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micropython-samples/astronomy/sun_moon.py

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# sun_moon.py MicroPython Port of lunarmath.c
# Calculate sun and moon rise and set times for any date and location
# Licensing and copyright: see README.md
# Source "Astronomy on the Personal Computer" by Montenbruck and Pfleger
# ISBN 978-3-540-67221-0
# Port from C++ to MicroPython performed by Peter Hinch 2023.
# Withcontributions from Raul Kompaß and Marcus Mendenhall: see
# https://github.com/orgs/micropython/discussions/13075
# Raul Kompaß perfomed major simplification of the maths for deriving rise and
# set_times with improvements in precision with 32-bit floats.
# Moon phase now in separate module
import time
from math import sin, cos, sqrt, fabs, atan, radians, floor, pi
LAT = 53.29756504536339 # Local defaults
LONG = -2.102811634540558
# MicroPython wanton epochs:
# time.gmtime(0)[0] = 1970 or 2000 depending on platform.
# On CPython:
# (date(2000, 1, 1) - date(1970, 1, 1)).days * 24*60*60 = 946684800
# (date(2000, 1, 1) - date(1970, 1, 1)).days = 10957
# Return time now in days relative to platform epoch.
# System time is set to local time, and MP has no concept of this. Hence
# time.time() returns secs since epoch 00:00:00 local time. If lto is local time
# offset to UTC, provided -12 < lto < 12, the effect of rounding ensures the
# right number of days for platform epoch at UTC.
def now_days() -> int:
secs_per_day = 86400 # 24 * 3600
t = RiSet.mtime() # Machine time as int. Can be overridden for test.
t -= t % secs_per_day # Previous Midnight
return round(t / secs_per_day) # Days since datum
def quad(ym, yz, yp):
# See Astronomy on the PC P48-49, plus contribution from Marcus Mendenhall
# finds the parabola throuh the three points (-1,ym), (0,yz), (1, yp)
# and returns the values of x where the parabola crosses zero
# (roots of the quadratic)
# and the number of roots (0, 1 or 2) within the interval [-1, 1]
nz = 0
a = 0.5 * (ym + yp) - yz
b = 0.5 * (yp - ym)
c = yz
xe = -b / (2 * a)
ye = (a * xe + b) * xe + c
dis = b * b - 4.0 * a * c # discriminant of y=a*x^2 +bx +c
if dis > 0: # parabola has roots
if b < 0:
z2 = (-b + sqrt(dis)) / (2 * a) # z2 is larger root in magnitude
else:
z2 = (-b - sqrt(dis)) / (2 * a)
z1 = (c / a) / z2 # z1 is always closer to zero
if fabs(z1) <= 1.0:
nz += 1
if fabs(z2) <= 1.0:
nz += 1
if z1 < -1.0:
z1 = z2
return nz, z1, z2, ye
return 0, 0, 0, 0 # No roots
# **** GET MODIFIED JULIAN DATE FOR DAY RELATIVE TO TODAY ****
# Returns modified julian day number defined as mjd = jd - 2400000.5
# Deals only in integer MJD's: the JD of just after midnight will always end in 0.5
# hence the MJD of an integer day number will always be an integer
# Re platform comparisons get_mjd returns the same value regardless of
# the platform's epoch: integer days since 00:00 UTC on 17 November 1858.
def get_mjd(ndays: int = 0) -> int:
secs_per_day = 86400 # 24 * 3600
days_from_epoch = now_days() + ndays # Days since platform epoch
mjepoch = 40587 # Modified Julian date of C epoch (1 Jan 70)
if time.gmtime(0)[0] == 2000:
mjepoch += 10957
return mjepoch + days_from_epoch # Convert days from 1 Jan 70 to MJD
def frac(x):
return x % 1
# Convert rise or set time to int. These can be None (no event).
def to_int(x):
return None if x is None else round(x)
def minisun(t):
# Output sin(dec), cos(dec), ra
# returns the ra and dec of the Sun
# in decimal hours, degs referred to the equinox of date and using
# obliquity of the ecliptic at J2000.0 (small error for +- 100 yrs)
# takes t centuries since J2000.0. Claimed good to 1 arcmin
coseps = 0.9174805004
sineps = 0.397780757938
m = 2 * pi * frac(0.993133 + 99.997361 * t)
dl = 6893.0 * sin(m) + 72.0 * sin(2 * m)
l = 2 * pi * frac(0.7859453 + m / (2 * pi) + (6191.2 * t + dl) / 1296000)
sl = sin(l)
x = cos(l)
y = coseps * sl
z = sineps * sl
# rho = sqrt(1 - z * z)
# dec = (360.0 / 2 * pi) * atan(z / rho)
# ra = ((48.0 / (2 * pi)) * atan(y / (x + rho))) % 24
return x, y, z
def minimoon(t):
# takes t and returns the geocentric ra and dec
# claimed good to 5' (angle) in ra and 1' in dec
# tallies with another approximate method and with ICE for a couple of dates
arc = 206264.8062
coseps = 0.9174805004
sineps = 0.397780757938
l0 = frac(0.606433 + 1336.855225 * t) # mean longitude of moon
l = 2 * pi * frac(0.374897 + 1325.552410 * t) # mean anomaly of Moon
ls = 2 * pi * frac(0.993133 + 99.997361 * t) # mean anomaly of Sun
d = 2 * pi * frac(0.827361 + 1236.853086 * t) # difference in longitude of moon and sun
f = 2 * pi * frac(0.259086 + 1342.227825 * t) # mean argument of latitude
# corrections to mean longitude in arcsec
dl = 22640 * sin(l)
dl += -4586 * sin(l - 2 * d)
dl += +2370 * sin(2 * d)
dl += +769 * sin(2 * l)
dl += -668 * sin(ls)
dl += -412 * sin(2 * f)
dl += -212 * sin(2 * l - 2 * d)
dl += -206 * sin(l + ls - 2 * d)
dl += +192 * sin(l + 2 * d)
dl += -165 * sin(ls - 2 * d)
dl += -125 * sin(d)
dl += -110 * sin(l + ls)
dl += +148 * sin(l - ls)
dl += -55 * sin(2 * f - 2 * d)
# simplified form of the latitude terms
s = f + (dl + 412 * sin(2 * f) + 541 * sin(ls)) / arc
h = f - 2 * d
n = -526 * sin(h)
n += +44 * sin(l + h)
n += -31 * sin(-l + h)
n += -23 * sin(ls + h)
n += +11 * sin(-ls + h)
n += -25 * sin(-2 * l + f)
n += +21 * sin(-l + f)
# ecliptic long and lat of Moon in rads
l_moon = 2 * pi * frac(l0 + dl / 1296000)
b_moon = (18520.0 * sin(s) + n) / arc
# equatorial coord conversion - note fixed obliquity
cb = cos(b_moon)
x = cb * cos(l_moon)
v = cb * sin(l_moon)
w = sin(b_moon)
y = coseps * v - sineps * w
z = sineps * v + coseps * w
# rho = sqrt(1.0 - z * z)
# dec = (360.0 / 2 * pi) * atan(z / rho)
# ra = ((48.0 / (2 * pi)) * atan(y / (x + rho))) % 24
return x, y, z
class RiSet:
verbose = True
# Riset.mtime() returns machine time as an int. The class variable tim is for
# test purposes only and allows the hardware clock to be overridden
tim = None
@classmethod
def mtime(cls):
return round(time.time()) if cls.tim is None else cls.tim
@classmethod
def set_time(cls, t): # Given time from Unix epoch set time
if time.gmtime(0)[0] == 2000: # Machine epoch
t -= 10957 * 86400
cls.tim = t
def __init__(self, lat=LAT, long=LONG, lto=0, tl=None, dst=lambda x: x): # Local defaults
self.sglat = sin(radians(lat))
self.cglat = cos(radians(lat))
self.long = long
self.check_lto(lto) # -15 < lto < 15
self.lto = round(lto * 3600) # Localtime offset in secs
self.tlight = sin(radians(tl)) if tl is not None else tl
self.dst = dst
self.mjd = None # Current integer MJD
# Times in integer secs from midnight on current day (in machine time adjusted for DST)
# [sunrise, sunset, moonrise, moonset, cvend, cvstart]
self._times = [None] * 6
self.set_day() # Initialise to today's date
if RiSet.verbose:
t = time.localtime()
print(f"Machine time: {t[2]:02}/{t[1]:02}/{t[0]:4} {t[3]:02}:{t[4]:02}:{t[5]:02}")
RiSet.verbose = False
# ***** API start *****
# Examine Julian dates either side of current one to cope with localtime.
# 707μs on RP2040 at standard clock and with local time == UTC
def set_day(self, day: int = 0):
mjd = get_mjd(day)
if self.mjd is None or self.mjd != mjd:
spd = 86400 # Secs per day
# ._t0 is time of midnight (local time) in secs since MicroPython epoch
# time.time() assumes MicroPython clock is set to geographic local time
self._t0 = ((self.mtime() + day * spd) // spd) * spd
self.update(mjd) # Recalculate rise and set times
return self # Allow r.set_day().sunrise()
# variants: 0 secs since 00:00:00 localtime. 1 secs since MicroPython epoch
# (relies on system being set to localtime). 2 human-readable text.
def sunrise(self, variant: int = 0):
return self._format(self._times[0], variant)
def sunset(self, variant: int = 0):
return self._format(self._times[1], variant)
def moonrise(self, variant: int = 0):
return self._format(self._times[2], variant)
def moonset(self, variant: int = 0):
return self._format(self._times[3], variant)
def tstart(self, variant: int = 0):
return self._format(self._times[4], variant)
def tend(self, variant: int = 0):
return self._format(self._times[5], variant)
def set_lto(self, t): # Update the offset from UTC
self.check_lto(t) # No need to recalc beause date is unchanged
self.lto = round(t * 3600) # Localtime offset in secs
def has_risen(self, sun: bool):
return self.has_x(True, sun)
def has_set(self, sun: bool):
return self.has_x(False, sun)
# Return current state of sun or moon. The moon has a special case where it
# rises and sets in a 24 hour period. If its state is queried after both these
# events or before either has occurred, the current state depends on the order
# in which they occurred (the sun always sets afer it rises).
# The case is (.has_risen(False) and .has_set(False)) and if it occurs then
# .moonrise() and .moonset() must return valid times (not None).
def is_up(self, sun: bool):
hr = self.has_risen(sun)
hs = self.has_set(sun)
rt = self.sunrise() if sun else self.moonrise()
st = self.sunset() if sun else self.moonset()
if rt is None and st is None: # No event in 24hr period.
return self.above_horizon(sun)
# Handle special case: moon has already risen and set or moon has neither
# risen nor set, yet there is a rise and set event in the day
if not (hr ^ hs):
if not ((rt is None) or (st is None)):
return rt > st
if not (hr or hs): # No event has yet occurred
return rt is None
return hr and not hs # Default case: up if it's risen but not set
# ***** API end *****
# Generic has_risen/has_set function
def has_x(self, risen: bool, sun: bool):
if risen:
st = self.sunrise(1) if sun else self.moonrise(1) # DST- adjusted machine time
else:
st = self.sunset(1) if sun else self.moonset(1)
if st is not None:
return st < self.dst(self.mtime()) # Machine time
return False
def above_horizon(self, sun: bool):
now = self.mtime() + self.lto # UTC
tutc = (now % 86400) / 3600 # Time as UTC hour of day (float)
return self.sin_alt(tutc, sun) > 0 # Object is above horizon
# Re-calculate rise and set times
def update(self, mjd):
for x in range(len(self._times)):
self._times[x] = None # Assume failure
days = (1, 2) if self.lto < 0 else (1,) if self.lto == 0 else (0, 1)
tr = None # Assume no twilight calculations
ts = None
for day in days:
self.mjd = mjd + day - 1
sr, ss = self.rise_set(True, False) # Sun
# Twilight: only calculate if required
if self.tlight is not None:
tr, ts = self.rise_set(True, True)
mr, ms = self.rise_set(False, False) # Moon
# Adjust for local time and DST. Store in ._times if value is in
# 24-hour local time window
self.adjust((sr, ss, mr, ms, tr, ts), day)
self.mjd = mjd
def adjust(self, times, day):
for idx, n in enumerate(times):
if n is not None:
n += self.lto + (day - 1) * 86400
n = self.dst(n) # Adjust for DST on day of n
h = n // 3600
if 0 <= h < 24:
self._times[idx] = n
def _format(self, n, variant):
if (n is not None) and (variant & 4): # Machine clock set to UTC
variant &= 0x03
n = self.dst(n + self._t0) - self._t0
if variant == 0: # Default: secs since Midnight (local time)
return n
elif variant == 1: # Secs since epoch of MicroPython platform
return None if n is None else n + self._t0
# variant == 2
if n is None:
return "--:--:--"
else:
hr, tmp = divmod(n, 3600)
mi, sec = divmod(tmp, 60)
return f"{hr:02d}:{mi:02d}:{sec:02d}"
def check_lto(self, t):
if not -15 < t < 15:
raise ValueError("Invalid local time offset.")
# See https://github.com/orgs/micropython/discussions/13075
def lstt(self, t, h):
# Takes the mjd and the longitude (west negative) and then returns
# the local sidereal time in degrees. Im using Meeus formula 11.4
# instead of messing about with UTo and so on
# modified to use the pre-computed 't' value from sin_alt
d = t * 36525
df = frac(0.5 + h / 24)
c1 = 360
c2 = 0.98564736629
dsum = c1 * df + c2 * d # dsum is still ~ 9000 on average, losing precision
lst = 280.46061837 + dsum + t * t * (0.000387933 - t / 38710000)
return lst
def sin_alt(self, hour, sun):
# Returns the sine of the altitude of the object (moon or sun)
# at an hour relative to the current date (mjd)
func = minisun if sun else minimoon
mjd = (self.mjd - 51544.5) + hour / 24.0
# mjd = self.mjd + hour / 24.0
t = mjd / 36525.0
x, y, z = func(t)
tl = self.lstt(t, hour) + self.long # Local mean sidereal time adjusted for logitude
return self.sglat * z + self.cglat * (x * cos(radians(tl)) + y * sin(radians(tl)))
# Calculate rise and set times of sun or moon for the current MJD. Times are
# relative to that 24 hour period.
def rise_set(self, sun, tl):
t_rise = None # Rise and set times in secs from midnight
t_set = None
if tl:
sinho = -self.tlight
else:
sinho = sin(radians(-0.833)) if sun else sin(radians(8 / 60))
# moonrise taken as centre of moon at +8 arcmin
# sunset upper limb simple refraction
# The loop finds the sin(alt) for sets of three consecutive
# hours, and then tests for a single zero crossing in the interval
# or for two zero crossings in an interval for for a grazing event
yp = self.sin_alt(0, sun) - sinho
for hour in range(1, 24, 2):
ym = yp
yz = self.sin_alt(hour, sun) - sinho
yp = self.sin_alt(hour + 1, sun) - sinho
nz, z1, z2, ye = quad(ym, yz, yp) # Find horizon crossings
if nz == 1: # One crossing found
if ym < 0.0:
t_rise = 3600 * (hour + z1)
else:
t_set = 3600 * (hour + z1)
# case where two events are found in this interval
# (rare but whole reason we are not using simple iteration)
elif nz == 2:
if ye < 0.0:
t_rise = 3600 * (hour + z2)
t_set = 3600 * (hour + z1)
else:
t_rise = 3600 * (hour + z1)
t_set = 3600 * (hour + z2)
if t_rise is not None and t_set is not None:
break # All done
return to_int(t_rise), to_int(t_set) # Convert to int preserving None values
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