def magnSatRing(JD, lon, lat):
"""Compute the apparent visual magnitude of Saturn's rings.
Args:
JD (float): Julian Day (days).
lon (float): Geocentric ecliptical longitude of Saturn (rad).
lat (float): Geocentric ecliptical latitude of Saturn (rad).
Returns:
float: magnSatRing: Apparent visual magnitude of the planet.
References:
- [Explanatory Supplement to the Astronomical Almanac 3rd Ed, Table 10.6, p.413 +
errata](https://aa.usno.navy.mil/publications/docs/exp_supp.php)
Note:
- This is a simplified expression, which uses phi instead of Delta U. The mean absolute deviation from
the full expression: is 0.014m, the maximum deviation found: 0.041m in 10^5 trials, over the last 5000
years.
"""
tJC = dt.jd2tjc(JD) # Time since 2000 in Julian centuries
incl = 0.49 # Inclination of Saturn's rotation axis (rad)
ascNod = 2.96 + 0.024 * tJC # Ascending node of Saturn's orbit (rad)
sinB = np.sin(incl) * np.cos(lat) * np.sin(lon - ascNod) - np.cos(
incl) * np.sin(lat)
magnSatRing = -2.60 * abs(sinB) + 1.25 * (sinB)**2
return magnSatRing
def precessHip(jd, ra,dec):
"""Compute precession in equatorial coordinates from the Hipparcos equinox (J2000) to that of the specified JD.
Arguments:
jd (float): Julian day (days).
ra (float): Right ascension (rad).
dec (float): Declination (rad).
Returns:
tuple (float,float): tuple containing (raTarget, decTarget):
- raNew (float): Right ascension for the target equinox (rad).
- decNew (float): Declination for the target equinox (rad).
"""
tJC = dt.jd2tjc(jd) # Time in Julian centuries since J2000.0
tJC2 = tJC**2
tJC3 = tJC*tJC2
zeta = (2306.2181*tJC + 0.30188*tJC2 + 0.017998*tJC3)*as2r
z = (2306.2181*tJC + 1.09468*tJC2 + 0.018203*tJC3)*as2r
theta = (2004.3109*tJC - 0.42665*tJC2 - 0.041833*tJC3)*as2r
raNew = (np.arctan2( np.sin(ra + zeta) * np.cos(dec), np.cos(ra + zeta) * m.cos(theta) * np.cos(dec) - m.sin(theta) * np.sin(dec) ) + z) % pi2
decNew = np.arcsin( np.cos(ra + zeta) * m.sin(theta) * np.cos(dec) + m.cos(theta) * np.sin(dec) )
return raNew,decNew
def properMotion(startJD,targetJD, ra,dec, pma,pmd):
"""Compute the proper motion from startJD to targetJD for the given positions and proper motions.
Arguments:
startJD (float): Julian day of the initial epoch (days).
targetJD (float): Julian day of the target epoch (days).
ra (float): Right ascension (numpy array, rad).
dec (float): Declination (numpy array, rad).
pma (float): Proper motion in right ascension (numpy array, rad/yr).
pmd (float): Proper motion in declination (numpy array, rad/yr).
Returns:
tuple (float,float): tuple containing (raTarget, decTarget):
- raTarget (float): Right ascension for the target epoch (rad).
- decTarget (float): Declination for the target epoch (rad).
"""
dtYr = (targetJD - startJD)/365.25
raTarget = ra + pma*dtYr / np.cos(dec)
decTarget = dec + pmd*dtYr
return raTarget,decTarget
def par2horiz(ha,dec, phi):
"""Convert parallactic coordinates to horizontal.
Arguments:
ha (float): Hour angle (rad).
dec (float): Declination (rad).
phi (float): Geographical latitude (rad, N>0).
Returns:
tuple (float,float): tuple containing (az, alt):
- az (float): Azimuth (rad, S=0).
- alt (float): Altitude (rad).
"""
az = np.arctan2( np.sin(ha), np.cos(ha) * m.sin(phi) - np.tan(dec) * m.cos(phi) ) % pi2
alt = np.arcsin( np.sin(dec) * m.sin(phi) + np.cos(ha) * np.cos(dec) * m.cos(phi) )
return az,alt
def eq2ecl(ra,dec, eps):
"""
Convert equatorial coordinates to ecliptical.
Arguments:
ra (float): Right ascension (rad).
dec (float): Declination (rad).
eps (float): Obliquity of the ecliptic (rad).
Returns:
tuple (float,float): tuple containing (lon, lat):
- lon (float): Ecliptical longitude (rad).
- lat (float): Ecliptical latitude (rad).
"""
lon = np.arctan2( np.sin(ra) * m.cos(eps) + np.tan(dec) * m.sin(eps), np.cos(ra) ) % pi2
lat = np.arcsin( np.sin(dec) * m.cos(eps) - np.cos(dec) * m.sin(eps) * np.sin(ra) )
return lon,lat
def ecl2eq(lon,lat, eps):
"""Convert (geocentric) spherical ecliptical coordinates to spherical equatorial coordinates.
Arguments:
lon (float): Ecliptical longitude (rad).
lat (float): Ecliptical latitude (rad).
eps (float): Obliquity of the ecliptic (rad).
Returns:
tuple (float,float): tuple containing (ra, dec):
- ra (float): Right ascension (rad).
- dec (float): Declination (rad).
References:
- [Explanatory Supplement to the Astronomical Almanac 3rd Ed,
Eq.14.43](https://aa.usno.navy.mil/publications/docs/exp_supp.php)
"""
ra = np.arctan2( np.sin(lon) * np.cos(eps) - np.tan(lat) * np.sin(eps), np.cos(lon) ) % pi2
dec = np.arcsin( np.sin(lat) * np.cos(eps) + np.cos(lat) * np.sin(eps) * np.sin(lon) )
return ra,dec