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Astronomical calculations in MicroPython

  1. Overview
    1.1 Applications
    1.2 Licensing and acknowledgements
    1.3 Installation
    1.4 Definitions Local and universal time.
  2. The RiSet class
    2.1 Constructor
    2.2 Methods
    2.3 Effect of local time
    2.4 Continuously running applications
  3. Utility functions
  4. Demo script
  5. Scheduling events
  6. The moonphase module
    6.1 Constructor
    6.2 Methods
    6.3 Usage examples
    6.4 DST Daylight savings time.
  7. Performance and accuracy
    7.1 RiSet class
    7.2 moonphase class

1. Overview

The sun_moon module enables sun and moon rise and set times to be determined at any geographical location. Times are in seconds from midnight and refer to any event in a 24 hour period starting at midnight. The midnight datum is defined in local time. The start is a day specified as the current day plus an offset in days. It can also compute Civil, Nautical or Astronomical twilight times.

The moonphase module enables the moon phase to be determined for any date, and the dates and times of lunar quarters to be calculated.

Caveat. I am not an astronomer. If there are errors in the fundamental algorithms I am unlikely to be able to offer an opinion, still less a fix.

Moon phase options have been removed from sun_moon because accuracy was poor.

1.1 Applications

There are two application areas. Firstly timing of events relative to sun or moon rise and set times, discussed later in this doc. Secondly constructing lunar clocks such as this one - the "lunartick": Image

1.2 Licensing and acknowledgements

sun_moon.py

Some code was ported from C/C++ as presented in "Astronomy on the Personal Computer" by Montenbruck and Pfleger, with mathematical improvements contributed by Marcus Mendenhall and Raul Kompaß. I (Peter Hinch) performed the port and enabled support for timezones. Raul Kompaß substantially improved the accuracy when run on hardware with 32-bit floating point.

The sourcecode exists in the book and also on an accompanying CD-R. The file CDR_license.txt contains a copy of the license file on the disk, which contains source, executable code, and databases. This module only references the source. I have not spotted any restrictions on use in the book. I am not a lawyer; I have no idea of the legal status of code based on sourcecode in a published work.

moonphase.py

This was derived from unrestricted public sources and is released under the MIT licence.

1.3 Installation

Installation copies files from the astronomy directory to a directory \lib\sched on the target. This directory eases optional use with the schedule module. Installation may be done with the official mpremote:

$ mpremote mip install "github:peterhinch/micropython-samples/astronomy"

On networked platforms it may alternatively be installed with mip.

>>> mip.install("github:peterhinch/micropython-samples/astronomy")

Currently these tools install to /lib on the built-in Flash memory. To install to a Pyboard's SD card rshell may be used. Clone the repo and move to micropython-samples on the PC, run rshell and issue:

> rsync astronomy /sd/sched

mip installs the following files in the sched directory.

  • sun_moon.py
  • sun_moon_test.py A test/demo script for the above.
  • moonphase.py Determine lunar quarters and phase. After installation the RiSet class may be accessed with
from sched.sun_moon import RiSet

1.4 Definitions

Time is a slippery concept when applied to global locations. This document uses the following conventions:

  • UTC The international time standard based on the Greenwich meridian.
  • LT (Local time) Time on a clock at the device's location. May include daylight saving time (DST).
  • MT (Machine time) Time defined by the platform's hardware clock.
  • LTO (Local time offset) A RiSet instance contains a user supplied LTO intended for timezone support. The class computes rise and set times in UTC, using LTO to compute results using RESULT = UTC + LTO. For output in LT there are two options: periodically adjust LTO to handle DST or (better) provide a dst function so that conversion is automatic.

2. The RiSet class

This holds the local geographic coordinates and the local time offset (LTO). An instance is initialised to the current date (defined by MT) and can provide the times of rise and set events occurring within a 24 hour window starting at 00:00:00 LT. A RiSet instance's date may be changed allowing rise and set times to be retrieved for other 24 hour windows. Continuously running applications should detect machine time (MT) date rollover and cause RiSet instances to re-calculate rise and set times for the new day. This is done by issuing .set_day().

Rise and set times may be retrieved in various formats including seconds from local midnight: this may be used to enable the timing of actions relative to a rise or set event.

2.1 Constructor

Args (float):

  • lat=LAT Latitude in degrees (-ve is South). Defaults are my location. :)
  • long=LONG Longitude in degrees (-ve is West).
  • lto=0 Local time offset in hours to UTC (-ve is West); the value is checked to ensure -15 < lto < 15. See section 2.3. The constructor sets the object's date to the system date as defined by machine time (MT).
  • tl=None If provided, set an offset in degrees for the definition of twilight (6 is Civil, 12 is Nautical, 18 is Astronomical). By default twilight times are not computed, saving some processor time. Offsets are positive numbers representing degrees below the horizon where twilight is deemed to start and end.
  • dst=lambda x: x This is an optional user defined function for Daylight Saving Time (DST). The assumption is that machine time is not changed, typically permanently in winter time. A dst function handles seasonal changes. The default assumes no DST is applicable. For how to write a DST function for a given country see section 6.4.

By default when an application instantiates RiSet for the first time the constructor prints the system date and time. This can be inhibited by setting the class variable verbose to False. The purpose is to alert the user to a common source of error where machine time is not set.

2.2 Methods

  • set_day(day: int = 0) day is an offset in days from the current system date. If the passed day differs from that stored in the instance, rise and set times are updated - otherwise return is "immediate". Returns the RiSet instance.
  • sunrise(variant: int = 0) See below for details and the variant arg.
  • sunset(variant: int = 0)
  • moonrise(variant: int = 0)
  • moonset(variant: int = 0)
  • tstart(variant: int = 0) Twilight start, Sun about to rise.
  • tend(variant: int = 0) Twilight end, (Sun has set).
  • is_up(sun: bool)-> bool Returns True if the selected object is above the horizon.
  • has_risen(sun: bool)->bool Returns True if the selected object has risen.
  • has_set(sun: bool)->bool Returns True if the selected object has set.
  • set_lto(t) Set local time offset LTO in hours relative to UTC. Primarily intended for timezone support, but this function can be used to support DST. The value is checked to ensure -15.0 < lto < 15.0. See section 2.3.

The return value of the rise and set method is determined by the variant arg. In all cases rise and set events are identified which occur in the current 24 hour period. Note that a given event may be absent in the period: this can occur with the moon at most locations, and with the sun in polar regions.

Variants:

  • 0 Return integer seconds since midnight LT (or None if no event).
  • 1 Return integer seconds since since epoch of the MicroPython platform (or None). This allows comparisons with machine time (MT) as per time.time().
  • 2 Return text of form hh:mm:ss (or --:--:--) being local time (LT).

If bit 2 of variant is set and a dst constructor arg has been passed, the dst function will be applied to the result. This caters for the case where the machine clock runs winter time and a dst-adjusted result is required. It should be noted that applying dst adjustment to a time close to midnight can result in rollover, i.e. a time > 24:00. Handling this case is the responsibility of the application.

Example constructor invocations:

r = RiSet()  # UK near Manchester
r = RiSet(lat=47.609722, long=-122.3306, lto=-8)  # Seattle 47°36′35″N 122°19′59″W
r = RiSet(lat=-33.87667, long=151.21, lto=11)  # Sydney 33°52′04″S 151°12′36″E

2.3 Effect of local time

MicroPython has no concept of timezones. The hardware platform has a clock which reports machine time (MT): this might be set to local winter time or summer time. The RiSet instances' LTO should be set to represent the difference between MT and UTC. In continuously running applications it is best to avoid changing the hardware clock (MT) for reasons discussed below. Daylight savings time may be implemented in one of two ways:

  • By changing the RiSet instances' LTO accordingly.
  • Or by providing a dst function as discussed in section 6.4. This is the preferred solution as DST is then handled automatically.

Rise and set times are computed relative to UTC and then adjusted using the RiSet instance's LTO before being returned (see .adjust()). This means that the accuracy of the hardware clock is not critical: only the date portion is used in determining rise and set times.

The .has_risen(), .has_set() and .is_up() methods do use machine time (MT) and rely on MT == UTC + LTO: if MT has drifted, precision will be lost at times close to rise and set events.

The constructor and the set_day() method set the instance's date relative to MT. They use only the date component of MT, hence they may be run at any time of day and are not reliant on MT accuracy.

2.4 Continuously running applications

Where an application runs continuously there is usually a need for RiSet instances to track the current date. One approach is this:

async def tomorrow(offs):
    now = round(time.time())
    tw = 86400 + 60 - (now % 86400)  # Time from now to one minute past next midnight
    await asyncio.sleep(tw)

rs = RiSet()  # May need args

async def keep_updated(rs):  # Keep a RiSet instance updated
    while True:
        await tomorrow()  # Wait until 1 minute past midnight
        rs.set_day()  # Update to new day

It is important that, at the time when .set_day() is called, the system time has a date which is correct. Most hardware uses crystal controlled clocks so drift is minimal. However with long run times it will accumulate. Care must be taken if periodically synchronising system time to a time source: the resultant sudden jumps in system time can cause havoc with uasyncio timing. If synchronisation is required it is best done frequently to minimise the size of jumps.

For this reason changing system time to accommodate daylight saving time is a bad idea. It is usually best to run winter time all year round and to use the dst constructor arg to handle time changes.

3. Utility functions

now_days() -> int Returns the current time as days since the platform epoch.

4. Demo script

This produces output for the fixed date 4th Dec 2023 at three geographical locations. It can therefore be run on platforms where the system time is wrong. To run issue:

import sched.sun_moon_test

Expected output:

>>> import sched.sun_moon_test
4th Dec 2023: Seattle UTC-8
Sun rise 07:40:09 set 16:18:15
Moon rise 23:38:11 set 12:53:40

4th Dec 2023: Sydney UTC+11
Sun rise 05:36:24 set 19:53:21
Moon rise 00:45:55 set 11:27:14

From 4th Dec 2023: UK, UTC
Day: 0
Sun rise 08:04:34 set 15:52:13
Moon rise 23:03:15 set 13:01:04
Day: 1
Sun rise 08:05:54 set 15:51:42
Moon rise --:--:-- set 13:10:35
Day: 2
Sun rise 08:07:13 set 15:51:13
Moon rise 00:14:40 set 13:18:59
Day: 3
Sun rise 08:08:28 set 15:50:49
Moon rise 01:27:12 set 13:27:08
Day: 4
Sun rise 08:09:42 set 15:50:28
Moon rise 02:40:34 set 13:35:56
Day: 5
Sun rise 08:10:53 set 15:50:10
Moon rise 03:56:44 set 13:46:27
Day: 6
Sun rise 08:12:01 set 15:49:56
Moon rise 05:18:32 set 14:00:11
Maximum error 0. Expect 0 on 64-bit platform, 30s on 32-bit
>>>

Code comments show times retrieved from timeanddate.com.

The script includes some commented out code at the end. This tests is_up, has_risen and has_set over 365 days. It is commented out to reduce printed output.

5. Scheduling events

A likely use case is to enable events to be timed relative to sunrise and set. In simple cases this can be done with asyncio. This will execute a payload at sunrise, and another at sunset, every day.

import uasyncio as asyncio
import time
from sched.sun_moon import RiSet

async def tomorrow(offs):  # Offset compensates for possible clock drift
    now = round(time.time())
    tw = 86400 + 60 * offs - (now % 86400)  # Time from now to one minute past next midnight
    await asyncio.sleep(tw)

async def do_sunrise():
    rs = RiSet()  # May need args
    while True:
        if (delay := rs.sunrise(1) - round(time.time())) > 0:  # Sun has not yet risen
            await asyncio.sleep(delay)  # Wait for it to rise
            # Sun has risen, execute payload e.g. turn off light
        await tomorrow(1)  # Wait until 1 minute past midnight
        rs.set_day()  # Update to new day

async def do_sunset():
    rs = RiSet()  # May need args
    while True:
        if (delay := rs.sunset(1) - round(time.time())) > 0:  # Sun has not yet set
            await asyncio.sleep(delay)  # Wait for it to set
            # Sun has risen, execute payload e.g. turn on light
        await tomorrow(1)  # Wait until 1 minute past midnight
        rs.set_day()  # Update to new day

async def main():
    sr = asyncio.create_task(do_sunrise())
    ss = asyncio.create_task(do_sunset())
    ayncio.gather(sr, ss)
try:
    asyncio.run(main())
finally:
    _ = asyncio.new_event_loop()

This code assumes that .sunrise() will never return None. At polar latitudes waiting for sunrise in winter would require changes - and patience.

Code may be simplified by using the schedule module. This may be installed with

$ mpremote mip install "github:peterhinch/micropython-async/v3/as_drivers/sched"

The following is a minimal example:

import uasyncio as asyncio
from sched.sched import schedule
from sched.sun_moon import RiSet

async def turn_off_lights(rs):  # Runs every day at 00:01:00
    rs.set_day()  # Re-calculate for new daylight
    await asyncio.sleep(rs.sunrise() - 60)
    # Actually turn them off

async def main():
    rs = RiSet()  # May need args for your location
    await schedule(turn_off_lights, rs, hrs=0, mins=1)  # Never terminates

try:
    asyncio.run(main())
finally:
    _ = asyncio.new_event_loop()

This approach lends itself to additional triggers and events:

import uasyncio as asyncio
from sched.sched import schedule, Sequence
from sched.sun_moon import RiSet

async def turn_off_lights(t):
    await asyncio.sleep(t)
    # Actually turn them off

async def main():
    rs = RiSet()  # May need args for your location
    seq = Sequence()  # A Sequence comprises one or more schedule instances
    asyncio.create_task(schedule(seq, "off", hrs=0, mins=1))
    # Can schedule other events here
    async for args in seq:
        if args[0] == "off":  # Triggered at 00:01 hrs (there might be other triggers)
            rs.set_day()  # Re-calculate for new day
            asyncio.create_task(turn_off_lights(rs.sunrise() - 60))

try:
    asyncio.run(main())
finally:
    _ = asyncio.new_event_loop()

6. The moonphase module

This contains a single class MoonPhase. The term "machine time" below refers to the time reported by the MicroPython time module. The "local time offset" (LTO) passed to the constructor specifies the difference between machine time and UTC based on system longitude. "Daylight saving time" (DST) allows reported times to be offset to compensate for DST. Internally phases are calculated in UTC, but where times are output they are adjusted for LTO and DST.

It is recommended that the machine clock is not adjusted for DST because large changes can play havoc with program timing as described above. To accommodate DST, a dst function can be provided to the constructor. The module uses this to adjust reported times.

A MoonPhase instance has a time datum, which defaults to the instantiation time. Phases are calculated with respect to this datum. It may be changed using .set_day to enable future and past phases to be determined or to enable long running applications to track time.

The module is imported as follows:

from sched.moonphase import MoonPhase

6.1 Constructor

  • lto:float=0, dst = lambda x: x Local time offset in hours to UTC (-ve is West); the value is checked to ensure -15 < lto < 15. dst is an optional user defined function for Daylight Saving Time (DST). See section 6.4

6.2 Methods

  • quarter(q: int, text: bool = True) Return the time of a given quarter. Five quarters are calculated around the instance datum. By default the time is last midnight machine time with an optional offset in days doff added. The quarter arg specifies the quarter with 0 and 4 being new moons and quarter 2 being full. The text arg determines how the value is returned: as text or as int is secs from the machine epoch. Results are adjusted for DST if a dst function is provided to the constructor.
  • phase() -> float) Returns moon phase where 0.0 <= phase < 1.0 with 0.5 being full moon. The phase is that pertaining to the datum.
  • nextphase(text: bool = True) This is a generator function. Each iteration of the generator returns three values: the phase number, the lunation number and the datetime of the phase. The text arg is as per .quarter(), defining the format of the datetime.
  • set_day(doff: float = 0) Set the MoonPhase datum time to machine time plus an offset in days: this may include a fractional part if .phase() is required to produce a time-precise value. The five quarters are calculated for the lunation including the midnight at the start of the specified day.
  • set_lto(t:float) Redefine the local time offset, t being in hours as per the constructor arg.
  • datum(text: bool = True) Returns the current datum in secs since local epoch or in human-readable text form.

6.3 Usage examples

from sched.moonphase import MoonPhase
mp = MoonPhase()  # datum is midnight last night
print(f"Full moon, current lunation {mp.quarter(2)}")
mp.set_day(0.5)  # Adjust datum to noon today machine time
print(f"Phase at Noon {mp.phase()}")
mp.set_day(182)  # Set datum ahead 6 months
print(f"Lunation 1st new moon: {mp.quarter(0)}, 2nd new moon: {mp.quarter(4)}")
mp.set_day(0)  # Reset datum to today
n = mp.nextphase()  # Instantiate generator
for _ in range(8):
    print(next(n))

6.4 DST

Daylight saving time depends on country and geographic location, and there is no built-in MicroPython support. The moonphase module supports DST via an optional user supplied function. DST does not affect the calculation of quarters or phase which is based on the machine clock. If the machine clock runs at a fixed offset to UTC (which is recommended), a DST function can be used to enable reported results to reflect local time.

A DST function takes as input a datetime measured in seconds since the machine epoch (as returned by time.time()) and returns that number adjusted for local time. The following example is for UK time, which adds one hour at 2:00 on the last Sunday in March, reverting to winter time at 2:00 on the last Sunday in October.

def uk_dst(secs_epoch: int):  # Change in March (3) and Oct (10)
    t = time.gmtime(secs_epoch)
    month = t[1]
    mday = t[2]
    wday = t[6]
    winter = secs_epoch
    summer = secs_epoch + 3600  # +1hr
    if month in (1, 2, 11, 12):  # Simple cases: depend only on month
        return winter
    if not month in (3, 10):
        return summer  # +1 hr
    # We are in March or October. Find the day in month of last Sunday.
    ld = (wday + 31 - mday) % 7  # weekday of 31st.
    lsun = 31 - (1 + ld) % 7  # Monthday of last Sunday
    thresh = time.mktime((t[0], month, lsun, 2, 0, 0, 6, 0))  # 2am last Sunday in month
    return summer if ((secs_epoch >= thresh) ^ (month == 10)) else winter

7. Performance and accuracy

7.1 RiSet class

A recalculation is triggered whenever the 24 hour local time window is changed, such as calling .set_day() where the stored date changes. Normally two days of data are calculated, except where the local time is UTC where only one day is required. The time to derive one day's data on RP2040 was 707μs (no twilight calculation, standard clock).

The accuracy of rise and set times was checked against online sources for several geographic locations. The online data had 1 minute resolution and the checked values corresponded with data computed on a platform with 64 bit floating point unit. The loss of precision from using a 32 bit FPU was no more than 3s.

7.2 MoonPhase class

This uses Python's arbitrary precision integers to overcome the limitations of 32-bit floating point units. Results on 32 bit platforms match those on 64-bits to within ~1 minute. Results match those on timeanddate.com within ~3 minutes.