Author: Behrouz Safari

Equation of time

Calculation and application of the equation of time

Quick start

Download this CSV file which is the table of equation of time for all days at 12:00:00 from 2020 to 2050. You can use it as you want, fit curve, interpolation, etc. You can also use the functions I have provided. All of these funtions have been embedded in the module time of hypatie python package.

Package hypatie.time

The package hypatie.time (here under the name eot.py) contains several functions that you can use easily to calculate equation of time with very high precision. Let's find mean solar time and true solar time for the city of Tehran with longitude of 51.3347.

from datetime import datetime, timedelta
from hypatie.time import get_eot

t = datetime.utcnow()
lon = 51.3347

print('UTC time now    :', t)
print('-'*44)
print('Tehran:')
print('-------')

mean_solar_time = t + timedelta(hours=(lon/15))
print('Mean solar time :', mean_solar_time)
    
equ_of_time = get_eot(t)
print('Equation of time (min) :', equ_of_time)

equ_of_time = timedelta(minutes=equ_of_time)
true_solar_time = mean_solar_time - equ_of_time
print('True solar time :', true_solar_time)

Here's the results:

UTC time now    : 2022-12-27 04:18:30.351416
--------------------------------------------
Tehran:
-------
Mean solar time : 2022-12-27 07:43:50.679416
Equation of time (min) : -0.8560962378834734
True solar time : 2022-12-27 07:44:42.045190

The most straight forward way of getting solar times is using the function solar_time:

from hypatie.time import solar_time
from datetime import datetime

t = datetime.utcnow()
lon = 51.3347

ture_st, mean_st = solar_time(t, lon)

Time of the noon

You can use the equation ot time to calculate the noon for a given longtitude. But for ease of use, I have created the function get_noon which gives the noon for a given longtitude in UTC.

from datetime import datetime
from hypatie.time import get_noon

t = datetime.utcnow()
lon = 51.3347

noon = get_noon(t, lon)
print(noon)

And the result is:

2022-12-27 08:35:36.301976

Equation of time for a time window

If you want to calculate the equation of time for a time interval, the fast way to do is using eot_time_window.

from datetime import datetime, timedelta
from hypatie.time import eot_time_window

t0 = datetime(2023, 12, 15)
time_window = [t0 + timedelta(days=i) for i in range(50)]
eot_arr = eot_time_window(time_window)
print(eot_arr)

The output is:

[  5.25224961   4.76996051   4.28386278   3.79457555   3.30270395
   2.808835     2.31353591   1.81735451   1.32082148   0.82445362
   0.32875763  -0.16576608  -0.65862038  -1.14930923  -1.63733655
  -2.12220615  -2.60342224  -3.08049063  -3.55291896  -4.02021874
  -4.48190398  -4.93749137  -5.38649874  -5.8284435   -6.26284094
  -6.68920347  -7.10704078  -7.51586183  -7.9151797   -8.30451867
  -8.68342306  -9.05146586  -9.4082556   -9.75344065 -10.08671092
 -10.40779741 -10.71647012 -11.01253466 -11.295828   -11.56621407
 -11.82357945 -12.06782971 -12.29888703 -12.51668874 -12.72118689
 -12.91234821 -13.09015412 -13.25460055 -13.40569681 -13.5434638 ]

See more examples at astrodatascience.net