
"""
jd = np.atleast_1d(jd)
T = jd_to_jcent(jd)
X = polynomial((1012395.0,
6189.03,
1.63,
0.012), (T + 1))/3600.0
X = d_to_r(X)
X = modpi2(X)
return _scalar_if_one(X)
def _longitude(self, jd):
"""Return the geocentric ecliptic longitude in radians.
"""
from astronomia.nutation import nutation_in_longitude
T = jd_to_jcent(jd)
L1, D, M, M1, F, A1, A2, A3, E, E2 = _constants(T)
lsum = 0.0
for tD, tM, tM1, tF, tl, tr in _tblLR:
arg = tD * D + tM * M + tM1 * M1 + tF * F
if abs(tM) == 1:
tl *= E
elif abs(tM) == 2:
tl *= E2
lsum += tl * np.sin(arg)
lsum += 3958 * np.sin(A1) + 1962 * np.sin(L1 - F) + 318 * np.sin(A2)
nutinlong = nutation_in_longitude(jd)
longitude = L1 + d_to_r(lsum / 1000000) + nutinlong
return longitude
def mean_longitude_perigee(self, jd):
"""Return mean longitude of solar perigee.
Parameters:
jd : Julian Day in dynamical time
Returns:
Longitude of solar perigee in radians
"""
T = jd_to_jcent(jd)
X = polynomial((1012395.0,
6189.03 ,
1.63 ,
0.012 ), (T + 1))/3600.0
X = d_to_r(X)
X = modpi2(X)
return X
def sidereal_time_greenwich(julian_day):
"""Return the mean sidereal time at Greenwich.
The Julian Day number must represent Universal Time.
Arguments:
- `julian_day` : (int) Julian Day number
Returns:
- sidereal time in radians : (float) 2pi radians = 24 hours
"""
T = jd_to_jcent(julian_day)
T2 = T * T
T3 = T2 * T
theta0 = 280.46061837 + \
360.98564736629*(julian_day - 2451545.0) + \
0.000387933*T2 - \
T3/38710000
result = d_to_r(theta0)
return modpi2(result)
def _longitude(self, jd):
"""Return the geocentric ecliptic longitude in radians.
"""
from astronomia.nutation import nutation_in_longitude
T = jd_to_jcent(jd)
L1, D, M, M1, F, A1, A2, A3, E, E2 = _constants(T)
lsum = 0.0
for tD, tM, tM1, tF, tl, tr in _tblLR:
arg = tD * D + tM * M + tM1 * M1 + tF * F
if abs(tM) == 1:
tl *= E
elif abs(tM) == 2:
tl *= E2
lsum += tl * np.sin(arg)
lsum += 3958*np.sin(A1) + 1962*np.sin(L1 - F) + 318*np.sin(A2)
nutinlong = nutation_in_longitude(jd)
longitude = L1 + d_to_r(lsum / 1000000) + nutinlong
return longitude
def equinox_approx(yr, season):
"""Returns the approximate time of a solstice or equinox event.
The year must be in the range -1000...3000. Within that range the
the error from the precise instant is at most 2.16 minutes.
Parameters:
yr : year
season : one of ("spring", "summer", "autumn", "winter")
Returns:
Julian Day of the event in dynamical time
"""
if not (-1000 <= yr <= 3000):
raise Error, "year is out of range"
if season not in astronomia.globals.season_names:
raise Error, "unknown season =" + season
yr = int(yr)
if -1000 <= yr <= 1000:
Y = yr / 1000.0
tbl = _approx_1000
else:
Y = (yr - 2000) / 1000.0
tbl = _approx_3000
jd = polynomial(tbl[season], Y)
T = jd_to_jcent(jd)
W = d_to_r(35999.373 * T - 2.47)
delta_lambda = 1 + 0.0334 * cos(W) + 0.0007 * cos(2 * W)
jd += 0.00001 * sum([A * cos(B + C * T)
for A, B, C in _terms]) / delta_lambda
return jd
def _longitude(self, jd):
"""Return the geocentric ecliptic longitude in radians.
A subset of the logic in dimension3()
"""
T = jd_to_jcent(jd)
L1, D, M, M1, F, A1, A2, A3, E, E2 = _constants(T)
lsum = 0.0
for tD, tM, tM1, tF, tl, tr in _tblLR:
arg = tD * D + tM * M + tM1 * M1 + tF * F
if abs(tM) == 1:
tl *= E
elif abs(tM == 2):
tl *= E2
lsum += tl * sin(arg)
lsum += 3958 * sin(A1) + \
1962 * sin(L1 - F) + \
318 * sin(A2)
longitude = L1 + d_to_r(lsum / 1000000)
return longitude
def _longitude(self, jd):
"""Return the geocentric ecliptic longitude in radians.
A subset of the logic in dimension3()
"""
T = jd_to_jcent(jd)
L1, D, M, M1, F, A1, A2, A3, E, E2 = _constants(T)
lsum = 0.0
for tD, tM, tM1, tF, tl, tr in _tblLR:
arg = tD * D + tM * M +tM1 * M1 + tF * F
if abs(tM) == 1:
tl *= E
elif abs(tM == 2):
tl *= E2
lsum += tl * sin(arg)
lsum += 3958 * sin(A1) + \
1962 * sin(L1 - F) + \
318 * sin(A2)
longitude = L1 + d_to_r(lsum / 1000000)
return longitude
def mean_longitude(self, jd):
"""Return mean longitude.
Parameters:
jd : Julian Day in dynamical time
Returns:
Longitude in radians
"""
T = jd_to_jcent(jd)
# From astrolabe
#X = polynomial((d_to_r(100.466457), d_to_r(36000.7698278), d_to_r(0.00030322), d_to_r(0.000000020)), T)
# From AA, Naughter
# Takes T/10.0
X = polynomial(
(d_to_r(100.4664567), d_to_r(360007.6982779), d_to_r(0.03032028),
d_to_r(1.0 / 49931), d_to_r(-1.0 / 15300), d_to_r(
-1.0 / 2000000)), T / 10.0)
X = modpi2(X + pi)
return X
def dimension3(self, jd):
"""Return geocentric ecliptic longitude, latitude and radius.
When we need all three dimensions it is more efficient to combine the
calculations in one routine.
Parameters:
jd : Julian Day in dynamical time
Returns:
longitude in radians
latitude in radians
radius in km, Earth's center to Moon's center
"""
T = jd_to_jcent(jd)
L1, D, M, M1, F, A1, A2, A3, E, E2 = _constants(T)
#
# longitude and radius
#
lsum = 0.0
rsum = 0.0
for tD, tM, tM1, tF, tl, tr in _tblLR:
arg = tD * D + tM * M + tM1 * M1 + tF * F
if abs(tM) == 1:
tl *= E
tr *= E
elif abs(tM == 2):
tl *= E2
tr *= E2
lsum += tl * sin(arg)
rsum += tr * cos(arg)
#
# latitude
#
bsum = 0.0
for tD, tM, tM1, tF, tb in _tblB:
arg = tD * D + tM * M + tM1 * M1 + tF * F
if abs(tM) == 1:
tb *= E
elif abs(tM) == 2:
tb *= E2
bsum += tb * sin(arg)
lsum += 3958 * sin(A1) + \
1962 * sin(L1 - F) + \
318 * sin(A2)
bsum += -2235 * sin(L1) + \
382 * sin(A3) + \
175 * sin(A1 - F) + \
175 * sin(A1 + F) + \
127 * sin(L1 - M1) - \
115 * sin(L1 + M1)
longitude = L1 + d_to_r(lsum / 1000000)
latitude = d_to_r(bsum / 1000000)
dist = 385000.56 + rsum / 1000
return longitude, latitude, dist
T = jd_to_jcent(jd)
D, M, M1, F, omega = _constants(T)
deltaEps = 0.0
for tD, tM, tM1, tF, tomega, tpsiK, tpsiT, tepsK, tepsT in _tbl:
arg = D * tD + M * tM + M1 * tM1 + F * tF + omega * tomega
deltaEps = deltaEps + (tepsK / 10000.0 +
tepsT / 100000.0 * T) * np.cos(arg)
deltaEps = deltaEps / 3600
deltaEps = d_to_r(deltaEps)
return deltaEps
#
# Constant terms
#
_el0 = (d_to_r(dms_to_d(23, 26, 21.448)), d_to_r(dms_to_d(0, 0, -46.8150)),
d_to_r(dms_to_d(0, 0, -0.00059)), d_to_r(dms_to_d(0, 0, 0.001813)))
def obliquity(jd):
"""Return the mean obliquity of the ecliptic.
Low precision, but good enough for most uses. [Meeus-1998: equation 22.2].
Accuracy is 1" over 2000 years and 10" over 4000 years.
Arguments:
- `jd` : Julian Day in dynamical time
Returns:
- obliquity, in radians
"winter": (1721414.39987, 365242.88257, -0.00769, -0.00933, -0.00006)}
#
# Meeus-1998 Table 27.B
#
_approx_3000 = {
"spring": (2451623.80984, 365242.37404, 0.05169, -0.00411, -0.00057),
"summer": (2451716.56767, 365241.62603, 0.00325, 0.00888, -0.00030),
"autumn": (2451810.21715, 365242.01767, -0.11575, 0.00337, 0.00078),
"winter": (2451900.05952, 365242.74049, -0.06223, -0.00823, 0.00032)}
#
# Meeus-1998 Table 27.C
#
_terms = [
(485, d_to_r(324.96), d_to_r( 1934.136)),
(203, d_to_r(337.23), d_to_r( 32964.467)),
(199, d_to_r(342.08), d_to_r( 20.186)),
(182, d_to_r( 27.85), d_to_r(445267.112)),
(156, d_to_r( 73.14), d_to_r( 45036.886)),
(136, d_to_r(171.52), d_to_r( 22518.443)),
( 77, d_to_r(222.54), d_to_r( 65928.934)),
( 74, d_to_r(296.72), d_to_r( 3034.906)),
( 70, d_to_r(243.58), d_to_r( 9037.513)),
( 58, d_to_r(119.81), d_to_r( 33718.147)),
( 52, d_to_r(297.17), d_to_r( 150.678)),
( 50, d_to_r( 21.02), d_to_r( 2281.226)),
( 45, d_to_r(247.54), d_to_r( 29929.562)),
( 44, d_to_r(325.15), d_to_r( 31555.956)),
( 29, d_to_r( 60.93), d_to_r( 4443.417)),
( 18, d_to_r(155.12), d_to_r( 67555.328)),
(1, 1, 0, -1, 223),
(1, 1, 0, 1, 223),
(0, 1, -2, -1, -220),
(2, 1, -1, -1, -220),
(1, 0, 1, 1, -185),
(2, -1, -2, -1, 181),
(0, 1, 2, 1, -177),
(4, 0, -2, -1, 176),
(4, -1, -1, -1, 166),
(1, 0, 1, -1, -164),
(4, 0, 1, -1, 132),
(1, 0, -1, -1, -119),
(4, -1, 0, -1, 115),
(2, -2, 0, 1, 107))
_kA1 = (d_to_r(119.75), d_to_r(131.849))
_kA2 = (d_to_r(53.09), d_to_r(479264.290))
_kA3 = (d_to_r(313.45), d_to_r(481266.484))
def _constants(T):
"""Calculate values required by several other functions"""
L1 = modpi2(polynomial(kL1, T))
D = modpi2(polynomial(kD, T))
M = modpi2(polynomial(kM, T))
M1 = modpi2(polynomial(kM1, T))
F = modpi2(polynomial(kF, T))
A1 = modpi2(polynomial(_kA1, T))
A2 = modpi2(polynomial(_kA2, T))
A3 = modpi2(polynomial(_kA3, T))
def test_ecl_to_equ(self):
ra, dec = ecl_to_equ(d_to_r(113.215630), d_to_r(6.684170), d_to_r(23.4392911))
self.assertAlmostEqual(r_to_d(ra), 116.328942, places=5)
self.assertAlmostEqual(r_to_d(dec), 28.026183, places=6)
#
T = jd_to_jcent(jd)
D, M, M1, F, omega = _constants(T)
deltaEps = 0.0
for tD, tM, tM1, tF, tomega, tpsiK, tpsiT, tepsK, tepsT in _tbl:
arg = D*tD + M*tM + M1*tM1 + F*tF + omega*tomega
deltaEps = deltaEps + (tepsK/10000.0 +
tepsT/100000.0 * T) * np.cos(arg)
deltaEps = deltaEps / 3600
deltaEps = d_to_r(deltaEps)
return deltaEps
#
# Constant terms
#
_el0 = (d_to_r(dms_to_d(23, 26, 21.448)),
d_to_r(dms_to_d(0, 0, -46.8150)),
d_to_r(dms_to_d(0, 0, -0.00059)),
d_to_r(dms_to_d(0, 0, 0.001813)))
def obliquity(jd):
"""Return the mean obliquity of the ecliptic.
Low precision, but good enough for most uses. [Meeus-1998: equation 22.2].
Accuracy is 1" over 2000 years and 10" over 4000 years.
Arguments:
- `jd` : Julian Day in dynamical time
Returns:
def test_ell_to_geo(self):
phi, theta, r = ell_to_geo(d_to_r(0), d_to_r(0), 10000)
self.assertAlmostEqual(r_to_d(modpi2(phi)), 203.23542197)
self.assertAlmostEqual(r_to_d(modpi2(theta)), 90.0)
self.assertAlmostEqual(r, 0.0)
Returns:
- longitude in radians
- latitude in radians
- radius in au
"""
L = self.dimension(jd, "L")
B = self.dimension(jd, "B")
R = self.dimension(jd, "R")
return L, B, R
#
# Constant terms
#
_kL0 = (d_to_r(280.46646), d_to_r(36000.76983), d_to_r(0.0003032))
_kM = (d_to_r(357.5291092), d_to_r(35999.0502909), d_to_r(-0.0001536),
d_to_r(1.0 / 24490000))
_kC = (d_to_r(1.914602), d_to_r(-0.004817), d_to_r(-0.000014))
_ck3 = d_to_r(0.019993)
_ck4 = d_to_r(-0.000101)
_ck5 = d_to_r(0.000289)
def longitude_radius_low(jd):
"""Return geometric longitude and radius vector.
Low precision. The longitude is accurate to 0.01 degree. The latitude
should be presumed to be 0.0. [Meeus-1998: equations 25.2 through 25.5
}
#
# Meeus-1998 Table 27.B
#
_approx_3000 = {
"spring": (2451623.80984, 365242.37404, 0.05169, -0.00411, -0.00057),
"summer": (2451716.56767, 365241.62603, 0.00325, 0.00888, -0.00030),
"autumn": (2451810.21715, 365242.01767, -0.11575, 0.00337, 0.00078),
"winter": (2451900.05952, 365242.74049, -0.06223, -0.00823, 0.00032)
}
#
# Meeus-1998 Table 27.C
#
_terms = [(485, d_to_r(324.96), d_to_r(1934.136)),
(203, d_to_r(337.23), d_to_r(32964.467)),
(199, d_to_r(342.08), d_to_r(20.186)),
(182, d_to_r(27.85), d_to_r(445267.112)),
(156, d_to_r(73.14), d_to_r(45036.886)),
(136, d_to_r(171.52), d_to_r(22518.443)),
(77, d_to_r(222.54), d_to_r(65928.934)),
(74, d_to_r(296.72), d_to_r(3034.906)),
(70, d_to_r(243.58), d_to_r(9037.513)),
(58, d_to_r(119.81), d_to_r(33718.147)),
(52, d_to_r(297.17), d_to_r(150.678)),
(50, d_to_r(21.02), d_to_r(2281.226)),
(45, d_to_r(247.54), d_to_r(29929.562)),
(44, d_to_r(325.15), d_to_r(31555.956)),
(29, d_to_r(60.93), d_to_r(4443.417)),
(18, d_to_r(155.12), d_to_r(67555.328)),
def test_geocentric_planet(self):
ra, dec = geocentric_planet(2448976.5, "Venus", d_to_r(dms_to_d(0, 0, 16.749)), d_to_r(23.439669), days_per_second)
np.testing.assert_array_almost_equal(r_to_d(ra), r_to_d(hms_to_fday(21, 4, 41.454) * pi2), decimal=5)
np.testing.assert_almost_equal(r_to_d(dec), dms_to_d(-18, 53, 16.84), decimal=5)
Returns:
- longitude in radians
- latitude in radians
- radius in au
"""
L = self.dimension(jd, "L")
B = self.dimension(jd, "B")
R = self.dimension(jd, "R")
return L, B, R
#
# Constant terms
#
_kL0 = (d_to_r(280.46646),
d_to_r(36000.76983),
d_to_r(0.0003032))
_kM = (d_to_r(357.5291092),
d_to_r(35999.0502909),
d_to_r(-0.0001536),
d_to_r(1.0/24490000))
_kC = (d_to_r(1.914602),
d_to_r(-0.004817),
d_to_r(-0.000014))
_ck3 = d_to_r(0.019993)
_ck4 = d_to_r(-0.000101)
_ck5 = d_to_r(0.000289)
def dimension3(self, jd):
"""Return geocentric ecliptic longitude, latitude and radius.
When we need all three dimensions it is more efficient to combine the
calculations in one routine.
Parameters:
jd : Julian Day in dynamical time
Returns:
longitude in radians
latitude in radians
radius in km, Earth's center to Moon's center
"""
T = jd_to_jcent(jd)
L1, D, M, M1, F, A1, A2, A3, E, E2 = _constants(T)
#
# longitude and radius
#
lsum = 0.0
rsum = 0.0
for tD, tM, tM1, tF, tl, tr in _tblLR:
arg = tD * D + tM * M + tM1 * M1 + tF * F
if abs(tM) == 1:
tl *= E
tr *= E
elif abs(tM == 2):
tl *= E2
tr *= E2
lsum += tl * sin(arg)
rsum += tr * cos(arg)
#
# latitude
#
bsum = 0.0
for tD, tM, tM1, tF, tb in _tblB:
arg = tD * D + tM * M + tM1 * M1 + tF * F
if abs(tM) == 1:
tb *= E
elif abs(tM) == 2:
tb *= E2
bsum += tb * sin(arg)
lsum += 3958 * sin(A1) + \
1962 * sin(L1 - F) + \
318 * sin(A2)
bsum += -2235 * sin(L1) + \
382 * sin(A3) + \
175 * sin(A1 - F) + \
175 * sin(A1 + F) + \
127 * sin(L1 - M1) - \
115 * sin(L1 + M1)
longitude = L1 + d_to_r(lsum / 1000000)
latitude = d_to_r(bsum / 1000000)
dist = 385000.56 + rsum / 1000
return longitude, latitude, dist
(-1, 0, 1, 0, 0, -4, 0, 0, 0),
(-2, 1, 0, 0, 0, -4, 0, 0, 0),
( 1, 0, 0, 0, 0, -4, 0, 0, 0),
( 0, 0, 1, 2, 0, 3, 0, 0, 0),
( 0, 0, -2, 2, 2, -3, 0, 0, 0),
(-1, -1, 1, 0, 0, -3, 0, 0, 0),
( 0, 1, 1, 0, 0, -3, 0, 0, 0),
( 0, -1, 1, 2, 2, -3, 0, 0, 0),
( 2, -1, -1, 2, 2, -3, 0, 0, 0),
( 0, 0, 3, 2, 2, -3, 0, 0, 0),
( 2, -1, 0, 2, 2, -3, 0, 0, 0))
#
# Constant terms.
#
_kD = (d_to_r(297.85036), d_to_r(445267.111480), d_to_r(-0.0019142), d_to_r( 1.0/189474))
_kM = (d_to_r(357.52772), d_to_r( 35999.050340), d_to_r(-0.0001603), d_to_r(-1.0/300000))
_kM1 = (d_to_r(134.96298), d_to_r(477198.867398), d_to_r( 0.0086972), d_to_r( 1.0/ 56250))
_kF = (d_to_r( 93.27191), d_to_r(483202.017538), d_to_r(-0.0036825), d_to_r( 1.0/327270))
_ko = (d_to_r(125.04452), d_to_r( -1934.136261), d_to_r( 0.0020708), d_to_r( 1.0/450000))
def _constants(T):
"""Return some values needed for both nut_in_lon() and nut_in_obl()"""
D = modpi2(polynomial(_kD, T))
M = modpi2(polynomial(_kM, T))
M1 = modpi2(polynomial(_kM1, T))
F = modpi2(polynomial(_kF, T))
omega = modpi2(polynomial(_ko, T))
return D, M, M1, F, omega
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Astronomia; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
"""
"""Useful constants terms.
Don't change these unless you are moving to a new universe.
"""
from astronomia.util import d_to_r
#
# Constant terms.
#
kL1 = (d_to_r(218.3164477), d_to_r(481267.88123421), d_to_r(-0.0015786),
d_to_r(1.0 / 538841), d_to_r(-1.0 / 65194000))
kD = (d_to_r(297.8501921), d_to_r(445267.1114034), d_to_r(-0.0018819),
d_to_r(1.0 / 545868), d_to_r(-1.0 / 113065000))
kM = (d_to_r(357.5291092), d_to_r(35999.0502909), d_to_r(-0.0001536),
d_to_r(1.0 / 24490000))
kM1 = (d_to_r(134.9633964), d_to_r(477198.8675055), d_to_r(0.0087414),
d_to_r(1.0 / 69699), d_to_r(-1.0 / 14712000))
kF = (d_to_r(93.2720950), d_to_r(483202.0175233), d_to_r(-0.0036539),
d_to_r(-1.0 / 3526000), d_to_r(1.0 / 863310000))
ko = (d_to_r(125.0445479), d_to_r(-1934.1362891), d_to_r(0.0020754),
d_to_r(1.0 / 467441.0), d_to_r(1.0 / 60616000.0))
from astronomia.calendar import sidereal_time_greenwich
from astronomia.constants import seconds_per_day, pi2, earth_equ_radius, \
standard_rst_altitude
from astronomia.dynamical import deltaT_seconds
from astronomia.util import d_to_r, interpolate_angle3, diff_angle, \
modpi2, interpolate3
from astronomia.coordinates import equ_to_horiz
import astronomia.globals
class Error(Exception):
"""local exception class"""
pass
_k1 = d_to_r(360.985647)
def _riseset(jd, raList, decList, h0, delta, mode,
longitude=astronomia.globals.longitude,
latitude=astronomia.globals.latitude):
# Private function since rise/set so similar
THETA0 = sidereal_time_greenwich(jd)
deltaT_days = deltaT_seconds(jd) / seconds_per_day
cosH0 = (np.sin(h0) - np.sin(latitude)*np.sin(decList[1])) / (
np.cos(latitude)*np.cos(decList[1]))
#
# future: return some indicator when the object is circumpolar or always
# below the horizon.
def test_equ_to_ecl(self):
longitude, latitude = equ_to_ecl(d_to_r(116.328942), d_to_r(28.026183), d_to_r(23.4392911))
self.assertAlmostEqual(r_to_d(longitude), 113.215630, places=6)
self.assertAlmostEqual(r_to_d(latitude), 6.684170, places=6)
from math import *
from astronomia.calendar import sidereal_time_greenwich
from astronomia.constants import seconds_per_day, pi2, earth_equ_radius, standard_rst_altitude
from astronomia.dynamical import deltaT_seconds
from astronomia.util import d_to_r, interpolate_angle3, diff_angle, r_to_d, modpi2, interpolate3, equ_to_horiz
import astronomia.globals
class Error(Exception):
"""local exception class"""
pass
_k1 = d_to_r(360.985647)
def rise(jd, raList, decList, h0, delta):
"""Return the Julian Day of the rise time of an object.
Parameters:
jd : Julian Day number of the day in question, at 0 hr UT
raList : a sequence of three right accension values, in radians,
for (jd-1, jd, jd+1)
decList : a sequence of three right declination values, in radians,
for (jd-1, jd, jd+1)
h0 : the standard altitude in radians
delta : desired accuracy in days. Times less than one minute are
infeasible for rise times because of atmospheric refraction.
Returns:
- longitude in radians
- latitude in radians
- radius in au
"""
L = self.dimension(jd, planet, "L")
B = self.dimension(jd, planet, "B")
R = self.dimension(jd, planet, "R")
return L, B, R
#
# Constant terms
#
_k0 = d_to_r(-1.397)
_k1 = d_to_r(-0.00031)
_k2 = d_to_r(dms_to_d(0, 0, -0.09033))
_k3 = d_to_r(dms_to_d(0, 0, 0.03916))
def vsop_to_fk5(jd, L, B):
"""Convert VSOP to FK5 coordinates.
This is required only when using the full precision of the
VSOP model. [Meeus-1998: pg 219]
Arguments:
- `jd` : Julian Day in dynamical time
- `L` : longitude in radians
- `B` : latitude in radians
(2, 1, -1, -1, -220),
(1, 0, 1, 1, -185),
(2, -1, -2, -1, 181),
(0, 1, 2, 1, -177),
(4, 0, -2, -1, 176),
(4, -1, -1, -1, 166),
(1, 0, 1, -1, -164),
(4, 0, 1, -1, 132),
(1, 0, -1, -1, -119),
(4, -1, 0, -1, 115),
(2, -2, 0, 1, 107))
#
# Constant terms.
#
_kL1 = (d_to_r(218.3164477), d_to_r(481267.88123421), d_to_r(-0.0015786),
d_to_r(1.0 / 538841), d_to_r(-1.0 / 65194000))
_kD = (d_to_r(297.8501921), d_to_r(445267.1114034), d_to_r(-0.0018819),
d_to_r(1.0 / 545868), d_to_r(-1.0 / 113065000))
_kM = (d_to_r(357.5291092), d_to_r(35999.0502909), d_to_r(-0.0001536),
d_to_r(1.0 / 24490000))
_kM1 = (d_to_r(134.9633964), d_to_r(477198.8675055), d_to_r(0.0087414),
d_to_r(1.0 / 69699), d_to_r(-1.0 / 14712000))
_kF = (d_to_r(93.2720950), d_to_r(483202.0175233), d_to_r(-0.0036539),
d_to_r(-1.0 / 3526000), d_to_r(1.0 / 863310000))
_kA1 = (d_to_r(119.75), d_to_r(131.849))
_kA2 = (d_to_r(53.09), d_to_r(479264.290))
_kA3 = (d_to_r(313.45), d_to_r(481266.484))
Returns:
- longitude in radians
- latitude in radians
- radius in au
"""
L = self.dimension(jd, planet, "L")
B = self.dimension(jd, planet, "B")
R = self.dimension(jd, planet, "R")
return L, B, R
#
# Constant terms
#
_k0 = d_to_r(-1.397)
_k1 = d_to_r(-0.00031)
_k2 = d_to_r(dms_to_d(0, 0, -0.09033))
_k3 = d_to_r(dms_to_d(0, 0, 0.03916))
def vsop_to_fk5(jd, L, B):
"""Convert VSOP to FK5 coordinates.
This is required only when using the full precision of the
VSOP model. [Meeus-1998: pg 219]
Arguments:
- `jd` : Julian Day in dynamical time
- `L` : longitude in radians
- `B` : latitude in radians
(2, 0, -2, 1, -451), (0, 0, 3, -1, 439), (2, 0, 2, 1, 422), (2, 0, -3,
-1, 421),
(2, 1, -1, 1, -366), (2, 1, 0, 1, -351), (4, 0, 0, 1, 331), (2, -1, 1,
1, 315),
(2, -2, 0, -1, 302), (0, 0, 1, 3, -283), (2, 1, 1, -1,
-229), (1, 1, 0, -1, 223),
(1, 1, 0, 1, 223), (0, 1, -2, -1, -220), (2, 1, -1, -1,
-220), (1, 0, 1, 1, -185),
(2, -1, -2, -1, 181), (0, 1, 2, 1, -177), (4, 0, -2, -1,
176), (4, -1, -1, -1, 166),
(1, 0, 1, -1, -164), (4, 0, 1, -1, 132), (1, 0, -1, -1,
-119), (4, -1, 0, -1,
115), (2, -2, 0, 1,
107))
_kA1 = (d_to_r(119.75), d_to_r(131.849))
_kA2 = (d_to_r(53.09), d_to_r(479264.290))
_kA3 = (d_to_r(313.45), d_to_r(481266.484))
def _constants(T):
"""Calculate values required by several other functions"""
L1 = modpi2(polynomial(kL1, T))
D = modpi2(polynomial(kD, T))
M = modpi2(polynomial(kM, T))
M1 = modpi2(polynomial(kM1, T))
F = modpi2(polynomial(kF, T))
A1 = modpi2(polynomial(_kA1, T))
A2 = modpi2(polynomial(_kA2, T))
A3 = modpi2(polynomial(_kA3, T))
You should have received a copy of the GNU General Public License
along with Astronomia; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
"""
"""Useful constants terms.
Don't change these unless you are moving to a new universe.
"""
from astronomia.util import d_to_r
#
# Constant terms.
#
kL1 = (d_to_r(218.3164477),
d_to_r(481267.88123421),
d_to_r(-0.0015786),
d_to_r(1.0/538841),
d_to_r(-1.0/65194000))
kD = (d_to_r(297.8501921),
d_to_r(445267.1114034),
d_to_r(-0.0018819),
d_to_r(1.0/545868),
d_to_r(-1.0/113065000))
kM = (d_to_r(357.5291092),
d_to_r(35999.0502909),
d_to_r(-0.0001536),
d_to_r(1.0/24490000))
kM1 = (d_to_r(134.9633964),
d_to_r(477198.8675055),
(2, 1, -1, -1, -220),
(1, 0, 1, 1, -185),
(2, -1, -2, -1, 181),
(0, 1, 2, 1, -177),
(4, 0, -2, -1, 176),
(4, -1, -1, -1, 166),
(1, 0, 1, -1, -164),
(4, 0, 1, -1, 132),
(1, 0, -1, -1, -119),
(4, -1, 0, -1, 115),
(2, -2, 0, 1, 107))
#
# Constant terms.
#
_kL1 = (d_to_r(218.3164477), d_to_r(481267.88123421), d_to_r(-0.0015786), d_to_r(1.0/538841), d_to_r(-1.0/65194000))
_kD = (d_to_r(297.8501921), d_to_r(445267.1114034), d_to_r(-0.0018819), d_to_r(1.0/545868), d_to_r(-1.0/113065000))
_kM = (d_to_r(357.5291092), d_to_r( 35999.0502909), d_to_r(-0.0001536), d_to_r(1.0/24490000))
_kM1 = (d_to_r(134.9633964), d_to_r(477198.8675055), d_to_r(0.0087414), d_to_r(1.0/69699), d_to_r(-1.0/14712000))
_kF = (d_to_r( 93.2720950), d_to_r(483202.0175233), d_to_r(-0.0036539), d_to_r(-1.0/3526000), d_to_r( 1.0/863310000))
_kA1 = (d_to_r(119.75), d_to_r( 131.849))
_kA2 = (d_to_r( 53.09), d_to_r(479264.290))
_kA3 = (d_to_r(313.45), d_to_r(481266.484))
def _constants(T):
"""Calculate values required by several other functions"""
L1 = modpi2(polynomial(_kL1, T))
D = modpi2(polynomial(_kD, T))
M = modpi2(polynomial(_kM, T))