Montunctions
In this notebook we calculate the conjunction between Mars and Aldebaran during the so-called stationary phases of the planet. This notebook and the derived plots were used in the context of the work “ESTUDIO DE LAS ORIENTACIONES ASTRONÓMICAS Y PAISAJÍSTICAS DE LOS MONUMENTOS DE SENENMUT EN LA NECRÓPOLIS TEBANA” presented as Ph. D. Thesis by Francisco Vivas Fernández (2023).
If you are running this script in Google Colab you need first to install the package and create a directory for saving plots:
[1]:
try:
from google.colab import drive
%pip install -Uq montu
except ImportError:
print("Not running in Colab, skipping installation")
import plotly.io as pio
pio.renderers.default = "notebook_connected"
%load_ext autoreload
%autoreload 2
# Create folders for figures and temporal files
!mkdir -p ./gallery/ ./montu_dem/
Not running in Colab, skipping installation
Goals of this notebook
The goal of this notebook is to determine the stable positions of mars across ancient Egypt history and check when this marsticies happened close to the winter solstice and in the Taurus constellation.
Loading tools
We need to load the packages and the required data for it (star database, planet position database, etc.):
[2]:
# Montu packages and data
%matplotlib inline
import montu
from montu import D2S, PRINTDF, TABLEDF, DEG, RAD
# Other libraries required
import pandas as pd
import copy
import matplotlib.pyplot as plt
import numpy as np
# Load allstars
allstars = montu.Stars()
MontuPython version 0.50.0. 𓇍𓇋𓇋𓏏𓅓𓊵 𓎛𓎡𓄿𓀭𓎛𓈖𓂝𓎡 (ii-ti m Htp, HkAx Hn'-k)
Loading stellar catalogue montu_stellar_catalogue_v38.csv
Marstices
Lets set observing conditions and initial time of exploration:
[3]:
Tebas = montu.Observer(lon=33,lat=24,height=0)
Our target body:
[4]:
mars = montu.Planet('Mars')
Now let’s predict all the Marstices:
[5]:
marstices = pd.DataFrame()
i = 0
# Range of years
# initial_year = -2500
initial_year = -2000
final_year = -500
mars.reset_store()
mtime = montu.Time(f'{initial_year}-01-01 00:00:00.00',scale='utc',calendar='proleptic')
marstices = []
for _ in montu.WHILE_TRUE():
jed1,jed2 = mars.next_planesticies(mtime)
mtime1 = montu.Time(jed1,format='jd',full=True)
mtime2 = montu.Time(jed2,format='jd',full=True)
# Stopping condition
if mtime2.readable.year > final_year:
break
marstices += [pd.DataFrame(dict(
datepro = [mtime1.readable.datepro,mtime2.readable.datepro],
datemix = [mtime1.readable.datemix,mtime2.readable.datemix],
type = ['first','second'],
jed = [mtime1.jed,mtime2.jed],
))]
mtime = mtime + 2*montu.YEAR
i += 1
marstices = pd.concat(marstices)
marstices.drop_duplicates(inplace=True)
marstices.reset_index(drop=True,inplace=True)
750it [00:00, 3932.12it/s]
[6]:
marstices
[6]:
| datepro | datemix | type | jed | |
|---|---|---|---|---|
| 0 | -2001-09-21 12:52:37.202864 | -2001-10-08 12:52:52 | first | 9.904730e+05 |
| 1 | -2001-12-09 02:02:01.397744 | -2001-12-26 02:02:02 | second | 9.905516e+05 |
| 2 | -1999-10-25 10:48:04.207680 | -1999-11-11 10:48:48 | first | 9.912380e+05 |
| 3 | -1998-01-14 00:58:12.599040 | -1998-01-31 00:58:58 | second | 9.913185e+05 |
| 4 | -1997-11-30 04:28:27.698864 | -1997-12-17 04:28:28 | first | 9.920037e+05 |
| ... | ... | ... | ... | ... |
| 1401 | -506-09-04 21:49:24.496304 | -506-09-10 21:49:49 | second | 1.536494e+06 |
| 1402 | -504-08-30 13:09:38.597744 | -504-09-05 13:09:09 | first | 1.537220e+06 |
| 1403 | -504-11-10 12:33:59.497920 | -504-11-16 12:33:33 | second | 1.537292e+06 |
| 1404 | -502-10-10 16:51:06.001920 | -502-10-16 16:51:51 | first | 1.537991e+06 |
| 1405 | -502-12-27 13:11:26.399040 | -501-01-02 13:11:11 | second | 1.538069e+06 |
1406 rows × 4 columns
Now we want to add to this information other relevant astronomical information:
Position of mars in the sky
Date of occurrence of winter solstices
Angular distance of Mars to Aldebaran
Position of Mars in the sky:
[7]:
mars.reset_store()
for index in montu.PROGRESS(marstices.index):
marstice = marstices.loc[index]
# Get MonTime object
mtime = montu.Time(marstice.jed,format='jd')
# Calculate Mars position and store it
mars.conditions_in_sky(mtime,Tebas,store=1)
mars.tabulate_store()
100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 1406/1406 [00:00<00:00, 5083.95it/s]
Positions are stored in a separate dataframe:
[8]:
mars_marstices = copy.deepcopy(mars.position)
mars_marstices['Vmag'] = mars.condition.Vmag
mars_marstices
[8]:
| tt | jed | Name | RAJ2000 | DecJ2000 | RAEpoch | DecEpoch | RAGeo | DecGeo | el | az | Vmag | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | -126236570942 | 9.904730e+05 | Mars | 7.026757 | 23.322960 | 3.073795 | 17.836212 | 3.073797 | 17.838371 | -48.159613 | 359.135417 | -0.67 |
| 1 | -126229784378 | 9.905516e+05 | Mars | 5.632474 | 26.221096 | 1.774031 | 13.756077 | 1.774203 | 13.757510 | -15.035019 | 292.899084 | -0.43 |
| 2 | -126170482464 | 9.912380e+05 | Mars | 9.479705 | 17.711436 | 5.517021 | 26.057501 | 5.517134 | 26.059545 | -29.869770 | 324.116464 | -0.39 |
| 3 | -126163519480 | 9.913185e+05 | Mars | 8.165966 | 24.253872 | 4.077912 | 24.892369 | 4.078105 | 24.893611 | 2.560390 | 296.310081 | -0.35 |
| 4 | -126104322889 | 9.920037e+05 | Mars | 11.642726 | 6.391030 | 8.006254 | 24.704358 | 8.006401 | 24.704688 | 46.465886 | 281.282326 | -0.40 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 1401 | -79060353742 | 1.536494e+06 | Mars | 23.006199 | -11.674151 | 20.715271 | -23.418157 | 20.715457 | -23.414697 | 32.736253 | 216.581241 | -1.98 |
| 1402 | -78997658558 | 1.537220e+06 | Mars | 3.772105 | 17.271194 | 1.514450 | 6.586747 | 1.514421 | 6.588904 | -58.778088 | 12.376669 | -1.44 |
| 1403 | -78991439897 | 1.537292e+06 | Mars | 2.614838 | 15.741818 | 0.423314 | 2.972830 | 0.423091 | 2.974326 | -2.157872 | 85.168320 | -1.02 |
| 1404 | -78931030900 | 1.537991e+06 | Mars | 6.919953 | 23.751538 | 4.395169 | 22.487648 | 4.394980 | 22.489512 | -16.465913 | 55.376534 | -0.76 |
| 1405 | -78924304895 | 1.538069e+06 | Mars | 5.538215 | 26.342942 | 3.047465 | 20.323564 | 3.047270 | 20.324541 | 17.519819 | 75.021603 | -0.49 |
1406 rows × 12 columns
Compute the date of the previous and next winter solstice, and the days elapsed to the closest one:
[9]:
# Loop on marstices
for index in montu.PROGRESS(marstices.index):
marstice = marstices.loc[index]
# Get MonTime object
mtime = montu.Time(marstice.jed,format='jd')
# Calculate next and previous solstices
prev_seasons = montu.Sun.previous_seasons(at=mtime)
next_seasons = montu.Sun.next_seasons(at=mtime)
# Get the closest solstice
closest_solstice = min(abs(mtime.jed - prev_seasons[3]),
abs(mtime.jed - next_seasons[3]))
# Add winter solstice to DataFrame
marstices.loc[index,'closest_solstice'] = closest_solstice
marstices
100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 1406/1406 [00:00<00:00, 3048.48it/s]
[9]:
| datepro | datemix | type | jed | closest_solstice | |
|---|---|---|---|---|---|
| 0 | -2001-09-21 12:52:37.202864 | -2001-10-08 12:52:52 | first | 9.904730e+05 | 89.858280 |
| 1 | -2001-12-09 02:02:01.397744 | -2001-12-26 02:02:02 | second | 9.905516e+05 | 11.310084 |
| 2 | -1999-10-25 10:48:04.207680 | -1999-11-11 10:48:48 | first | 9.912380e+05 | 55.435827 |
| 3 | -1998-01-14 00:58:12.599040 | -1998-01-31 00:58:58 | second | 9.913185e+05 | 25.154548 |
| 4 | -1997-11-30 04:28:27.698864 | -1997-12-17 04:28:28 | first | 9.920037e+05 | 20.186209 |
| ... | ... | ... | ... | ... | ... |
| 1401 | -506-09-04 21:49:24.496304 | -506-09-10 21:49:49 | second | 1.536494e+06 | 106.888026 |
| 1402 | -504-08-30 13:09:38.597744 | -504-09-05 13:09:09 | first | 1.537220e+06 | 111.737487 |
| 1403 | -504-11-10 12:33:59.497920 | -504-11-16 12:33:33 | second | 1.537292e+06 | 39.762245 |
| 1404 | -502-10-10 16:51:06.001920 | -502-10-16 16:51:51 | first | 1.537991e+06 | 71.062716 |
| 1405 | -502-12-27 13:11:26.399040 | -501-01-02 13:11:11 | second | 1.538069e+06 | 6.784743 |
1406 rows × 5 columns
[10]:
marstices.iloc[:10]
[10]:
| datepro | datemix | type | jed | closest_solstice | |
|---|---|---|---|---|---|
| 0 | -2001-09-21 12:52:37.202864 | -2001-10-08 12:52:52 | first | 990473.036542 | 89.858280 |
| 1 | -2001-12-09 02:02:01.397744 | -2001-12-26 02:02:02 | second | 990551.584738 | 11.310084 |
| 2 | -1999-10-25 10:48:04.207680 | -1999-11-11 10:48:48 | first | 991237.950049 | 55.435827 |
| 3 | -1998-01-14 00:58:12.599040 | -1998-01-31 00:58:58 | second | 991318.540424 | 25.154548 |
| 4 | -1997-11-30 04:28:27.698864 | -1997-12-17 04:28:28 | first | 992003.686432 | 20.186209 |
| 5 | -1996-02-18 07:27:10.992944 | -1996-03-06 07:27:27 | second | 992083.810544 | 59.937904 |
| 6 | -1994-01-10 01:13:45.304320 | -1994-01-27 01:13:13 | first | 992775.551219 | 21.198671 |
| 7 | -1994-03-27 17:44:02.307824 | -1994-04-13 17:44:44 | second | 992852.238916 | 97.886368 |
| 8 | -1992-03-07 22:03:49.904640 | -1992-03-24 22:03:03 | first | 993563.419328 | 78.589665 |
| 9 | -1992-05-14 16:51:47.404800 | -1992-05-31 16:51:51 | second | 993631.202632 | 146.372970 |
Now we want to compute the angular distance to Aldebaran. For this purpose, we need to get the information about the star from the database:
[11]:
aldebaran = allstars.get_stars(ProperName='Aldebaran')
aldebaran
[11]:
1 star(s):
| | MN | HD | HR | HIP | Gl | Name | OtherDesignations | ProperName | Bayer | Flamsteed | Constellation | RAJ2000 | DecJ2000 | GalLonJ2000 | GalLatJ2000 | pmRA | pmDec | RadVel | Distance | Vmag | Vmag_min | Vmag_max | B-V | SpType | Luminosity | XJ2000 | YJ2000 | ZJ2000 | VXJ2000 | VYJ2000 | VZJ2000 | Primary | MultipleID | IsMultiple | IsVariable |
|----|------|-------|------|-------|-----------|-----------|---------------------------------------------------------------------------------------|--------------|---------|-------------|-----------------|-----------|------------|---------------|---------------|--------|---------|----------|------------|--------|------------|------------|-------|----------|--------------|----------|----------|----------|-----------|-----------|-----------|-----------|--------------|--------------|--------------|
| 14 | 15 | 29139 | 1457 | 21421 | Gl 171.1A | Aldebaran | 87 Tau/87Alp Tau/Aldebaran/Gl 171.1A/HD 29139/HIP 21421/HR 1457/HYG 21368/MN 15/α Tau | Aldebaran | α Tau | 87 Tau | Tau | 4.59868 | 16.5093 | 180.972 | -20.2483 | 62.78 | -189.36 | 54.5 | 20.4332 | 0.87 | 0.888 | 0.858 | 1.538 | K5III | 163.23 | 7.02722 | 18.2876 | 5.80666 | 1.528e-05 | 5.709e-05 | -2.14e-06 | 21368 | Gl 171.1 | 1 | 1 |
Now we will compute for each marstice, the angular distance to Aldebaran:
[12]:
# Loop on marstices
for index in montu.PROGRESS(marstices.index):
# Get marstice information and location of mars
marstice = marstices.loc[index]
mars_location = mars_marstices.loc[index]
# Propagate aldebaran to epoch
mtime = montu.Time(marstice.jed,format='jd')
aldebaran.where_in_space(at=mtime,inplace=True)
# Compute angular distance
aldebaran_angdist = montu.Util.haversine_distance(
mars_location.DecJ2000*DEG,15*mars_location.RAJ2000*DEG,
aldebaran.scalar('DecJ2000t')*DEG,15*aldebaran.scalar('RAJ2000t')*DEG
)*RAD
# uncomment to check
"""
print(marstice.jed,marstice.datemix)
print(D2S(mars_location.DecJ2000),D2S(mars_location.RAJ2000))
print(D2S(aldebaran.scalar('DecJ2000t')),D2S(aldebaran.scalar('RAJ2000t')))
print(D2S(aldebaran_angdist))
break
#"""
# Angular distance
marstices.loc[index,'aldebaran_angdist'] = aldebaran_angdist
marstices
100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 1406/1406 [00:00<00:00, 1988.75it/s]
[12]:
| datepro | datemix | type | jed | closest_solstice | aldebaran_angdist | |
|---|---|---|---|---|---|---|
| 0 | -2001-09-21 12:52:37.202864 | -2001-10-08 12:52:52 | first | 9.904730e+05 | 89.858280 | 34.820239 |
| 1 | -2001-12-09 02:02:01.397744 | -2001-12-26 02:02:02 | second | 9.905516e+05 | 11.310084 | 17.306733 |
| 2 | -1999-10-25 10:48:04.207680 | -1999-11-11 10:48:48 | first | 9.912380e+05 | 55.435827 | 69.517868 |
| 3 | -1998-01-14 00:58:12.599040 | -1998-01-31 00:58:58 | second | 9.913185e+05 | 25.154548 | 50.461178 |
| 4 | -1997-11-30 04:28:27.698864 | -1997-12-17 04:28:28 | first | 9.920037e+05 | 20.186209 | 103.062474 |
| ... | ... | ... | ... | ... | ... | ... |
| 1401 | -506-09-04 21:49:24.496304 | -506-09-10 21:49:49 | second | 1.536494e+06 | 106.888026 | 87.553815 |
| 1402 | -504-08-30 13:09:38.597744 | -504-09-05 13:09:09 | first | 1.537220e+06 | 111.737487 | 11.832605 |
| 1403 | -504-11-10 12:33:59.497920 | -504-11-16 12:33:33 | second | 1.537292e+06 | 39.762245 | 28.523663 |
| 1404 | -502-10-10 16:51:06.001920 | -502-10-16 16:51:51 | first | 1.537991e+06 | 71.062716 | 33.393108 |
| 1405 | -502-12-27 13:11:26.399040 | -501-01-02 13:11:11 | second | 1.538069e+06 | 6.784743 | 16.322561 |
1406 rows × 6 columns
[13]:
marstices.aldebaran_angdist.describe()
[13]:
count 1406.000000
mean 84.160880
std 50.362013
min 3.311582
25% 39.914786
50% 81.051776
75% 126.587916
max 176.560331
Name: aldebaran_angdist, dtype: float64
Now we will mark the marstices according to closest solstice and aldebaran angular distance:
[14]:
max_days_to_solstice = 15 # days
max_aldebaran_angdist = 15 # degrees
max_aldebaran_conjunc = 5 # degrees
marstices['close_solstice'] = False
marstices['close_aldebaran'] = False
marstices['conj_aldebaran'] = False
marstices['montunctions'] = False
cond_solstices = (marstices['closest_solstice']<=max_days_to_solstice)
marstices.loc[cond_solstices,'close_solstice'] = True
print("Number of marstices close to solstices: ",cond_solstices.sum())
cond_aldebaran = (marstices['aldebaran_angdist']<=max_aldebaran_angdist)
marstices.loc[cond_aldebaran,'close_aldebaran'] = True
print("Number of marstices close to Aldebaran: ",cond_aldebaran.sum())
cond_montunctions = (cond_solstices) & (cond_aldebaran)
marstices.loc[cond_montunctions,'montunctions'] = True
print("Number of Montunctions: ",cond_montunctions.sum())
cond_conjunction = (marstices['aldebaran_angdist']<=max_aldebaran_conjunc)
marstices.loc[cond_conjunction,'conj_aldebaran'] = True
print("Number of close conjunctions: ",cond_conjunction.sum())
Number of marstices close to solstices: 146
Number of marstices close to Aldebaran: 121
Number of Montunctions: 24
Number of close conjunctions: 15
These are the dates:
[15]:
mtime_start = montu.Time('bce1050-01-01 00:00:00.00')+(-10*montu.YEAR)
mtime_end = montu.Time('bce1050-01-01 00:00:00.00')+10*montu.YEAR
cond = (marstices.jed>=mtime_start.jed) & (marstices.jed<=mtime_end.jed)
marstices[cond]
[15]:
| datepro | datemix | type | jed | closest_solstice | aldebaran_angdist | close_solstice | close_aldebaran | conj_aldebaran | montunctions | |
|---|---|---|---|---|---|---|---|---|---|---|
| 882 | -1059-06-03 00:48:55.802880 | -1059-06-13 00:48:48 | first | 1.334422e+06 | 164.897449 | 101.821584 | False | False | False | False |
| 883 | -1059-08-02 10:56:53.096656 | -1059-08-12 10:56:56 | second | 1.334482e+06 | 139.920916 | 111.666625 | False | False | False | False |
| 884 | -1057-08-07 06:00:19.500480 | -1057-08-17 06:00:00 | first | 1.335217e+06 | 135.620189 | 29.896782 | False | False | False | False |
| 885 | -1057-10-15 18:54:00.596160 | -1057-10-25 18:54:54 | second | 1.335286e+06 | 66.082908 | 45.237112 | False | False | False | False |
| 886 | -1055-09-19 17:26:40.695360 | -1055-09-29 17:26:26 | first | 1.335991e+06 | 91.629515 | 19.539714 | False | False | False | False |
| 887 | -1055-12-05 05:15:46.794240 | -1055-12-15 05:15:15 | second | 1.336068e+06 | 15.137084 | 7.563516 | False | True | False | False |
| 888 | -1053-10-26 01:12:23.595824 | -1053-11-05 01:12:12 | first | 1.336758e+06 | 55.790945 | 56.637174 | False | False | False | False |
| 889 | -1052-01-13 21:06:54.097920 | -1052-01-23 21:06:06 | second | 1.336837e+06 | 24.038575 | 37.863884 | False | False | False | False |
| 890 | -1051-11-28 14:37:33.896640 | -1051-12-08 14:37:37 | first | 1.337522e+06 | 21.721740 | 90.114387 | False | False | False | False |
| 891 | -1050-02-17 08:54:18.201600 | -1050-02-27 08:54:54 | second | 1.337603e+06 | 59.039884 | 70.931521 | False | False | False | False |
| 892 | -1048-01-05 10:51:15.998416 | -1048-01-15 10:51:51 | first | 1.338290e+06 | 15.631285 | 124.671995 | False | False | False | False |
| 893 | -1048-03-24 13:37:48.797760 | -1048-04-03 13:37:37 | second | 1.338369e+06 | 94.746943 | 106.237353 | False | False | False | False |
| 894 | -1046-02-21 15:09:06.497280 | -1046-03-03 15:09:09 | first | 1.339068e+06 | 63.329107 | 165.916162 | False | False | False | False |
| 895 | -1046-05-05 21:09:13.201936 | -1046-05-15 21:09:09 | second | 1.339141e+06 | 136.579185 | 149.931005 | False | False | False | False |
| 896 | -1044-05-01 23:08:53.802240 | -1044-05-11 23:08:08 | first | 1.339868e+06 | 133.184542 | 132.748457 | False | False | False | False |
| 897 | -1044-07-02 22:14:13.202880 | -1044-07-12 22:14:14 | second | 1.339930e+06 | 170.098364 | 142.427358 | False | False | False | False |
| 898 | -1042-07-16 09:04:26.302080 | -1042-07-26 09:04:04 | first | 1.340674e+06 | 157.130109 | 55.004732 | False | False | False | False |
| 899 | -1042-09-19 15:45:53.507520 | -1042-09-29 15:45:45 | second | 1.340739e+06 | 91.851322 | 68.038361 | False | False | False | False |
| 900 | -1040-09-03 21:59:01.104000 | -1040-09-13 21:59:59 | first | 1.341454e+06 | 107.078913 | 4.128862 | False | True | True | False |
| 901 | -1040-11-17 02:44:51.806400 | -1040-11-27 02:44:44 | second | 1.341529e+06 | 32.880409 | 16.925303 | False | False | False | False |
Periodicity of marstices and montunctions
Now we want to calculate the periodicities of Marstices and Montunctions by calculating the difference in time between consecutive phenomena.
Setting parameters for winter marstices, aldebaran conjunctions and montunctions
[16]:
max_days_to_solstice = 15 # days
max_aldebaran_angdist = 15 # degrees
marstices['close_solstice'] = False
marstices['close_aldebaran'] = False
marstices['conj_aldebaran'] = False
marstices['montunctions'] = False
cond_solstices = (marstices['closest_solstice']<=max_days_to_solstice)
marstices.loc[cond_solstices,'close_solstice'] = True
print("Number of marstices close to solstices: ",cond_solstices.sum())
cond_aldebaran = (marstices['aldebaran_angdist']<=max_aldebaran_angdist)
marstices.loc[cond_aldebaran,'close_aldebaran'] = True
print("Number of marstices close to Aldebaran: ",cond_aldebaran.sum())
cond_montunctions = (cond_solstices) & (cond_aldebaran)
marstices.loc[cond_montunctions,'montunctions'] = True
print("Number of Montunctions: ",cond_montunctions.sum())
cond_conjunction = (marstices['aldebaran_angdist']<=max_aldebaran_conjunc)
marstices.loc[cond_conjunction,'conj_aldebaran'] = True
print("Number of close conjunctions: ",cond_conjunction.sum())
montunctions = marstices.loc[marstices.montunctions]
Number of marstices close to solstices: 146
Number of marstices close to Aldebaran: 121
Number of Montunctions: 24
Number of close conjunctions: 15
Periodicity of marstices
[17]:
times = marstices.jed.to_numpy()
delta1 = times[2::2]-times[:-2:2]
delta2 = times[1::2]-times[:-1:2]
Histogram of times:
[18]:
fig,axs = plt.subplots(1,2,figsize=(10,5),sharey=True)
ax = axs[0]
hs1 = ax.hist(delta1,bins=50)
ax.set_xlabel("Time [day]")
ax.set_ylabel("Number of pair of marstices")
ax.set_title("Difference between synodic marstices")
ax.grid()
ax = axs[1]
hs2 = ax.hist(delta2,bins=50)
ax.set_title("Difference between consecutive marstices")
ax.set_xlabel("Time [day]")
ax.grid()
fig.tight_layout()
[19]:
print(f"Periodicity of synodic marstices: {hs1[1][0]:.1f} - {hs1[1][-1]:.1f}")
print(f"Periodicity of consecutive marstices: {hs2[1][0]:.1f} - {hs2[1][-1]:.1f}")
Periodicity of synodic marstices: 764.5 - 809.9
Periodicity of consecutive marstices: 60.3 - 80.9
Periodicity of winter marstices
Let’s extract the winter marstices:
[20]:
winter_marstices = marstices[marstices.close_solstice]
Let’s get the periodicity:
[21]:
times = winter_marstices.jed.to_numpy()
delta = (times[1:]-times[:-1])*montu.DAY/montu.YEAR
hs = plt.hist(delta,bins=200)
plt.show()
Get the periodicities:
[22]:
# Times
ts = (hs[1][1:]+hs[1][:-1])/2
# Frequencies
fs = hs[0]
# Times with a positive frequency
cond = fs>0
isort = fs[cond].argsort()[::-1]
Ps = ts[cond][isort]
print("Periods of winter marstices [years]: ", Ps)
Periods of winter marstices [years]: [11.0162576 4.03507962 17.03451448 21.00656402 27.98774199]
Periodicity of Aldebaran conjunctions
Let’s extract the Aldebaran conjunctions:
[23]:
aldebaran_marstices = marstices[marstices.close_aldebaran]
len(aldebaran_marstices)
[23]:
121
Let’s get the periodicity:
[24]:
times = aldebaran_marstices.jed.to_numpy()
delta = (times[1:]-times[:-1])*montu.DAY/montu.YEAR
hs = plt.hist(delta,bins=100)
plt.show()
Get the periodicities:
[25]:
# Times
ts = (hs[1][1:]+hs[1][:-1])/2
# Frequencies
fs = hs[0]
# Times with a positive frequency
cond = fs>0
isort = fs[cond].argsort()[::-1]
Ps = ts[cond][isort]
print("Periods of winter marstices [years]: ", Ps)
Periods of winter marstices [years]: [14.80330875 17.19389575 0.28903055 14.97406496 2.33810512]
Periodicity of Montunctions
Let’s extract the Aldebaran conjunctions:
[26]:
len(montunctions)
[26]:
24
Let’s get the periodicity:
[27]:
times = montunctions.jed.to_numpy()
delta = (times[1:]-times[:-1])*montu.DAY/montu.YEAR
hs = plt.hist(delta,bins=100)
plt.xlabel("Period [years]")
plt.ylabel("Number of Montunctions")
plt.show()
Get the periodicities:
[28]:
# Times
ts = (hs[1][1:]+hs[1][:-1])/2
# Frequencies
fs = hs[0]
# Times with a positive frequency
cond = fs>0
isort = fs[cond].argsort()[::-1]
Ps = ts[cond][isort]
print("Periods of Montunctions [years]: ", Ps)
Periods of Montunctions [years]: [ 46.31123293 78.61829458 31.1079098 204.04571042 15.90458667]
Lines chart of marstices and montunctions
[29]:
# Selection of marstices
selection = marstices.loc[:]
nmarstices = len(selection)
jed_min = (1-1e-3)*selection.jed.min()
jed_max = (1+1e-3)*selection.jed.max()
# Number of panels
npanels = 6
delta_jed = (jed_max - jed_min)/npanels
[30]:
import datetime
[31]:
fig,axs = plt.subplots(npanels,1,figsize=(12,10))
axts = []
for ax in axs:
axts += [ax.twinx()]
alpha_marst = 0.05
alpha_wmarst = 0.3
alpha_aldeb = 0.3
alpha_montu = 1
alpha_mag = 0.3
# Loop on marstices
for index in selection.index:
# Get marstice information and location of mars
marstice = selection.loc[index]
mars_location = mars_marstices.loc[index]
# Get MonTime object
mtime = montu.Time(marstice.jed,format='jd')
# Get panel
i = int(np.floor((mtime.jed - jed_min)/delta_jed))
# Plot line for marstices
axs[i].axvline(mtime.jed,color='k',alpha=alpha_marst)
# Plot line for winter marstices
if marstice.close_solstice:
axs[i].axvline(mtime.jed,color='b',lw=2,alpha=alpha_wmarst)
# Plot line for aldebaran conjunctions
if marstice.close_aldebaran:
axs[i].axvline(mtime.jed,color='r',lw=2,alpha=alpha_aldeb)
# Plot line for aldebaran close conjunctions
if marstice.conj_aldebaran:
axs[i].axvline(mtime.jed,color='g',lw=5,alpha=alpha_montu)
# Plot line for montunctions
if marstice.close_solstice and marstice.close_aldebaran:
axs[i].axvline(mtime.jed,color='k',lw=5,alpha=alpha_montu)
# Plot distance
for i,axt in enumerate(axts):
jed_ax_min = jed_min + i*delta_jed
jed_ax_max = jed_ax_min + delta_jed
cond = (marstices.jed>=jed_ax_min)&(marstices.jed<=jed_ax_max)
#axt.plot(marstices[cond].jed,mars.df[cond].site_distance,'k',alpha=0.4)
axt.plot(marstices[cond].jed,mars_marstices[cond].Vmag,'k--',alpha=0.4)
# Loop on marstices
for index in selection.index:
# Get MonTime object
mtime = montu.Time(marstice.jed,format='jd')
# Get marstice information and location of mars
marstice = selection.loc[index]
# Get panel
i = int(np.floor((mtime.jed - jed_min)/delta_jed))
# Plot line for aldebaran close conjunctions
if marstice.conj_aldebaran:
mmin,mmax = axts[i].get_ylim()
t = axts[i].text(mtime.jed,0.95*mmax,f"a.d.{marstice.aldebaran_angdist:.1f}",
ha='center',va='center',fontsize=8)
# Decoration
for i,ax in enumerate(axs):
ax.margins(0)
ax.get_yaxis().set_visible(False)
jed_ax_min = jed_min + i*delta_jed
jed_ax_max = jed_ax_min + delta_jed
ax.set_xticks(np.linspace(jed_ax_min,jed_ax_max,10))
# Change xticks
for ax in axs:
xticks = ax.get_xticks()
xtick_labels = []
for xt in xticks:
mtime = montu.Time(xt,format='jd',full=True)
xtick_labels += [f'{mtime.readable.year}']
ax.set_xticklabels(xtick_labels)
for ax in axts:
ax.margins(0)
ax.set_yticks(np.arange(-2.5,0.0,0.5))
ax.get_yaxis().set_visible(False)
# Legends
axs[0].plot([],[],'k-',alpha=alpha_marst,label='Regular marstices')
axs[0].plot([],[],'b-',alpha=alpha_wmarst,label='Winter marstices')
axs[0].plot([],[],'r-',alpha=alpha_aldeb,label='Taurus marstices')
axs[0].plot([],[],'k-',alpha=alpha_montu,lw=3,label='Montunctions')
axs[0].plot([],[],'g-',alpha=alpha_montu,lw=3,label='Aldebaran conjunctions')
axs[0].plot([],[],'k--',alpha=alpha_mag,label='Mars magnitude')
axs[0].legend(bbox_to_anchor=(0.5,1.4),ncol=6,fontsize=9,loc='upper center')
# Other decoration
axs[-1].set_xlabel('Year')
axs[0].text(0.5,1.5,f"Marstices ({len(marstices)}), Aldebaran Conjunctions ({selection.conj_aldebaran.sum()}) and Montunctions ({len(montunctions)}) in Ancient Egypt",
transform=axs[0].transAxes,fontsize=17,ha='center')
"""
# Spans
# Montuhotep II
iax = 1
j1 = montu.Time('-2066-01-01').jed
j2 = montu.Time('-1957-01-01').jed
jk = (j1+j2)/2
mmin,mmax = axs[iax].get_ylim()
axs[iax].axvspan(j1,j2,color='k',alpha=0.2)
t = axs[iax].text(jk,0.0,'Montuhotep II',ha='center',va='center',fontsize=10)
t.set_bbox(dict(facecolor='white', edgecolor='white'))
"""
# Senenmut
iax = 2
j1 = montu.Time('-1480-01-01').jed
j2 = montu.Time('-1458-01-01').jed
jmin,jmax = axs[iax].get_xlim()
j1 = max(j1,jmin)
j2 = min(j2,jmax)
jk = (j1+j2)/2
mmin,mmax = axs[iax].get_ylim()
axs[iax].axvspan(j1,j2,color='k',alpha=0.2)
t = axs[iax].text(jk,0.0,'Senenmut',ha='center',va='center',fontsize=10)
t.set_bbox(dict(facecolor='white', edgecolor='white'))
# Mentuemhat
iax = 5
j1 = montu.Time('-700-01-01').jed
j2 = montu.Time('-650-01-01').jed
jk = (j1+j2)/2
mmin,mmax = axs[iax].get_ylim()
axs[iax].axvspan(j1,j2,color='k',alpha=0.2)
t = axs[iax].text(jk,0.0,'Mentuemhat',ha='center',va='center',fontsize=10)
t.set_bbox(dict(facecolor='white', edgecolor='white'))
fig.tight_layout()
Magnitude at Montunctions:
[32]:
cond = cond_montunctions = (cond_solstices) & (cond_aldebaran)
hs = plt.hist(mars_marstices[cond].Vmag,color='r',alpha=0.3,
weights=[1/len(mars_marstices[cond])]*len(mars_marstices[cond]))
hs = plt.hist(mars_marstices.Vmag,color='b',alpha=0.3,
weights=[1/len(mars_marstices)]*len(mars_marstices))
plt.show()
Montunctions visualization
Let’s see one of this montunctions in the sky:
[33]:
# Time of montunction
mtime_montunction = montu.Time(montunctions.iloc[-5].jed,format='jd',full=True)
t = mtime_montunction.tt
mars.reset_store()
for t in np.linspace(-50*montu.DAY,0*montu.DAY,50):
# Get MonTime object
mtime = mtime_montunction + t
# Calculate Mars position and store it
mars.where_in_sky(mtime,Tebas,store=1)
mars.tabulate_store()
Create a map of montunction:
[34]:
# Plot Hyades
hyades = allstars.get_stars_around(center=[aldebaran.data.RAJ2000,aldebaran.data.DecJ2000],radius=10,Vmag=[-1,5])
fig,ax = hyades.plot_stars(pad=0.0,labels=True,figargs=dict(figsize=(8,8)))
for index in mars.position.index:
mars_position = mars.position.loc[index]
ax.plot(15*mars_position.RAJ2000,mars_position.DecJ2000,'ro',ms=10,alpha=0.3)
ax.set_title(f"Mars Montunction at {mtime_montunction.readable.datespice}",fontsize=14)
montu.Util.montu_mark(ax);
Interesting montunctions
We are interested in the Montunctions happening around the date of birth or dead of Senenmut who, according to several chronologies lived between 1480bce and 1458 bce. Let’s select the montunctions in this range:
[35]:
mtime_start = montu.Time('bce1480-01-01 00:00:00.00')+(-50*montu.YEAR)
mtime_end = montu.Time('bce1480-01-01 00:00:00.00')+50*montu.YEAR
cond = (montunctions.jed>=mtime_start.jed) & (montunctions.jed<=mtime_end.jed)
print("Number of montunctions in the desired interval: ",cond.sum())
montunctions_selected = montunctions.loc[cond]
montunctions_selected
Number of montunctions in the desired interval: 2
[35]:
| datepro | datemix | type | jed | closest_solstice | aldebaran_angdist | close_solstice | close_aldebaran | conj_aldebaran | montunctions | |
|---|---|---|---|---|---|---|---|---|---|---|
| 459 | -1512-12-10 23:40:17.296304 | -1512-12-24 23:40:40 | second | 1.169158e+06 | 8.282254 | 14.651087 | True | True | False | True |
| 503 | -1465-12-06 03:30:47.802240 | -1465-12-19 03:30:30 | second | 1.186319e+06 | 14.549713 | 9.723496 | True | True | False | True |
Let’s see the montunctions:
[36]:
# Time of montunction
isel = 1
mtime_montunction = montu.Time(montunctions_selected.iloc[isel].jed,format='jd',full=True)
t = mtime_montunction.tt
mars.reset_store()
for t in np.linspace(-20*montu.DAY,20*montu.DAY,20):
# Get MonTime object
mtime = mtime_montunction + t
# Calculate Mars position and store it
mars.where_in_sky(mtime,Tebas,store=1)
mars.tabulate_store()
# Plot Hyades
hyades = allstars.get_stars_around(center=[aldebaran.data.RAJ2000,aldebaran.data.DecJ2000],radius=15,Vmag=[-1,5])
fig,ax = hyades.plot_stars(pad=0.0,labels=True,label_mag=4,figargs=dict(figsize=(8,8)))
for index in mars.position.index:
mars_position = mars.position.loc[index]
ax.plot(15*mars_position.RAJ2000,mars_position.DecJ2000,'ro',ms=10,alpha=0.3)
ax.set_title(f"Mars montunction at {-mtime_montunction.readable.year+1} \
b.c.e. {mtime_montunction.readable.month:02d}-{mtime_montunction.readable.day:02d} (Senenmut)",fontsize=13)
montu.Util.montu_mark(ax);
We are interested in the Montunctions happening around the date of birth or dead of Mentuhotep (2119 - 2103)
[37]:
mtime_start = montu.Time('bce600-01-01 00:00:00.00')+(-70*montu.YEAR)
mtime_end = montu.Time('bce600-01-01 00:00:00.00')+70*montu.YEAR
cond = (montunctions.jed>=mtime_start.jed) & (montunctions.jed<=mtime_end.jed)
print("Number of montunctions in the desired interval: ",cond.sum())
montunctions_selected = montunctions.loc[cond]
montunctions_selected
Number of montunctions in the desired interval: 5
[37]:
| datepro | datemix | type | jed | closest_solstice | aldebaran_angdist | close_solstice | close_aldebaran | conj_aldebaran | montunctions | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1257 | -660-12-20 23:18:09.103680 | -660-12-27 23:18:18 | second | 1.480354e+06 | 0.604677 | 13.079182 | True | True | False | True |
| 1301 | -613-12-14 20:15:27.293760 | -613-12-21 20:15:15 | second | 1.497514e+06 | 5.938564 | 8.667736 | True | True | False | True |
| 1331 | -581-12-25 06:26:22.200016 | -581-12-31 06:26:26 | second | 1.509212e+06 | 3.708349 | 14.680452 | True | True | False | True |
| 1345 | -566-12-08 08:31:32.096640 | -566-12-14 08:31:31 | second | 1.514674e+06 | 12.862503 | 8.097878 | True | True | False | True |
| 1375 | -534-12-18 05:15:19.604160 | -534-12-24 05:15:15 | second | 1.526372e+06 | 2.773414 | 9.781388 | True | True | False | True |
[38]:
# Time of montunction
isel = 0
mtime_montunction = montu.Time(montunctions_selected.iloc[isel].jed,format='jd',full=True)
t = mtime_montunction.tt
mars.reset_store()
for t in np.linspace(-20*montu.DAY,20*montu.DAY,20):
# Get MonTime object
mtime = mtime_montunction + t
# Calculate Mars position and store it
mars.where_in_sky(mtime,Tebas,store=1)
mars.tabulate_store()
# Plot Hyades
hyades = allstars.get_stars_around(center=[aldebaran.data.RAJ2000,aldebaran.data.DecJ2000],radius=15,Vmag=[-1,5])
fig,ax = hyades.plot_stars(pad=0.0,labels=True,label_mag=4,figargs=dict(figsize=(8,8)))
for index in mars.position.index:
mars_position = mars.position.loc[index]
ax.plot(15*mars_position.RAJ2000,mars_position.DecJ2000,'ro',ms=10,alpha=0.3)
ax.set_title(f"Mars montunction at {-mtime_montunction.readable.year+1} \
b.c.e. {mtime_montunction.readable.month:02d}-{mtime_montunction.readable.day:02d} (Mentuemhat)",fontsize=13)
montu.Util.montu_mark(ax);
Conjunctions
We are interested in the Montunctions happening around the date of birth or dead of Mentuhotep (2119 - 2103)
[39]:
mtime_start = montu.Time('bce1050-08-01 00:00:00.00')+(-1*montu.YEAR)
mtime_end = montu.Time('bce1050-08-01 00:00:00.00')+1*montu.YEAR
cond = (marstices.jed>=mtime_start.jed) & (marstices.jed<=mtime_end.jed)
print("Number of marstices in the desired interval: ",cond.sum())
marstices_selected = marstices.loc[cond]
marstices_selected
Number of marstices in the desired interval: 2
[39]:
| datepro | datemix | type | jed | closest_solstice | aldebaran_angdist | close_solstice | close_aldebaran | conj_aldebaran | montunctions | |
|---|---|---|---|---|---|---|---|---|---|---|
| 892 | -1048-01-05 10:51:15.998416 | -1048-01-15 10:51:51 | first | 1.338290e+06 | 15.631285 | 124.671995 | False | False | False | False |
| 893 | -1048-03-24 13:37:48.797760 | -1048-04-03 13:37:37 | second | 1.338369e+06 | 94.746943 | 106.237353 | False | False | False | False |
[40]:
# Time of montunction
isel = 0
mtime_marstice = montu.Time(marstices_selected.iloc[isel].jed,format='jd',full=True)
t = mtime_marstice.tt
mars.reset_store()
for t in np.linspace(-20*montu.DAY,20*montu.DAY,50):
# Get MonTime object
mtime = mtime_marstice + t
# Calculate Mars position and store it
mars.where_in_sky(mtime,Tebas,store=1)
mars.tabulate_store()
# Plot Hyades
hyades = allstars.get_stars_around(center=[aldebaran.data.RAJ2000,aldebaran.data.DecJ2000],radius=15,Vmag=[-1,5])
fig,ax = hyades.plot_stars(pad=0.0,labels=True,label_mag=4,figargs=dict(figsize=(8,8)))
for index in mars.position.index:
mars_position = mars.position.loc[index]
ax.plot(15*mars_position.RAJ2000,mars_position.DecJ2000,'ro',ms=10,alpha=0.3)
ax.set_title(f"Aldebaran conjunction during marstice at {-mtime_marstice.readable.year+1} \
b.c.e. {mtime_marstice.readable.month:02d}-{mtime_marstice.readable.day:02d} (Montuhotep II)",fontsize=13)
montu.Util.montu_mark(ax);
[41]:
mtime_start = montu.Time('bce1580-08-01 00:00:00.00')+(-100*montu.YEAR)
mtime_end = montu.Time('bce1580-08-01 00:00:00.00')+100*montu.YEAR
cond = (marstices.jed>=mtime_start.jed) & (marstices.jed<=mtime_end.jed) & (marstices.aldebaran_angdist<=max_aldebaran_conjunc)
print("Number of marstices in the desired interval: ",cond.sum())
marstices_selected = marstices.loc[cond]
marstices_selected
Number of marstices in the desired interval: 2
[41]:
| datepro | datemix | type | jed | closest_solstice | aldebaran_angdist | close_solstice | close_aldebaran | conj_aldebaran | montunctions | |
|---|---|---|---|---|---|---|---|---|---|---|
| 412 | -1561-08-22 22:36:39.098880 | -1561-09-05 22:36:36 | first | 1.151150e+06 | 119.410078 | 4.893175 | False | True | True | False |
| 486 | -1482-08-26 07:38:10.302720 | -1482-09-08 07:38:38 | first | 1.180008e+06 | 116.239785 | 3.616589 | False | True | True | False |
[42]:
# Time of montunction
isel = 1
mtime_marstice = montu.Time(marstices_selected.iloc[isel].jed,format='jd',full=True)
t = mtime_marstice.tt
mars.reset_store()
for t in np.linspace(-20*montu.DAY,20*montu.DAY,50):
# Get MonTime object
mtime = mtime_marstice + t
# Calculate Mars position and store it
mars.where_in_sky(mtime,Tebas,store=1)
mars.tabulate_store()
# Plot Hyades
hyades = allstars.get_stars_around(center=[aldebaran.data.RAJ2000,aldebaran.data.DecJ2000],radius=15,Vmag=[-1,5])
fig,ax = hyades.plot_stars(pad=0.0,labels=True,label_mag=4,figargs=dict(figsize=(8,8)))
for index in mars.position.index:
mars_position = mars.position.loc[index]
ax.plot(15*mars_position.RAJ2000,mars_position.DecJ2000,'ro',ms=10,alpha=0.3)
ax.set_title(f"Aldebaran conjunction during marstice at {-mtime_marstice.readable.year+1} \
b.c.e. {mtime_marstice.readable.month:02d}-{mtime_marstice.readable.day:02d} (Senenmut)",fontsize=13)
montu.Util.montu_mark(ax);
Powered by MontuPython. For more examples see MontuPython GitHub repo.
Jorge I. Zuluaga © 2023-present