Getting latitude and longitude of the Sun on a world map with PyEphem

Question

I'm trying to determine the latitude and longitude of say the Sun, the Moon and Mars. I need the result relative to the Earth's equator and the Prime Meridian in order to produce a result similar to this map.

I believe that's also what the author of this question wanted, however the answer there doesn't add up for me (comparing with values from the first link).

Expected result, obtained from the page linked to earlier:

On Thursday, 1 January 2015, 00:00:00 UTC the Sun is at its zenith at Latitude: 23° 02' South, Longitude: 179° 29' West

>>> import ephem; from math import degrees
>>> b = ephem.Sun(epoch='date'); b.compute('2015/1/1 00:00:00')
>>> print("{},{}".format(degrees(b.dec), degrees(b.ra)))
-23.040580418272267,281.12827017399906

So the latitude/declination seems about right, but no 180° wraparound will fix that right ascension, probably because it starts at the Vernal Equinox.

I have also unsuccessfully tried to use an observer at 0,0.

Can this be done using PyEphem, Skyfield or astropy? It seems odd that artificial satellites in PyEphem have the convenient sublat and sublong attributes, but it's so hard for celestial bodies.

Answer 1

I finally figured it out. Sort of. Actually I just ported the relevant bits of libastro to Python. Note that this code runs against the current git version of Skyfield (be6c7296).

Here goes (gist version):

#!/usr/bin/env python3

from datetime import datetime, timezone
from math import atan, atan2, degrees, floor, pi, radians, sin, sqrt

from skyfield.api import earth, JulianDate, now, sun


def earth_latlon(x, y, z, time):
    """
    For an object at the given XYZ coordinates relative to the center of
    the Earth at the given datetime, returns the latitude and longitude
    as it would appear on a world map.

    Units for XYZ don't matter.
    """
    julian_date = JulianDate(utc=time).tt
    # see https://en.wikipedia.org/wiki/Julian_date#Variants
    # libastro calls this "mjd", but the "Modified Julian Date" is
    # something entirely different
    dublin_julian_date = julian_date - 2415020

    # the following block closely mirrors libastro, so don't blame me
    # if you have no clue what the variables mean or what the magic
    # numbers are because I don't either
    sidereal_solar = 1.0027379093
    sid_day = floor(dublin_julian_date)
    t = (sid_day - 0.5) / 36525
    sid_reference = (6.6460656 + (2400.051262 * t) + (0.00002581 * (t**2))) / 24
    sid_reference -= floor(sid_reference)
    lon = 2 * pi * ((dublin_julian_date - sid_day) *
                    sidereal_solar + sid_reference) - atan2(y, x)
    lon = lon % (2 * pi)
    lon -= pi
    lat = atan(z / sqrt(x**2 + y**2))

    return degrees(lat), degrees(-lon)


if __name__ == '__main__':
    print("2015-01-01 00:00:00:")
    time = datetime(2015, 1, 1, tzinfo=timezone.utc)
    x, y, z = earth(JulianDate(utc=time)).observe(sun).apparent().position.au
    print(earth_latlon(x, y, z, time))

    print("now:")
    time = datetime.now(timezone.utc)
    x, y, z = earth(JulianDate(utc=time)).observe(sun).apparent().position.au
    print(earth_latlon(x, y, z, time))

Output:

2015-01-01 00:00:00:
(-23.05923949080624, -179.2173856294249)
now:
(-8.384551051991025, -47.12917634395421)

As you can see, the values for 2015-01-01 00:00:00 match the reference values from the question. Not precisely, but it's good enough for me. For all I know, my values might be better.

Due to my ignorance about the undocumented magic numbers used in the libastro code, I cannot make this work for bodies other than Earth.

@BrandonRhodes: Let me know if you're interested in having this functionality in Skyfield, then I'll try to throw together a pull request.