Module pymap3d.vallado
converts right ascension, declination to azimuth, elevation and vice versa. Normally do this via AstroPy. These functions are fallbacks for those wihtout AstroPy.
Michael Hirsch implementation of algorithms from D. Vallado
Source code
"""
converts right ascension, declination to azimuth, elevation and vice versa.
Normally do this via AstroPy.
These functions are fallbacks for those wihtout AstroPy.
Michael Hirsch implementation of algorithms from D. Vallado
"""
from datetime import datetime
try:
from numpy import sin, cos, degrees, radians, arcsin as asin, arctan2 as atan2
except ImportError:
from math import sin, cos, degrees, radians, asin, atan2
from typing import Tuple
from .sidereal import datetime2sidereal
__all__ = ["azel2radec", "radec2azel"]
def azel2radec(
az_deg: float, el_deg: float, lat_deg: float, lon_deg: float, time: datetime, usevallado: bool = True
) -> Tuple[float, float]:
"""
converts azimuth, elevation to right ascension, declination
Parameters
----------
az_deg : float
azimuth (clockwise) to point [degrees]
el_deg : float
elevation above horizon to point [degrees]
lat_deg : float
observer WGS84 latitude [degrees]
lon_deg : float
observer WGS84 longitude [degrees]
time : datetime.datetime
time of observation
Results
-------
ra_deg : float
right ascension to target [degrees]
dec_deg : float
declination of target [degrees]
from D.Vallado Fundamentals of Astrodynamics and Applications
p.258-259
"""
if abs(lat_deg) > 90:
raise ValueError("-90 <= lat <= 90")
az = radians(az_deg)
el = radians(el_deg)
lat = radians(lat_deg)
lon = radians(lon_deg)
# %% Vallado "algorithm 28" p 268
dec = asin(sin(el) * sin(lat) + cos(el) * cos(lat) * cos(az))
lha = atan2(-(sin(az) * cos(el)) / cos(dec), (sin(el) - sin(lat) * sin(dec)) / (cos(dec) * cos(lat)))
lst = datetime2sidereal(time, lon) # lon, ra in RADIANS
""" by definition right ascension [0, 360) degrees """
return degrees(lst - lha) % 360, degrees(dec)
def radec2azel(
ra_deg: float, dec_deg: float, lat_deg: float, lon_deg: float, time: datetime, usevallado: bool = True
) -> Tuple[float, float]:
"""
converts right ascension, declination to azimuth, elevation
Parameters
----------
ra_deg : float
right ascension to target [degrees]
dec_deg : float
declination to target [degrees]
lat_deg : float
observer WGS84 latitude [degrees]
lon_deg : float
observer WGS84 longitude [degrees]
time : datetime.datetime
time of observation
Results
-------
az_deg : float
azimuth clockwise from north to point [degrees]
el_deg : float
elevation above horizon to point [degrees]
from D. Vallado "Fundamentals of Astrodynamics and Applications "
4th Edition Ch. 4.4 pg. 266-268
"""
if abs(lat_deg) > 90:
raise ValueError("-90 <= lat <= 90")
ra = radians(ra_deg)
dec = radians(dec_deg)
lat = radians(lat_deg)
lon = radians(lon_deg)
lst = datetime2sidereal(time, lon) # RADIANS
# %% Eq. 4-11 p. 267 LOCAL HOUR ANGLE
lha = lst - ra
# %% #Eq. 4-12 p. 267
el = asin(sin(lat) * sin(dec) + cos(lat) * cos(dec) * cos(lha))
# %% combine Eq. 4-13 and 4-14 p. 268
az = atan2(-sin(lha) * cos(dec) / cos(el), (sin(dec) - sin(el) * sin(lat)) / (cos(el) * cos(lat)))
return degrees(az) % 360.0, degrees(el)Functions
def azel2radec(az_deg, el_deg, lat_deg, lon_deg, time, usevallado=True)-
converts azimuth, elevation to right ascension, declination
Parameters
az_deg:float- azimuth (clockwise) to point [degrees]
el_deg:float- elevation above horizon to point [degrees]
lat_deg:float- observer WGS84 latitude [degrees]
lon_deg:float- observer WGS84 longitude [degrees]
time:datetime.datetime- time of observation
Results
ra_deg:float- right ascension to target [degrees]
dec_deg:float- declination of target [degrees]
from D.Vallado Fundamentals of Astrodynamics and Applications p.258-259
Source code
def azel2radec( az_deg: float, el_deg: float, lat_deg: float, lon_deg: float, time: datetime, usevallado: bool = True ) -> Tuple[float, float]: """ converts azimuth, elevation to right ascension, declination Parameters ---------- az_deg : float azimuth (clockwise) to point [degrees] el_deg : float elevation above horizon to point [degrees] lat_deg : float observer WGS84 latitude [degrees] lon_deg : float observer WGS84 longitude [degrees] time : datetime.datetime time of observation Results ------- ra_deg : float right ascension to target [degrees] dec_deg : float declination of target [degrees] from D.Vallado Fundamentals of Astrodynamics and Applications p.258-259 """ if abs(lat_deg) > 90: raise ValueError("-90 <= lat <= 90") az = radians(az_deg) el = radians(el_deg) lat = radians(lat_deg) lon = radians(lon_deg) # %% Vallado "algorithm 28" p 268 dec = asin(sin(el) * sin(lat) + cos(el) * cos(lat) * cos(az)) lha = atan2(-(sin(az) * cos(el)) / cos(dec), (sin(el) - sin(lat) * sin(dec)) / (cos(dec) * cos(lat))) lst = datetime2sidereal(time, lon) # lon, ra in RADIANS """ by definition right ascension [0, 360) degrees """ return degrees(lst - lha) % 360, degrees(dec) def radec2azel(ra_deg, dec_deg, lat_deg, lon_deg, time, usevallado=True)-
converts right ascension, declination to azimuth, elevation
Parameters
ra_deg:float- right ascension to target [degrees]
dec_deg:float- declination to target [degrees]
lat_deg:float- observer WGS84 latitude [degrees]
lon_deg:float- observer WGS84 longitude [degrees]
time:datetime.datetime- time of observation
Results
az_deg:float- azimuth clockwise from north to point [degrees]
el_deg:float- elevation above horizon to point [degrees]
from D. Vallado "Fundamentals of Astrodynamics and Applications " 4th Edition Ch. 4.4 pg. 266-268
Source code
def radec2azel( ra_deg: float, dec_deg: float, lat_deg: float, lon_deg: float, time: datetime, usevallado: bool = True ) -> Tuple[float, float]: """ converts right ascension, declination to azimuth, elevation Parameters ---------- ra_deg : float right ascension to target [degrees] dec_deg : float declination to target [degrees] lat_deg : float observer WGS84 latitude [degrees] lon_deg : float observer WGS84 longitude [degrees] time : datetime.datetime time of observation Results ------- az_deg : float azimuth clockwise from north to point [degrees] el_deg : float elevation above horizon to point [degrees] from D. Vallado "Fundamentals of Astrodynamics and Applications " 4th Edition Ch. 4.4 pg. 266-268 """ if abs(lat_deg) > 90: raise ValueError("-90 <= lat <= 90") ra = radians(ra_deg) dec = radians(dec_deg) lat = radians(lat_deg) lon = radians(lon_deg) lst = datetime2sidereal(time, lon) # RADIANS # %% Eq. 4-11 p. 267 LOCAL HOUR ANGLE lha = lst - ra # %% #Eq. 4-12 p. 267 el = asin(sin(lat) * sin(dec) + cos(lat) * cos(dec) * cos(lha)) # %% combine Eq. 4-13 and 4-14 p. 268 az = atan2(-sin(lha) * cos(dec) / cos(el), (sin(dec) - sin(el) * sin(lat)) / (cos(el) * cos(lat))) return degrees(az) % 360.0, degrees(el)