Physics

In this example, we’ll show how to generate a sun path diagram for any given day for a preselected location. By using the skyfield library, we can obtain extremely accurate predictions of the sun’s position in the sky, and in contrast to many other libraries, we can use the same method to predict the position of other celestial bodies.

#!/usr/bin/env python3
from skyfield import api
from skyfield import almanac
from datetime import datetime
from datetime import timedelta
from matplotlib import pyplot as plt
import pytz
import dateutil.parser
from collections import namedtuple
from UliEngineering.Utils.Date import *
import matplotlib.ticker as mtick

# Matplotlib formatter
def format_degrees(value, pos=None):
    return f'{value:.0f} °'

ts = api.load.timescale()
ephem = api.load_file('de421.bsp')

sun = ephem["Sun"]
earth = ephem["Earth"]

# Data types
AltAz = namedtuple("AltAz", ["altitude", "azimuth", "distance"])
TimeAltAz = namedtuple("TimeAltAz", ["time", "altitude", "azimuth", "distance"])

def sun_altaz(planet_at_location, ts):
    # Compute the sun position as seen from the observer at <location>
    sun_pos = planet_at_location.at(ts).observe(sun).apparent()
    # Compute apparent altitude & azimuth for the sun's position
    altitude, azimuth, distance = sun_pos.altaz()
    return AltAz(altitude, azimuth, distance)

def sun_altaz_for_day(location, year, month, day, tz):
    earth_at_location = (earth + location)
    
    minutes = list(yield_minutes_on_day(year=year, month=month, day=day, tz=tz))
    skyfield_minutes = ts.from_datetimes(minutes)

    minutely_altaz = [sun_altaz(earth_at_location, ts) for ts in skyfield_minutes]
    # Extract components for plotting
    minutely_alt = [altaz.altitude.degrees for altaz in minutely_altaz]
    minutely_az = [altaz.azimuth.degrees for altaz in minutely_altaz]
    minutely_distance = [altaz.distance for altaz in minutely_altaz]

    return TimeAltAz(minutes, minutely_alt, minutely_az, minutely_distance)

# Random location near Munich
location = api.Topos('48.324777 N', '11.405610 E', elevation_m=519)
# Compute Alt/Az for two different days
jun = sun_altaz_for_day(location, 2022, 6, 15, pytz.timezone("Europe/Berlin"))
dec = sun_altaz_for_day(location, 2022, 12, 15, pytz.timezone("Europe/Berlin"))

# Plot!
plt.gca().yaxis.set_major_formatter(mtick.FuncFormatter(format_degrees))
plt.gca().xaxis.set_major_formatter(mtick.FuncFormatter(format_degrees))

plt.plot(jun.azimuth, jun.altitude, label="15th of June")
plt.plot(dec.azimuth, dec.altitude, label="15th of December")
plt.ylim([0, None]) # Do not show sun angles below the horizon
plt.ylabel("Sun altitude")
plt.xlabel("Sun azimuth")
plt.title("Apparent sun position at our office")
plt.grid() 
plt.gca().legend()
plt.gcf().set_size_inches(10,5)

plt.savefig("Sun path.svg")

The following code computes the position of the sun (in azimuth/altitude coordinates) in the sky using the skyfield library. Note that you need to download de421.bsp .

from skyfield import api
from skyfield import almanac
from datetime import datetime
from datetime import timedelta
import dateutil.parser
from calendar import monthrange

ts = api.load.timescale()
ephem = api.load_file('de421.bsp')

sun = ephem["Sun"]
earth = ephem["Earth"]

# Compute sunrise & sunset for random location near Munich
location = api.Topos('48.324777 N', '11.405610 E', elevation_m=519)
# Compute the sun position as seen from the observer at <location>
sun_pos = (earth + location).at(ts.now()).observe(sun).apparent()
# Compute apparent altitude & azimuth for the sun's position
altitude, azimuth, distance = sun_pos.altaz()

# Print results (example)
print(f"Altitude: {altitude.degrees:.4f} °")
print(f"Azimuth: {azimuth.degrees:.4f} °")

Example output

Altitude: -3.3121 °
Azimuth: 48.4141 °

Factors influencing the accuracy of the calculation

This way of calculating the position takes into account:

• The slight shift in position caused by light speed
• The very very slight shift in position caused by earth’s gravity

But it does not take into account:

• Atmospheric distortions shifting the sun’s position
• The extent of the sun’s disk causing the sun to emanate not from a point but apparently from an area

The following code will compute the sunrise & sunset at a specific location & elevation using the skyfield library. Note that you need to download de413.bsp .

from skyfield import api
from skyfield import almanac
from datetime import datetime
from datetime import timedelta
import dateutil.parser
from calendar import monthrange

ts = api.load.timescale()
ephem = api.load_file('de413.bsp')

def compute_sunrise_sunset(location, year=2019, month=1, day=1):
    t0 = ts.utc(year, month, day, 0)
    # t1 = t0 plus one day
    t1 = ts.utc(t0.utc_datetime() + timedelta(days=1))
    t, y = almanac.find_discrete(t0, t1, almanac.sunrise_sunset(ephem, location))
    sunrise = None
    for time, is_sunrise in zip(t, y):
        if is_sunrise:
            sunrise = dateutil.parser.parse(time.utc_iso())
        else:
            sunset = dateutil.parser.parse(time.utc_iso())
    return sunrise, sunset

# Compute sunrise & sunset for random location near Munich
location = api.Topos('48.324777 N', '11.405610 E', elevation_m=519)
now = datetime.now()
sunrise, sunset = compute_sunrise_sunset(location, now.year, now.month, now.day)

# Print result (example)
print(f'Sunrise today: {sunrise}')
print(f'Sunset today: {sunset}')

Definition of sunrise & sunset in this context

According to the skyfield documentation:

Skyfield uses the same definition as the United States Naval Observatory: the Sun is up when its center is 0.8333 degrees below the horizon, which accounts for both its apparent radius of around 16 arcminutes and also for the 34 arcminutes by which atmospheric refraction on average lifts the image of the Sun.

Other caveats

• Note that obstructions like mountains are not taken into account for this model
• Note that the resulting timestamps are UTC, if you want local time, you’ll have to convert them appropriately

Example output:

Sunrise today: 2022-06-19 03:12:56+00:00
Sunset today: 2022-06-19 19:18:38+00:00