def eqeqx(tdb):
"""The equation of the equinoxes (IAU 1994).
Inputs:
- tdb (MJD): TDB (loosely ET) as a Modified Julian Date
Returns eqeqx, where:
Greenwich apparent sidereal time = Greenwich mean sidereal time + eqeqx
Based on Pat Wallace's EQEQX, which in turn is based on:
IAU Resolution C7, Recommendation 3 (1994)
Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275, 645-650 (1993)
History:
Patrick Wallace Starlink 21 November 1994
2002-07-11 ROwen Converted to Python
"""
# TDB - J2000 in centuries
t=(tdb-51544.5)/36525.0
# Longitude of the mean ascending node of the lunar orbit on the
# ecliptic, measured from the mean equinox of date
om=RO.PhysConst.RadPerArcSec*(450160.280+(-5.0*_ArcSecPerRev-482890.539 \
+(7.455+0.008*t)*t)*t)
# Nutation
dpsi, deps, eps0 = nutc(tdb)
# Equation of the equinoxes
return dpsi*math.cos(eps0)+RO.PhysConst.RadPerArcSec*(0.00264*math.sin(om)+ \
0.000063*math.sin(om+om))
def eqeqx(tdb):
"""The equation of the equinoxes (IAU 1994).
Inputs:
- tdb (MJD): TDB (loosely ET) as a Modified Julian Date
Returns eqeqx, where:
Greenwich apparent sidereal time = Greenwich mean sidereal time + eqeqx
Based on Pat Wallace's EQEQX, which in turn is based on:
IAU Resolution C7, Recommendation 3 (1994)
Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275, 645-650 (1993)
History:
Patrick Wallace Starlink 21 November 1994
2002-07-11 ROwen Converted to Python
"""
# TDB - J2000 in centuries
t = (tdb - 51544.5) / 36525.0
# Longitude of the mean ascending node of the lunar orbit on the
# ecliptic, measured from the mean equinox of date
om=RO.PhysConst.RadPerArcSec*(450160.280+(-5.0*_ArcSecPerRev-482890.539 \
+(7.455+0.008*t)*t)*t)
# Nutation
dpsi, deps, eps0 = nutc(tdb)
# Equation of the equinoxes
return dpsi*math.cos(eps0)+RO.PhysConst.RadPerArcSec*(0.00264*math.sin(om)+ \
0.000063*math.sin(om+om))
def nut(tdb):
"""
Form the matrix of nutation for a given TDB - IAU 1980 theory
(double precision)
References:
Final report of the IAU Working Group on Nutation,
chairman P.K.Seidelmann, 1980.
Kaplan,G.H., 1981, USNO circular no. 163, pA3-6.
Inputs:
- TDB TDB date (loosely et) as Modified Julian Date
Returns the nutation matrix as a 3x3 numpy.array
The matrix is in the sense V(true) = rmatn * V(mean)
"""
# Nutation components and mean obliquity
dpsi, deps, eps0 = nutc(tdb)
# Rotation matrix
return euler((
(0, eps0), (2, -dpsi), (0, -(eps0+deps))
))