およそ５等星以上の恒星データや星座線，惑星の軌道要素などを使ってある年月日，時刻の星空を再現するプログラムを作ってみました。惑星位置の元期は2008年で，200年前後なら月や惑星の位置にそれほど誤差は生じません（ステラナビゲータで確認しました）。また，1000年単位では，歳差の影響が出ますので，その補正も追加しました。ソースコードはおよそ700行もあって，長いかもしれません。すなわちあまり上手なプログラムとは言えないしろものですが，教材として参考にしていただけたらと思います。恒星データは Astro Commons (アストロ・コモンズ)。 http://astronomy.webcrow.jp/help/ から。計算などは，中野主一著「マイコンで解く天体の謎」と長沢工著「天体の位置計算」をもとにしています。実行には，numpyモジュールを同梱しているAnacondaをインストールする必要があります。下記のCSVファイルを同一ディレクトリに置いてpythonを起動して試してください。
- 恒星データ star.csv
- 星座名データ con-name.csv
- 星座線データ con-line.csv
- 惑星軌道要素データ planet-element-2008.csv
- 月の略算位置データ luna-element.csv
import tkinter as tk
import csv
import math
import numpy as np
import pandas as pd
def JDT(mjd): #ユリウス日をグレゴリオ暦に直す計算（こよみ便利帳より）
jd = mjd + 2400000.5
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)
DD = B - K - int(30.6001 * E) + (jd + 0.5) - int(jd + 0.5)
if E < 13.5:
MM = E -1
else:
MM = E -13
if MM > 2.5:
YY = C - 4716
else:
YY = C - 4715
if MM >= 13:
YY = YY + 1
MM = MM -12
hh = DD - int(DD)
DD = int(DD)
hh = round(hh*24 + 9)
return [YY,MM,DD,hh]
def koseji(mjd): # 恒星時の計算
ST = 0.67239 + 1.00273781*(mjd-40000) + 139.754/360
ST = (ST - int(ST))*24
return ST
def rotate_X1(deg): # X軸回転の行列
r = np.radians(deg)
C = np.cos(r)
S = np.sin(r)
R_x = np.matrix((
(1, 0, 0),
(0, C, S),
(0, -S, C)
))
return R_x
def rotate_Y1(deg): # 緯度を天頂方向にY軸回転の行列
r = np.radians(deg)
C = np.cos(r)
S = np.sin(r)
R_y = np.matrix((
(C, 0, -S),
(0, 1, 0),
(S, 0, C)
))
return R_y
def rotate_Z1(deg): # 恒星時に直すZ軸回転の行列
r = np.radians(deg)
C = np.cos(r)
S = np.sin(r)
R_z = np.matrix((
(C, S, 0),
(-S, C, 0),
(0, 0, 1)
))
return R_z
def yogen_AD(arfa,drta): #方向余弦の計算
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)
AD = np.array([L,M,N])
AD = AD.reshape(3,1)
return AD
def saisa_hosei(ad): #歳差補正(ニューカムのパラメータによる）
t = T1/100
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
a = rotate_Z1(-z-90)
b = rotate_X1(s)
c = rotate_Z1(90-f)
e = a * b * c * ad
return e
def horizon(ad): # 地平座標の計算（ST;恒星時 F;緯度 ad;方向余弦)
a = rotate_Y1(90 - F)
b = rotate_Z1(ST)
c = a * b * ad
h = math.asin(c[2])
h = math.degrees(h)
A = math.atan(-c[1]/c[0])
A = math.degrees(A)
if c[0] < 0. :
A = A + 180.
return [h,A]
def dispXY(hh,AA):
dot = 580 #画面のパラメータ 中心座標（600,450)
r = dot * math.sin(math.radians((90-hh)/2))
x = r * math.sin(math.radians(AA)) + 600
y = r * math.cos(math.radians(AA)) + 450
return [x,y]
def kepler(e,L0,n): #ケプラー方程式の解を求める
L1 = n * T0 + L0
L1 = math.radians(L1)
u0 = L1
du = (L1 - u0 + e*math.sin(u0))/(1 - e*math.cos(u0))
u1 = u0 + du
while du > 0.00000001:
du = (L1 - u1 + e*math.sin(u1))/(1 - e*math.cos(u1))
u1 = u1 + du
return u1
def solarpos(x,y,i,Om,w): #惑星の日心赤道座標の計算
i = math.radians(i)
Om = math.radians(Om)
w = math.radians(w)
c = 0.917436958
s = 0.397881172
xc = x*(math.cos(Om)*math.cos(w) - math.sin(Om)*math.cos(i)*math.sin(w)) - \
y*(math.cos(Om)*math.sin(w) + math.sin(Om)*math.cos(i)*math.cos(w))
yc = x*(math.sin(Om)*math.cos(w) + math.cos(Om)*math.cos(i)*math.sin(w)) - \
y*(math.sin(Om)*math.sin(w) - math.cos(Om)*math.cos(i)*math.cos(w))
zc = x*math.sin(i)*math.sin(w) + y*math.sin(i)*math.cos(w)
xq = xc
yq = yc*c - zc*s
zq = yc*s + zc*c
r = [xq,yq,zq]
return r
def magnitude(m):
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.linRae = 0
self.linDce = 0
class Star: #星クラス
def __init__(self):
self.stcnum = 0
self.stRA = 0
self.stDC = 0
self.stMg = 0
class Constelation: #星座クラス
def __init__(self):
self.con_name = ""
self.con_Ra = 0
self.con_Dc = 0
class Planet: #惑星クラス
def __init__(self):
self.pl_name = ""
self.pl_a = 0
self.pl_e = 0
self.pl_i = 0
self.pl_w = 0
self.pl_O = 0
self.pl_L0 = 0
self.pl_n = 0
self.pl_CL = 0
self.pl_mag = 0
class Planetarium: #プラネタリウムクラス
# 惑星表示のための変数
Xq = [0.0] * 8
Yq = [0.0] * 8
Zq = [0.0] * 8
Aq = [0.0] * 8
Bq = [0.0] * 8
Cq = [0.0] * 8
R = [0.0] * 8
pR = [0.0] * 8
pmag = [0.0] * 8
pl_RA = [0.0] * 8
pl_DC = [0.0] * 8
ph = [0.0] * 8
pA = [0.0] * 8
pname = [0] * 8
pcolor = [0] * 8
xp = [0.0] * 8
yp = [0.0] * 8
dr = [0.0] * 8
plane_counter = 0
#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
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 = list()
self.conline_list = list()
self.conste_list = list()
self.planet_list = list()
for i in range(3215):
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())
for i in range(8):
self.planet_list.append(Planet())
#データ読み込み
with open("star.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].stcnum = int(row[1])
self.star_list[i].stRA = float(row[2])*15 #赤経
self.star_list[i].stDC = float(row[3]) #赤緯
self.star_list[i].stMg = float(row[4])
i += 1
with open("con-line.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 = int(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].linRae = float(row[3]) #終点
self.conline_list[i].linDce = float(row[4])
i +=1
with open("con-name.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
with open("planet-element-2008.csv","r") as f:
t=csv.reader(f,delimiter=",")
i=0
for row in t:
self.planet_list[i].pl_a = float(row[0])
self.planet_list[i].pl_e = float(row[1])
self.planet_list[i].pl_i = float(row[2])
self.planet_list[i].pl_w = float(row[3])
self.planet_list[i].pl_O = float(row[4])
self.planet_list[i].pl_L0 = float(row[6])
self.planet_list[i].pl_n = float(row[5])
self.planet_list[i].pl_name =row[7]
self.planet_list[i].pl_CL = row[8]
self.planet_list[i].pl_mag = float(row[9])
i +=1
def star_culc(self): #恒星表示メソッド
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)
h = horizon(ad)
if h[0] < 8.0:
continue
self.hLs[m] = h[0]
self.ALs[m] = h[1]
ad = yogen_AD(line.linRae,line.linDce)
ad = saisa_hosei(ad)
h = horizon(ad)
self.hLe[m] = h[0]
self.ALe[m] = h[1]
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] = xy[0]
self.y1[i] = xy[1]
xy= dispXY(self.hLe[i],self.ALe[i])
self.x2[i] = xy[0]
self.y2[i] = xy[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] < 0.0:
continue
if star.stMg > 4.8:
continue
self.hh[n] = h[0]
self.AA[n] = h[1]
self.MG[n] = star.stMg
n += 1
self.star_counter = n
for i in range(self.star_counter):
xy= dispXY(self.hh[i],self.AA[i])
self.XX[i] = xy[0]
self.YY[i] = xy[1]
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] < 0.0:
continue
self.nh[n] = h[0]
self.nA[n] = h[1]
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] = xy[0]
self.yn[i] = xy[1]
def star_display(self):
# 星座線を引く
for i in range( self.line_counter):
c0.create_line(self.x1[i],self. y1[i], self.x2[i], self.y2[i], fill = 'blue')
c0.pack()
# 星のプロット
for i in range(self.star_counter):
self.rd[i] = magnitude(self.MG[i])
self.rd[i] = self.rd[i]/2
c0.create_oval(self.XX[i]-self.rd[i], self.YY[i]-self.rd[i],self.XX[i]+self.rd[i],self.YY[i]+self.rd[i],fill = 'white')
#星座名の表示
for i in range(self.con_counter):
c0.create_text(self.xn[i],self.yn[i],text = self.coname[i],font = ('',8),fill = 'red')
c0.pack()
def planet_culc(self): #惑星の位置計算と表示
i = 0
for p in self.planet_list:
self.pname[i] = p.pl_name
self.pcolor[i] = p.pl_CL
self.pmag[i] = p.pl_mag
u = kepler(p.pl_e,p.pl_L0,p.pl_n)
x = p.pl_a*(math.cos(u) - p.pl_e)
y = p.pl_a*math.sqrt(1-p.pl_e**2)*math.sin(u)
r = solarpos(x,y,p.pl_i,p.pl_O,p.pl_w)
self.Xq[i] = r[0]
self.Yq[i] = r[1]
self.Zq[i] = r[2]
self.pR[i] = math.sqrt(self.Xq[i]**2 + self.Yq[i]**2 + self.Zq[i]**2)
if i == 2: #地球の座標から太陽の方向を求める
eu = self.Xq[i]
ev = self.Yq[i]
ew = self.Zq[i]
self.Xq[i] = -self.Xq[i]
self.Yq[i] = -self.Yq[i]
self.Zq[i] = -self.Zq[i]
dE = math.sqrt(eu*eu + ev*ev + ew*ew) #地球と太陽の距離
i += 1
for i in range(8): # 地心赤道座標への変換
if i ==2:
self.Aq[i] = self.Xq[i]
self.Bq[i] = self.Yq[i]
self.Cq[i] = self.Zq[i]
else:
self.Aq[i] = self.Xq[i] - eu
self.Bq[i] = self.Yq[i] - ev
self.Cq[i] = self.Zq[i] - ew
self.R[i] = math.sqrt(self.Aq[i]**2 + self.Bq[i]**2 +self. Cq[i]**2)
self.pl_RA[i] = math.degrees(math.atan(self.Bq[i]/self.Aq[i]))
if self.Aq[i] <= 0.0:
self.pl_RA[i] = self.pl_RA[i] + 180
self.pl_DC[i] = math.degrees(math.asin(self.Cq[i]/self.R[i]))
if i == 2:
continue
mg = self.pmag[i] + 5*math.log10(self.pR[i]*self.R[i])
self.dr[i] = magnitude(mg)
self.plane_counter = 0 #惑星の地平座標を計算
for i in range(8):
ad = yogen_AD(self.pl_RA[i],self.pl_DC[i])
ad = saisa_hosei(ad)
h = horizon(ad)
if h[0] < 0.0 :
continue
self.ph[self.plane_counter] = h[0]
self.pA[self.plane_counter] = h[1]
self.pname[self.plane_counter] =self. pname[i]
self.dr[self.plane_counter] = self.dr[i]
self.pcolor[self.plane_counter] = self.pcolor[i]
self.plane_counter += 1
for i in range(self.plane_counter):
self.xy= dispXY(self.ph[i],self.pA[i])
self.xp[i] = self.xy[0]
self.yp[i] = self.xy[1]
def planet_display(self):
#惑星の表示
for i in range(self.plane_counter):
if self.pname[i] == "Solar":
c0.create_oval(self.xp[i]-6, self.yp[i]-6, self.xp[i]+6, self.yp[i]+6, fill = self.pcolor[i])
c0.create_text(self.xp[i]-10,self.yp[i]-12,text = self.pname[i], fill = 'white')
else:
self.dr[i] = self.dr[i]/2
c0.create_oval(self.xp[i]-self.dr[i], self.yp[i]-self.dr[i], self.xp[i]+self.dr[i], self.yp[i]+self.dr[i], fill = self.pcolor[i])
c0.create_text(self.xp[i]-10,self.yp[i]-8,text = self.pname[i], fill = 'white')
c0.pack()
def luna_display(self): #月の位置計算と表示
df = pd.read_csv('luna-element.csv',encoding='Shift_JIS')
A = 0
for i in range(64,68):
A = A + df.iat[i,1] * math.sin(math.radians(df.iat[i,2] + df.iat[i,3]*T1))
B = 0
for i in range(48,53):
B = B + df.iat[i,5] * math.sin(math.radians(df.iat[i,6] + df.iat[i,7]*T1))
sigmaA = 0
for i in range(0,62):
sigmaA = sigmaA + df.iat[i,1] * math.sin(math.radians(df.iat[i,2]+df.iat[i,3]*T1))
sigmaB = 0
for i in range(0,46):
sigmaB = sigmaB + df.iat[i,5] * math.sin(math.radians(df.iat[i,6]+df.iat[i,7]*T1))
ramda = 218.3161 + 4812.67881 * T1 + 6.2887 * math.sin(math.radians(134.961 \
+ 4771.9886 * T1 + A)) + sigmaA
beta = 5.1282 * math.sin(math.radians(93.273 + 4832.0202 * T1 + B)) + sigmaB
ramda = 360*(ramda/360 - int(ramda/360))
#黄道座標から赤道座標へ変換
U = math.cos(math.radians(beta)) * math.cos(math.radians(ramda))
V = math.cos(math.radians(beta)) * math.sin(math.radians(ramda))
W = math.sin(math.radians(beta))
c = 0.917436958
s = 0.397881172
xq = U
yq = V*c - W*s
zq = V*s + W*c
r = math.sqrt(xq*xq + yq*yq + zq*zq)
luna_RA = math.degrees(math.atan(yq/xq))
if xq <= 0.0:
luna_RA = luna_RA + 180
luna_DC = math.degrees(math.asin(zq/r))
ad = yogen_AD(luna_RA,luna_DC)
ad = saisa_hosei(ad)
h = horizon(ad)
if h[0] > 0.0 :
xy= dispXY(h[0],h[1])
c0.create_oval(xy[0]-6, xy[1]-6, xy[0]+6,xy[1]+6, fill ='pink')
c0.create_text(xy[0]-8,xy[1]-12,text = "Moon", fill = 'white')
class Time:
def __init__(self,Y,D):
self.Ydate = Y
self.Dtime = D
self.F = 35
self.MJD = 0
self.ST = 0
self.T0 = 0
self.T1 = 0
def Julian(self): #（修正ユリウス日）の計算
self.MJD = 0
if self.Ydate != abs(self.Ydate):
SP1 = -1
self.Ydate = abs(self.Ydate)
else:
SP1 = 1
YY = int(self.Ydate/10000)
MD = int(self.Ydate-10000*YY)
MM = int(MD/100)
DD = MD - 100 * MM
HH = int(self.Dtime/100)
MS = self.Dtime-100*HH
if SP1 < 0:
YY = YY * SP1
SP2 = YY + (MM-1)/12 + DD/365.25
if MM <= 2 :
MM = MM + 12
YY = YY - 1
if SP2 > 1582.78: #グレゴリオ暦以降
self.MJD = int(365.25*YY) + int(YY/400) - int(YY/100) + int(30.59*(MM-2)) - 678912
elif YY < 0:
self.MJD = int(365.25*YY) + int(30.59*(MM-2)) - 678915
else:
self.MJD = int(365.25*YY) + int(30.59*(MM-2)) - 678914
self.MJD = self.MJD + DD
self.MJD = self.MJD + HH/24 + MS/1440 - 0.375 #日本標準時で
self.ST = koseji(self.MJD)*15 # ST 恒星時(度で）
self.T0 = self.MJD - 54799.625 # 元期2008年11月1日
self.T1 = (self.MJD - 51544.5)/ 365.25 #月の略算引数用
def update(event):
global F
global ymd
global ST
global T0
global T1
global MJD
Ydate = inputbox2.get()
Ydate = int(Ydate)
tm = Time(Ydate,2000)
tm.Julian()
MJD = tm.MJD
ST = tm.ST
T0 = tm.T0
T1 = tm.T1
ymd = JDT(MJD)
F = inputbox1.get()
F = int(F)
refresh_draw()
p.star_culc()
p.star_display()
p.planet_culc()
p.planet_display()
p.luna_display()
def Timeforward():
global ST
global T0
global T1
ymd[3] = ymd[3] + 1
ST = ST + 15
T0 = T0 + (1/24)
T1 = T1 + (1/24)/365.25
refresh_draw()
p.star_culc()
p.star_display()
p.planet_culc()
p.planet_display()
p.luna_display()
def Timeback():
global ST
global T0
global T1
ymd[3] = ymd[3] - 1
ST = ST - 15
T0 = T0 - (1/24)
T1 = T1 - (1/24)/365.25
refresh_draw()
p.star_culc()
p.star_display()
p.planet_culc()
p.planet_display()
p.luna_display()
def Dateforward():
global ST
global T0
global T1
ymd[2] = ymd[2] + 1
ST = ST + 1.002738
T0 = T0 + 1
T1 = T1 + 1/365.25
refresh_draw()
p.star_culc()
p.star_display()
p.planet_culc()
p.planet_display()
p.luna_display()
def Dateback():
global ST
global T0
global T1
ymd[2] = ymd[2] - 1
ST = ST - 1.002738
T0 = T0 - 1
T1 = T1 - 1/365.25
refresh_draw()
p.star_culc()
p.star_display()
p.planet_culc()
p.planet_display()
p.luna_display()
def refresh_draw():
# 再表示
c0.itemconfigure(id, fill = '#001766')
lb3 = tk.Label(text=f"{ymd[0]}年 {ymd[1]}月 {ymd[2]}日 夜 {ymd[3] - 12} 時の星空 ", fg='white', \
bg="#001766", anchor='w', font=('', 14))
lb3.place(x=30, y=25)
lb4 = tk.Label(text=f"緯度= {F}°経度 139.74°(東京)", fg='white', bg="#001766", anchor \
='w', font=('', 14))
lb4.place(x=30, y=60)
c0.create_oval(185, 35, 1015, 865, fill='black', outline='skyblue', width=1)
lb5 = tk.Label(text=f" 修正ユリウス日は = {round(MJD, 2)} 日 ", fg='white', bg="#001766", anchor \
='w', font=('', 10))
lb5.place(x=30, y=750)
lb6 = tk.Label(text=f" 恒星時は = {round(ST / 15, 1)} 時 ", fg='white', bg="#001766", anchor \
='w', font=('', 10))
lb6.place(x=30, y=780)
# ====== 星座早見プログラム ======
# Tkinterによる画面の設定
p = Planetarium()
root = tk.Tk()
c0 = tk.Canvas(root, width = 1200, height = 900,bg="#001766")
root.title(u"星座早見")
id = c0.create_oval(185, 35, 1015, 865, fill = 'black',outline = 'skyblue',width =1)
c0.pack
c0.create_text(600 ,20 ,text = "N",font = ('',18),fill ="yellow")
c0.create_text(600 ,880,text = "S",font = ('',18),fill ="yellow")
c0.create_text(170 ,450,text = "E",font = ('',18),fill ="yellow")
c0.create_text(1030,450,text = "W",font = ('',18),fill ="yellow")
c0.create_text(1055,720, text = "その日の時刻を１時間",font = ('',12),anchor = 'c',fill ="white")
c0.create_text(1055,785, text = "日付を１日",font = ('',12),anchor = 'c',fill='white')
c0.create_text(35, 820,text = "惑星位置の元期は2008年11月1日",font = ('',10),fill = 'white',anchor = 'w')
# 日時の計算
tm = Time(20190101,2000)
tm.Julian()
MJD = tm.MJD
ST = tm.ST
T0 = tm.T0
T1 = tm.T1
F = tm.F #Fは緯度
ymd = JDT(MJD)
refresh_draw()
p.star_culc()
p.star_display()
p.planet_culc()
p.planet_display()
p.luna_display()
lb1 = tk.Label(text= u"観測地の緯度(南緯は－）で",fg = 'white',bg = "#001766",anchor ='w',font = ('',14)).place(x=900,y=35)
inputbox1 = tk.Entry(width = 5,font = ('',14))
inputbox1.place(x=980,y=65)
inputbox1.insert(tk.END,"35")
inputbox1.bind("<KeyPress-Return>",update)
lb2 = tk.Label(text= "日付(YYYYMMDD)を入力してください",fg = 'white',bg = "#001766",anchor ='w',font = ('',14)).place(x=900,y=95)
inputbox2 = tk.Entry(width = 10,font = ('',14))
inputbox2.place(x=980,y=120)
inputbox2.insert(tk.END,"20190101")
inputbox2.bind("<KeyPress-Return>",update)
lb3 = tk.Label(text=u'Enterで夜８時を表示します',width=22,font = ('',12),fg='#001766',bg='skyblue').place(x=980 , y=165)
Button1 = tk.Button(text=u'進む>>',command = Timeforward,width=10,font = ('',10) ).place(x=1060 , y=740)
Button2 = tk.Button(text=u'<<もどる',command = Timeback,width=10,font = ('',10) ).place(x=960 , y=740)
Button3 = tk.Button(text=u'進む>',command = Dateforward,width=10 ,font = ('',10)).place(x=1060 , y=800)
Button4 = tk.Button(text=u'<もどる',command = Dateback,width=10 ,font = ('',10)).place(x=960 , y=800)
root.resizable(width=False, height=False)
root.mainloop()