Computing the true position of the Sun

[1]:

# Imports

from kanon.calendars import Calendar, Date
from kanon.tables import HTable
from kanon.units import Sexagesimal
from kanon.units.precision import set_precision, TruncatureMode
import astropy.units as u

[2]:

# 3rd of July 1327

year = 1327
month = 7
day = 3

[3]:

# Day computation

# We're using the Julian A.D. calendar

calendar = Calendar.registry["Julian A.D."]
date = Date(calendar, (year, month, day))

# We need to express the numbers of days from the start of the calendar
# in Sexagesimal representation.

days = Sexagesimal.from_int(int(date.days_from_epoch()))

days

[3]:

02,14,35,04 ;

[4]:

# Defining a function resolving a position from a mean motion table

def position_from_table(tab, radix, zodiac_offset=4):
    # Starting with the radix

    result = radix * u.degree

    # Adding days
    for i, v in enumerate(days[:]):
        result += tab.get(v) >> i + zodiac_offset

    # Conversion in degrees modulo 6 zodiacal signs

    result %= Sexagesimal(6, 0) * u.degree
    return result

[5]:

# Sun mean position

# Reading the table from DISHAS
tab_mean_motion = HTable.read(193)
tab_mean_motion

[5]:
HTable length=60
DaysEntries
ddeg
IntegerAndSexagesimalSexagesimal
1 ;59,08,19,37,19,13,56 ;
2 ;01,58,16,39,14,38,27,52 ;
3 ;02,57,24,58,51,57,41,48 ;
4 ;03,56,33,18,29,16,55,44 ;
5 ;04,55,41,38,06,36,09,40 ;
6 ;05,54,49,57,43,55,23,36 ;
7 ;06,53,58,17,21,14,37,32 ;
8 ;07,53,06,36,58,33,51,28 ;
9 ;08,52,14,56,35,53,05,24 ;
......
51 ;50,16,04,40,43,20,50,36 ;
52 ;51,15,13,00,20,40,04,32 ;
53 ;52,14,21,19,57,59,18,28 ;
54 ;53,13,29,39,35,18,32,24 ;
55 ;54,12,37,59,12,37,46,20 ;
56 ;55,11,46,18,49,57,00,16 ;
57 ;56,10,54,38,27,16,14,12 ;
58 ;57,10,02,58,04,35,28,08 ;
59 ;58,09,11,17,41,54,42,04 ;
60 ;59,08,19,37,19,13,56,00 ;
[6]:

# Mean position from days, table, and radix

mean_sun_pos = position_from_table(tab_mean_motion, Sexagesimal("4,38;21,0,30,28"))
mean_sun_pos

[6]:
$01,47 ; 58,21,32,17,28,35,44 \; \mathrm{{}^{\circ}}$
[7]:

# Fixed stars

tab_fixed_stars = HTable.read(236)

mean_fixed_star_pos = position_from_table(tab_fixed_stars, Sexagesimal(0))
mean_fixed_star_pos

[7]:
$09 ; 44,44,33,52,35,08,48 \; \mathrm{{}^{\circ}}$
[8]:

# Access and recess position

tab_access_recess = HTable.read(237)

access_recess_pos = position_from_table(
    tab_access_recess, Sexagesimal("5,59;12,34"), zodiac_offset=2
)
access_recess_pos

[8]:
$01,07 ; 25,45,56,14,16 \; \mathrm{{}^{\circ}}$
[9]:

# Access and recess equation

tab_eq_access_recess = HTable.read(238)

with set_precision(tmode=TruncatureMode.ROUND):
    eq_access_recess = tab_eq_access_recess.get(access_recess_pos)
eq_access_recess

[9]:
$8 ; 18,19 \; \mathrm{{}^{\circ}}$
[10]:

# Sun apogee

with set_precision(tmode=TruncatureMode.ROUND):
    solar_apogee_pos = (
        mean_fixed_star_pos + eq_access_recess + Sexagesimal("1,11;25,23") * u.degree
    )
solar_apogee_pos

[10]:
$01,29 ; 28,26,33,52,35,08,48 \; \mathrm{{}^{\circ}}$
[11]:

# Sun mean argument

with set_precision(tmode=TruncatureMode.ROUND):
    mean_arg_sun = mean_sun_pos - solar_apogee_pos
    if mean_arg_sun < 0:
        mean_arg_sun += 360
mean_arg_sun

[11]:
$18 ; 29,54,58,24,53,26,56 \; \mathrm{{}^{\circ}}$
[12]:

# Sun equation

tab_eq_sun = HTable.read(180)
with set_precision(tmode=TruncatureMode.ROUND):
    eq_sun = tab_eq_sun.get(mean_arg_sun)
eq_sun

[12]:
$-00 ; 39,33,19,21,38,41,08 \; \mathrm{{}^{\circ}}$
[13]:

# Sun true position

with set_precision(pmode=2, tmode=TruncatureMode.ROUND):
    true_pos_sun = mean_sun_pos + eq_sun
    if true_pos_sun < 0:
        true_pos_sun += 360
true_pos_sun

[13]:
$01,47 ; 18,48 \; \mathrm{{}^{\circ}}$