星座早見プログラムを少し変更して，赤緯45°以上の天の北極の歳差運動による変化を見られるようにしました。より短いプログラムですので，実行ファイル形式でも利用してもらえると思います。古代エジプトのピラミッド建設で，正確な東西南北方向を決める方法として紀元前2500年ころには，こぐま座のコカブと北斗七星のミザールを結ぶ線が使われたという説を確かめたり出来ます。
実行ファイルは→こちらからダウンロード
ソースコードをパイソンで実行する場合には，同じフォルダーに恒星，星座名，星座線データのCSVファイルを入れて実行します。ファイルは→こちらにあります。
'''
******************************************************
Star chart program by Python（Archaeoastronomy version）
2019.08.18 Ver1.0 Archaeoastronomy version1.2
2020.03.13 from Ver.2.0 Execute file form
星座早見プログラムをもとに，天の北極の星々の変化を表示するプログラムへ
******************************************************
'''
import os
import tkinter as tk
import csv
import math
# Calculation to cure Julius day in the Gregorian calendar
def JDT(jd):
Z = int(jd + 0.5)
if Z >= 2299161:
a = int((Z - 1867216.25) / 36524.25)
A = Z + 1 + a - int(a / 4)
else:
A = Z
B = A + 1524
C = int((B - 122.1) / 365.25)
K = int(365.25 * C)
E = int((B - K)/30.6001)
D = B - K - int(30.6001 * E) + (jd + 0.5) - int(jd + 0.5)
if E < 13.5:
M = E -1
else:
M = E -13
if M > 2.5:
Y = C - 4716
else:
Y = C - 4715
if M >= 13:
Y = Y + 1
M = M -12
if Y <= 0:
Y = Y -1
h = D - int(D)
D = int(D)
h = h*24
lh = round(long/15)
h = h +lh
if h >= 24.0:
h = h - 24
D = D + 1
if D >= 32:
D = D - 31
M = M + 1
if M >= 13:
Y = Y + 1
M = M - 12
h = round(h,1)
return [Y,M,D,h]
def koseji(jd,long): # Calculate sidereal time
B = jd - 2415020.0
R = 366.2422/365.2422
ST = 18.6461 + 24*B*R + 3.24e-14*B*B + long/15
ST = 24*(ST/24-int(ST/24))
if ST < 0:
ST = ST + 24
return ST
def yogen_AD(arfa,drta): # Calculation of the direction cosine
a = math.radians(arfa)
d = math.radians(drta)
L = math.cos(a) * math.cos(d)
M = math.cos(d) * math.sin(a)
N = math.sin(d)
return [L,M,N]
def horizon(ad): # to horizontal coordinate（ST;sideral time LAT;latitude ad; direction cosine)
sT = math.sin(math.radians(ST))
cT = math.cos(math.radians(ST))
# sL = math.sin(math.radians(LAT)) ** = 1
# cL = math.cos(math.radians(LAT)) ** = 0
L = cT*ad[0] + sT*ad[1] # - cL*ad[2]
M = -sT*ad[0] + cT*ad[1]
N = ad[2] # + cL*sT*ad[1] + cL*cT*ad[0]
if L == 0:
L = 0.01
h = math.asin(N)
h = math.degrees(h)
A = math.atan(-M/L)
A = math.degrees(A)
if L < 0. :
A = A + 180.
return [h,A]
def proper_move(RA,DC,V1,V2): # proper monve
T = Cent - 1
RA = RA + V1*T/3600000/math.cos(math.radians(DC))
DC = DC + V2*T/3600000
return [RA , DC]
def saisa_hosei(ad): # 歳差補正
t = Cent - 1
f = 0.640616 * t + 0.0000839* t*t + 0.000005*t**3
z = 0.640616 * t + 0.000304 * t*t + 0.00000506*t**3
s = 0.556753 * t - 0.000119 * t*t - 0.0000116*t**3
sF = math.sin(math.radians(f))
cF = math.cos(math.radians(f))
sZ = math.sin(math.radians(z))
cZ = math.cos(math.radians(z))
sS = math.sin(math.radians(s))
cS = math.cos(math.radians(s))
L = (- sZ*sF + cZ*cS*cF)*ad[0] + (- sZ*cF - cZ*cS*sF)*ad[1] - cZ*sS*ad[2]
M = (cZ*sF + sZ*cS*cF)*ad[0] + (cZ*cF - sZ*cS*sF)*ad[1] - sZ*sS*ad[2]
N = sS*cF*ad[0] - sS*sF*ad[1] + cS*ad[2]
return [L, M, N]
def dispXY(hh, AA):
dot = 480 # 画面のパラメータ 中心座標（540,375)
r = dot * math.sin(math.radians(90-hh))
x = -r * math.sin(math.radians(AA)) + 540
y = -r * math.cos(math.radians(AA)) + 375
return [x, y]
def sekido(): # 赤経赤緯の描画
xl = [0.0]*182
yl = [0.0]*182
rad = [0.0]*182
for i in range(180):
rad[i] = i*2
for i in range(181):
xy= dispXY(80,rad[i])
xl[i] ,yl[i]= xy
for i in range(180):
app.co_line(xl[i], yl[i], xl[i+1], yl[i+1], '#710071')
for i in range(181):
xy= dispXY(60,rad[i])
xl[i] ,yl[i] = xy
for i in range(180):
app.co_line(xl[i], yl[i], xl[i+1], yl[i+1], '#710071')
xy = dispXY(45,ST)
x1 ,y1 = xy
xy = dispXY(45,ST+180)
x2, y2 = xy
app.co_line(x1, y1, x2, y2, '#710071')
app.text_in(x1 + 5, y1, "0h", "white")
app.text_in(x2 + 5, y2, "12h", "white")
xy = dispXY(45, ST+90)
x1, y1 = xy
xy = dispXY(45, ST+270)
x2, y2 = xy
app.co_line(x1, y1, x2, y2, '#710071')
app.text_in(x1 + 5, y1, "18h", "white")
app.text_in(x2 + 5, y2, "6h", "white")
app.co_line(540, 38, 540, 710, "#999900")
def star_color(CL): # 恒星の色 CL：color index
if CL < -0.16:
c = "#a09eff"
elif CL < 0.15:
c = "#a0d7ff"
elif CL < 0.45:
c = "#d7e8ff"
elif CL < 0.68:
c = "#ffffff"
elif CL < 1.15:
c = "#ffffdc"
elif CL < 1.6:
c = "#ffe6aa"
else:
c = "#ffd7b1"
return c
def magnitude(m): # 等級を星の大きさに
if m < 0.0:
rd = 7
elif m < 1.0:
rd = 6
elif m < 2.0:
rd = 5
elif m < 3.0:
rd = 4
elif m < 4.0:
rd = 3
else:
rd = 2
return rd
class Conline: # 星座線クラス
def __init__(self):
self.lcnum = 0
self.linRas = 0
self.linDcs = 0
self.linV1s = 0
self.linV2s = 0
self.linRae = 0
self.linDce = 0
self.linV1e = 0
self.linV2e = 0
class Star: # 星クラス
def __init__(self):
self.stnum = 0
self.stV1 = 0
self.stV2 = 0
self.stRA = 0
self.stDC = 0
self.stMg = 0
self.stCL = 0
class Constelation: # 星座クラス
def __init__(self):
self.con_name = ""
self.con_Ra = 0
self.con_Dc = 0
class Planetarium: # プラネタリウムクラス
# 星表示のための変数
XX = [0.0] * 1000
YY = [0.0] * 1000
hh = [0.0] * 1000
AA = [0.0] * 1000
MG = [0.0] * 1000
CLs = [0.0] * 1000
rd = [0] * 1000
hLs = [0.0] * 500
hLe = [0.0] * 500
ALs = [0.0] * 500
ALe = [0.0] * 500
x1 = [0.0] * 500
y1 = [0.0] * 500
x2 = [0.0] * 500
y2 = [0.0] * 500
nh = [0.0] * 60
nA = [0.0] * 60
xn = [0.0] * 60
yn = [0.0] * 60
coname = [""] * 60
star_counter = 0
line_counter = 0
con_counter = 0
def __init__(self):
# 星、星座線リストを作る
self.star_list = []
self.conline_list = []
self.conste_list = []
for i in range(1263):
self.star_list.append(Star())
for i in range(673):
self.conline_list.append(Conline())
for i in range(89):
self.conste_list.append(Constelation())
# データ読み込み
with open("starData1263.csv", "r") as f: # 恒星ファイル読み込み
stDATA = csv.reader(f, delimiter=",")
i = 0
for row in stDATA:
self.star_list[i].stnum = int(row[4]) # No.
self.star_list[i].stV1 = float(row[1]) # 固有運動RA
self.star_list[i].stV2 = float(row[2]) # DC
self.star_list[i].stRA = float(row[6]) # 赤経
self.star_list[i].stDC = float(row[7]) # 赤緯
self.star_list[i].stMg = float(row[5]) # 光度
self.star_list[i].stCL = float(row[8]) # 色指数
i += 1
with open("cons_lineData.csv", "r") as f: #星座線ファイル読み込み
szL=csv.reader(f,delimiter=",")
i = 0
for row in szL:
self.conline_list[i].lcnum = str(row[0]) #星座コード
self.conline_list[i].linRas = float(row[1]) #始点
self.conline_list[i].linDcs = float(row[2])
self.conline_list[i].linV1s = float(row[3])
self.conline_list[i].linV2s = float(row[4])
self.conline_list[i].linRae = float(row[5]) #終点
self.conline_list[i].linDce = float(row[6])
self.conline_list[i].linV1e = float(row[7])
self.conline_list[i].linV2e = float(row[8])
i += 1
with open("cons_nameData.csv", "r") as f: # 星座名ファイル読み込み
szM=csv.reader(f,delimiter=",")
i = 0
for row in szM:
self.conste_list[i].con_name = str(row[0]) # 星座名
self.conste_list[i].con_Ra = float(int(row[1])*15+int(row[2])*0.25)
self.conste_list[i].con_Dc = float(row[3])
i += 1
def star_culc(self): # 恒星表示メソッド
for lin in self.conline_list: #恒星座標 固有運動の補正
ads = proper_move(lin.linRas,lin.linDcs,lin.linV1s,lin.linV2s)
lin.linRas = ads[0]
lin.linDcs = ads[1]
ade = proper_move(lin.linRae,lin.linDce,lin.linV1e,lin.linV2e)
lin.linRae = ade[0]
lin.linDce = ade[1]
m = 0 # 星座線の地平座標計算
for line in self.conline_list:
ad = yogen_AD(line.linRas,line.linDcs)
ad = saisa_hosei(ad)
hs = horizon(ad)
if hs[0] < 45.0:
continue
ad = yogen_AD(line.linRae,line.linDce)
ad = saisa_hosei(ad)
he = horizon(ad)
if he[0] < 45.0:
continue
self.hLs[m],self.ALs[m] = hs
self.hLe[m],self.ALe[m] = he
m += 1
self.line_counter = m
i = 0
for i in range( self.line_counter): # 画面上の座標
xy= dispXY(self.hLs[i],self.ALs[i])
self.x1[i] ,self.y1[i] = xy
xy= dispXY(self.hLe[i],self.ALe[i])
self.x2[i] ,self.y2[i] = xy
# 恒星の処理 ******
for star in self.star_list: # 固有運動の補正
ad = proper_move(star.stRA,star.stDC,star.stV1,star.stV2)
star.stRA = ad[0]
star.stDC = ad[1]
n = 0 # 恒星の地平座標計算
for star in self.star_list:
ad = yogen_AD(star.stRA,star.stDC)
ad = saisa_hosei(ad)
h = horizon(ad)
if h[0] < 45.0:
continue
self.hh[n],self.AA[n] = h
self.MG[n] = star.stMg
self.CLs[n] = star.stCL
n += 1
self.star_counter = n
for i in range(self.star_counter):
xy= dispXY(self.hh[i],self.AA[i])
self.XX[i] ,self.YY[i] = xy
# 星座名の処理 *******
n = 0 #星座名表示の地平座標計算
for c in self.conste_list:
ad = yogen_AD(c.con_Ra,c.con_Dc)
ad = saisa_hosei(ad)
h = horizon(ad)
if h[0] < 45.0:
continue
self.nh[n] ,self.nA[n] = h
self.coname[n] = c.con_name
n += 1
self.con_counter = n
for i in range(self.con_counter):
xy= dispXY(self.nh[i],self.nA[i])
self.xn[i] ,self.yn[i] = xy
def star_display(self):
# 星座線を引く
for i in range( self.line_counter):
app.co_line(self.x1[i], self.y1[i], self.x2[i], self.y2[i], 'blue')
# 星のプロット
for i in range(self.star_counter):
self.rd[i] = magnitude(self.MG[i])
color = star_color(self.CLs[i])
app.point_star(self.XX[i], self.YY[i], self.rd[i]/2, color)
#星座名の表示
for i in range(self.con_counter):
app.text_in(self.xn[i], self.yn[i], self.coname[i], 'red')
class Time:
def __init__(self,Y,D,lo):
self.Ydate = Y
self.Dtime = D
self.LAT = 34.5
self.JD = 0
self.ST = 0
self.Cent = 0
self.YY = 0
self.long = lo
def Julian(self): # （ユリウス日）の計算
self.JD = 0
if self.Ydate != abs(self.Ydate):
SP1 = -1
self.Ydate = abs(self.Ydate)
else:
SP1 = 1
self.YY = int(self.Ydate/10000)
MD = int(self.Ydate-10000*self.YY)
MM = int(MD/100)
DD = MD - 100 * MM
HH = int(self.Dtime/100)
MS = self.Dtime-100*HH
if SP1 < 0:
self.YY = self.YY * SP1 # +1 BC.でなく，BC1年を0年として－で入力する
SP2 = self.YY + (MM-1)/12 + DD/365.25
if MM <= 2 :
MM = MM + 12
self.YY = self.YY - 1
if self.YY < 0:
self.JD = math.floor(365.25*self.YY) + int(30.59*(MM-2)) + DD - self.long/360 + 1721086.5
else:
self.JD = int(365.25*self.YY) + int(30.59*(MM-2)) + DD - self.long/360 + 1721086.5
if SP2 > 1582.78: # グレゴリオ暦以降
self.JD = self.JD + int(self.YY/400) - int(self.YY/100) + 2
if MM > 12:
MM = MM - 12
self.YY = self.YY + 1
self.JD = self.JD + HH/24 + MS/1440
self.ST = koseji(self.JD,self.long)*15 # ST 恒星時(度)
self.Cent = (self.JD - 2415021.0)/36525 # 元期1900年I.1 0.5
def Batch():
app.refresh()
plt.star_culc()
plt.star_display()
def update(event):
global LAT
global long
global ymd
global ST
global Cent
global YY
global JD
gvl.getV()
Dtime = gvl.D_time
Dtime = float(Dtime)
Ydate = gvl.Y_date
Ydate = float(Ydate)
long = gvl.LONG
long = float(long)
LAT = gvl.Lat
LAT = float(LAT)
tm = Time(Ydate, Dtime, long)
tm.Julian()
JD = tm.JD
ST = tm.ST
Cent = tm.Cent
YY = tm.YY
ymd = JDT(JD)
Batch()
def Timeforward():
global ST
global JD
global ymd
ymd[3] = ymd[3] + 1
ST = ST + 15
JD = JD + (1/24)
ymd = JDT(JD)
Batch()
def Timeback():
global ST
global JD
global ymd
ST = ST - 15
JD = JD - (1/24)
ymd = JDT(JD)
Batch()
def Dateforward():
global ST
global JD
global ymd
ST = ST + 1.002738
JD = JD + 1
ymd = JDT(JD)
Batch()
def Dateback():
global ST
global JD
global ymd
ST = ST - 1.002738
JD = JD -1
ymd = JDT(JD)
Batch()
class Application(tk.Frame):
def __init__(self,master = None):
super().__init__(master)
master.title(u"北極星野（星図）の表示プログラム_Ver.1.1")
master.geometry("1100x750")
self.c0 = tk.Canvas(master=None, width = 1100, height = 750, bg="#001766")
self.pack()
self.create_widgets()
def create_widgets(self):
self.c0.create_text(955, 570, text="その日の時刻を１時間", font=('', 12), anchor='c', fill="white")
self.c0.create_text(955, 635, text="日付を１日", font=('', 12), anchor='c', fill='white')
self.c0.create_text(25, 667, text=" 紀元前はB.C.1年を0年として計算する。入力は-１で", font=('', 10), fill='white', anchor='w')
self.lb1 = tk.Label(text=u"観測地の緯度・経度(南緯は－，東経は＋）", fg='white', bg="#001766", anchor='w', font=('', 14)).place(x=730,
y=30)
self.inputbox1 = tk.Entry(width=4, font=('', 14))
self.inputbox1.place(x=820, y=60)
self.inputbox1.insert(tk.END, "34.5")
self.inputbox1.bind("<KeyPress-Return>", update)
self.inputbox2 = tk.Entry(width=6, font=('', 14))
self.inputbox2.place(x=900, y=60)
self.inputbox2.insert(tk.END, "135.8")
self.inputbox2.bind("<KeyPress-Return>", update)
self.lb2 = tk.Label(text="日付(YYYYMMDD) 時刻(hhmm)", fg='white', bg="#001766", anchor='w', font=('', 14)).place(x=800,
y=95)
self.inputbox3 = tk.Entry(width=10, font=('', 14))
self.inputbox3.place(x=850, y=120)
self.inputbox3.insert(tk.END, "6970822")
self.inputbox3.bind("<KeyPress-Return>", update)
self.inputbox4 = tk.Entry(width=6, font=('', 14))
self.inputbox4.place(x=980, y=120)
self.inputbox4.insert(tk.END, "2100")
self.inputbox4.bind("<KeyPress-Return>", update)
self.lb3 = tk.Label(text=u'入力→Enterで再表示します', width=25, font=('', 10), fg='#001766', bg='skyblue').place(x=870, y=165)
self.Button1 = tk.Button(text=u'進む>>', command=Timeforward, width=10, font=('', 10)).place(x=960, y=590)
self.Button2 = tk.Button(text=u'<<もどる', command=Timeback, width=10, font=('', 10)).place(x=860, y=590)
self.Button3 = tk.Button(text=u'進む>', command=Dateforward, width=10, font=('', 10)).place(x=960, y=650)
self.Button4 = tk.Button(text=u'<もどる', command=Dateback, width=10, font=('', 10)).place(x=860, y=650)
def refresh(self): # 再表示
global img_moon # create_imageに必要
self.c0.create_oval(170, 10, 910, 745, fill="#001766", outline="#001766")
self.c0.create_text(540, 20, text="S", font=('', 18), fill="yellow")
self.c0.create_text(540, 730, text="N", font=('', 18), fill="yellow")
self.c0.create_text(180, 375, text="W", font=('', 18), fill="yellow")
self.c0.create_text(900, 375, text="E", font=('', 18), fill="yellow")
self.c0.create_oval(200, 35, 880, 715, fill='black', outline='skyblue', width=1)
self.c0.pack()
if ymd[0] <= 0:
self.lb4 = tk.Label(text=f"B.C. {-ymd[0]}年 {ymd[1]}月 {ymd[2]}日 {ymd[3]} 時の北極 ", fg='white', \
bg="#001766", anchor='w', font=('', 14))
else:
self.lb4 = tk.Label(text=f"A.D. {ymd[0]}年 {ymd[1]}月 {ymd[2]}日 {ymd[3]} 時の北極 ", fg='white', \
bg="#001766", anchor='w', font=('', 14))
self.lb4.place(x=25, y=25)
self.lb5 = tk.Label(text=f"緯度= {LAT}°経度= {long}°", fg='white', bg="#001766", anchor \
='w', font=('', 14))
self.lb5.place(x=25, y=60)
# self.c0.create_oval(185, 35, 1015, 865, fill='black', outline='skyblue', width=1)
self.lb6 = tk.Label(text=f" ユリウス日は = {round(JD, 3)} 日 ", fg='white', bg="#001766", anchor \
='w', font=('', 10))
self.lb6.place(x=25, y=600)
self.lb7 = tk.Label(text=f" 恒星時は = {round(ST / 15, 1)} 時 ", fg='white', bg="#001766", anchor \
='w', font=('', 10))
self.lb7.place(x=25, y=630)
self.lb8 = tk.Label(text=f" 赤緯45°以上を示す 内側の円は赤緯80° 外側は60°", fg='white', bg="#001766", anchor \
='w', font=('', 10))
self.lb8.place(x=25, y=690)
sekido()
def point_star(self, X, Y, dir, color):
self.c0.create_oval(X-dir, Y-dir, X+dir, Y+dir, fill = color)
self.c0.pack()
def co_line(self, X1, Y1, X2, Y2, color):
self.c0.create_line(X1, Y1, X2, Y2, fill = color, smooth = "True")
self.c0.pack()
def text_in(self, X, Y, name, color):
self.c0.create_text(X, Y, text = name, font = ('',10), fill = color)
self.c0.pack()
def point_eclip(self, X, Y, dir, color):
self.c0.create_oval(X-dir, Y-dir, X+dir, Y+dir, outline = color, )
self.c0.pack()
class Get_Value(Application):
def __init__(self,master=None):
super().__init__(master)
self.Lat = 0
self.LONG = 0
self.Y_date = 0
self.D_time = 0
def getV(self):
self.Lat = self.inputbox1.get()
self.LONG = self.inputbox2.get()
self.Y_date = self.inputbox3.get()
self.D_time = self.inputbox4.get()
plt = Planetarium()
root = tk.Tk()
root.resizable(width=False, height=False)
app = Application(master=root) # tkinter(GUI)
gvl = Get_Value(master=root) # 設定変更値の取得
# 日時の計算
tm = Time(6970822, 2100, 135.8) # 初期設定（年月日，時刻，経度
tm.Julian()
JD = tm.JD
ST = tm.ST
Cent = tm.Cent
YY = tm.YY
long = tm.long # 経度
LAT = tm.LAT # 緯度
ymd = JDT(JD)
Batch()
if __name__ == '__main__':
app.mainloop()