ティコの天体観測#
ティコ・ブラーエの火星の観測結果を検証する#
(1546–1601) Tycho Brahe - Wikipedia
(1571–1630) Johannes Kepler - Wikipedia
ルドルフ表#
(1627) Rudolphine Tables - Wikipedia
(1576–1612) Rudolf II, Holy Roman Emperor - Wikipedia
ティコの観測ノート (全集)#
“Tychonis Brahe Dani Opera Omnia” Internet Archive: Digital Library of Free & Borrowable Books, Movies, Music & Wayback Machine
惑星の逆行#
%%ai vioras
惑星の逆行について
惑星の逆行は、一般的に地球から見た他の惑星の視覚的な動きに関連しています。通常、惑星は天空の中で「順行」し、東から西へと動きます。しかし、特定の期間に、惑星は「逆行」を開始し、西から東へと動くように見えます。これは、地球がその他の惑星よりも速く自転しているために起こります。これは、ある車がハイウェイで別の車を追い越すときのようなものです。追い越される車は後ろに移動しているように見えますが、実際には前方に進んでいます。
この現象は、主に水星、金星、火星、木星、土星の5つの惑星で観察されます。これらの惑星が逆行するとき、それは地球がそれらの惑星の周りの自転軌道を追い越しているという意味です。これらの惑星が逆行する期間は、それぞれの惑星と地球の相対的な位置と速度によります。
ここで重要なことは、逆行は視覚的な現象であるということです。実際には、惑星は自分の軌道を順方向に進み続けています。
例えば、火星の場合、約2年に一度逆行します。逆行の期間は数週間から数か月に及び、その間火星は西から東へと動くように見えます。しかし、これは我々が地球から見ているだけで、火星自体の動きが変わったわけではありません。
逆行は、古代の天文学者たちにとって大きな問題でした。彼らは地球が宇宙の中心で、全ての惑星が地球の周りを回っていると考えていたからです。この地球中心のモデルでは、惑星が逆行する理由を説明することができませんでした。しかし、16世紀にコペルニクスが太陽中心のモデルを提唱したことで、この問題は解決しました。太陽中心のモデルでは、地球が他の惑星を追い越すことにより、惑星が逆行するように見えることを説明できます。
地球から観測した火星の逆行をプロットする#
Center point (origin)
Earth (Geocentric)
Sun (Heliocentric)
%%ai_continue
heliocentricとgeocentricに適切な日本語はありますか？
heliocentricは「太陽中心の」、geocentricは「地球中心の」と訳されます。
%%ai_continue
赤道座標と黄道座標について
赤道座標とは、天球上の赤道を基準にして星座の位置を表す座標系です。赤道座標では、天球上の赤道を0度とし、北極星を90度として、その他の星座の位置を角度で表します。
一方、黄道座標とは、天球上の黄道を基準にして星座の位置を表す座標系です。黄道座標では、天球上の黄道を0度とし、春分点を90度として、その他の星座の位置を角度で表します。
赤道座標は、天体の運動を追跡するのに適しており、黄道座標は、太陽系の天体の運動を追跡するのに適しています。
%%ai_continue
太陽中心の赤道座標系と黄道座標系に違いはありますか？
太陽中心の赤道座標系と黄道座標系は、地球中心の赤道座標系と黄道座標系と同様に、基準点が異なるために異なります。
太陽中心の赤道座標系では、基準面は太陽の赤道面であり、基準点は春分点です。一方、太陽中心の黄道座標系では、基準面は太陽の黄道面であり、基準点は春分点です。
地球中心の赤道座標系と黄道座標系と同様に、太陽中心の赤道座標系と黄道座標系も、天体の位置を表すために使用されます。太陽系の天体の運動を追跡するためには、太陽中心の座標系が使用されます。
%%ai_continue
太陽の赤道面と黄道面は違いますか？
はい、太陽の赤道面と黄道面は異なります。太陽の赤道面は、太陽の自転軸に対して傾いており、地球から見ると太陽の北極と南極が存在します。一方、太陽の黄道面は、地球の公転面と太陽の赤道面の交点を基準に定義され、地球の公転軌道と交差する面です。太陽の黄道面は、地球から見ると、黄道と呼ばれる惑星の軌道面と交わる点が存在します。
!pip install -U solarsystem
Collecting solarsystem
Downloading solarsystem-0.1.5.tar.gz (15 kB)
Preparing metadata (setup.py) ... ?25ldone
?25hBuilding wheels for collected packages: solarsystem
Building wheel for solarsystem (setup.py) ... ?25ldone
?25h Created wheel for solarsystem: filename=solarsystem-0.1.5-py3-none-any.whl size=16608 sha256=5da010852820910e444d117b4ca9e6feb7fa71b62b1d2cd2ad7eeeb22419adfe
Stored in directory: /home/jovyan/.cache/pip/wheels/20/9c/87/dba03b1f814a064853b99b9e76da94672226c1608e910fd5c7
Successfully built solarsystem
Installing collected packages: solarsystem
Successfully installed solarsystem-0.1.5
import solarsystem
H = solarsystem.Heliocentric(year=2020, month=1, day=1, hour=12, minute=0 )
H.planets()
{'Mercury': (263.83033031837124, -4.057599521202387, 0.4659797616165433),
'Venus': (5.228267566604346, -3.2222136733454767, 0.7262291936644325),
'Earth': (100.5289245858366, 0.0, 0.9833180862528658),
'Mars': (214.38221616457562, 0.4891253753974966, 1.5891803735433014),
'Jupiter': (276.10498313633025, 0.10374961050190847, 5.228112674603031),
'Saturn': (292.512767008796, 0.05134540100060894, 10.05212207219113),
'Uranus': (35.35030250536327, 359.5159538071305, 19.809355998647174),
'Neptune': (348.0172656026235, -1.039905299592724, 29.914939199387618),
'Pluto': (292.7499413549187, 359.3290225249272, 33.87680754878506),
'Ceres': (290.86531789432115, -5.404211011344595, 2.9204640444111933),
'Chiron': (4.327136751763591, 2.943432379699923, 18.810534112295773),
'Eris': (23.548094614031402, -11.74427433497789, 95.99830322945104)}
G = solarsystem.Geocentric(year=1584, month=1, day=1, hour=12, minute=0 )
G.position()['Mars']
(277.79300336467145, -0.8614115012318369, 2.4085976885499947)
l = []
for y in range(1583,1600):
for m in range(1,13):
for d in range(1,30):
G = solarsystem.Geocentric(year=y, month=m, day=d, hour=12, minute=0 )
l.append(G.position()['Mars'][0])
l
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len(l)
5916
import matplotlib.pyplot as plt
import numpy as np
np.radians(l)
array([1.92940403, 1.92279211, 1.91608465, ..., 2.41407093, 2.41289642,
2.4114855 ])
plt.plot(range(5916), -np.radians(l))
[<matplotlib.lines.Line2D at 0x7b338b870410>]
位相アンラップ処理をして逆行だけを取り出す#
火星の公転周期: 687日
約1年11ヶ月で逆行が観測できる
plt.plot(range(5916), np.unwrap(np.radians(l))-np.linspace(0,57,num=5916))
[<matplotlib.lines.Line2D at 0x7b338b748710>]
時間指定が厄介なので、他のソフトを使う#
!pip install -U ephem
Collecting ephem
Downloading ephem-4.1.5-cp311-cp311-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (6.0 kB)
Downloading ephem-4.1.5-cp311-cp311-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (1.8 MB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 1.8/1.8 MB 33.0 MB/s eta 0:00:0000:01
?25hInstalling collected packages: ephem
Successfully installed ephem-4.1.5
import ephem
import matplotlib.pyplot as plt
import numpy as np
m = ephem.Mars()
m.compute('1584/1/1')
# 日心経度, 日心緯度
m.hlon, m.hlat
(4.880208969116211, -0.02591746859252453)
m0 = ephem.Mars(ephem.Date('1584/1/1'))
m1 = ephem.Mars(ephem.Date('1584/1/1')+1)
def hops(body): return body.hlon, body.hlat
ephem.separation(hops(m0), hops(m1))
0.010442553936505066
# 赤経, 赤緯
m.ra, m.dec
(4.89811066895129, -0.4190875793738444)
d = ephem.Date('1582/11/1')
l = []
for _ in range(1,365*(1600-1582)):
m0 = ephem.Mars(ephem.Date(d))
l.append(m0.ra)
d+=1
l;
len(l)
6569
#plt.plot(range(len(l)), np.unwrap(l)-np.linspace(0,60,num=len(l)))
plt.plot(range(len(l)), -np.array(l))
[<matplotlib.lines.Line2D at 0x7b338b7a0e10>]
チコの観測の検証#
import pandas as pd
import datetime
df = pd.read_excel('http://www.pafko.com/tycho/mars.xls', header=5)
df
| Unnamed: 0 | Year | Day | Time | Quote | Volume | Page | Unnamed: 7 | Year.1 | Month | ... | Day (adj) | Hour | Min | Days since 1 AD | Date | Unnamed: 16 | Dec (deg) | Dec (min) | Dec (sec) | Declination | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | NaN | 1582 | DIE 12 NOUEMBRIS, MANE. | NaN | Declinatio [MS] 23 7 B | 10 | 174 | NaN | 1582 | 11 | ... | 22 | NaN | NaN | 578150.500000 | 1582.889802 | 1 | 23 | 7 | NaN | 23.116667 |
| 1 | NaN | 1582 | DIE 30 DECEMBRIS | NaN | Afc. R. [MS] 107o 56' Declin. 26o 36' B. | 10 | 197 | NaN | 1582 | 12 | ... | 40 | NaN | NaN | 578198.500000 | 1583.021218 | 1 | 26 | 56 | NaN | 26.933333 |
| 2 | NaN | 1582 | DIE 27 DECEMBRIS | NaN | declinatio [MS] 26o 22 1/3' et Afcenfio Recta... | 10 | 200 | NaN | 1582 | 12 | ... | 37 | NaN | NaN | 578195.500000 | 1583.013005 | 1 | 26 | 22 | 20.0 | 26.372222 |
| 3 | NaN | 1583 | DIE 18 JANUARIJ, VESPERI. | NaN | Declinatio 27 18 minus bona | 10 | 244 | NaN | 1583 | 1 | ... | 28 | NaN | NaN | 578217.500000 | 1583.073238 | 1 | 27 | 18 | NaN | 27.300000 |
| 4 | NaN | 1584 | DIE 13 NOUEMBRIS, A.M. | H.13 26 P.M. | Declinatio [MS] B. 15 54 | 10 | 321 | NaN | 1584 | 11 | ... | 23 | 13.0 | 26.0 | 578883.059722 | 1584.895441 | 1 | 15 | 54 | NaN | 15.900000 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 918 | NaN | 1600 | 24 Januarij. | NaN | Declinatio [MS] 21 56 10 B. | 13 | 221 | NaN | 1600 | 1 | ... | 34 | 10.0 | NaN | 584432.916667 | 1600.090121 | 1 | 21 | 56 | 10.0 | 21.936111 |
| 919 | NaN | 1600 | Die 2 Martij. | H.10 P.M. | Declinatio [MS] 24 8 0 B. | 13 | 224 | NaN | 1600 | 3 | ... | 12 | 10.0 | NaN | 584470.916667 | 1600.194159 | 1 | 24 | 8 | 0.0 | 24.133333 |
| 920 | NaN | 1600 | Die 9 Martij | H.9 1/2 P.M. | Declinatio [MS] 23 59 0 | 13 | 224 | NaN | 1600 | 3 | ... | 19 | 9.0 | NaN | 584477.875000 | 1600.213210 | 1 | 23 | 59 | 0.0 | 23.983333 |
| 921 | NaN | 1600 | Die 15 Martij | H.9 1/3 | Declinatio [MS] 23 41 40 | 13 | 224 | NaN | 1600 | 3 | ... | 25 | 9.0 | NaN | 584483.875000 | 1600.229637 | 1 | 23 | 41 | 40.0 | 23.694444 |
| 922 | NaN | 1600 | Die 16 Martij | H. 9 1/4 | Declinatio [MS] 23 37 30 | 13 | 224 | NaN | 1600 | 3 | ... | 26 | 9.0 | NaN | 584484.875000 | 1600.232375 | 1 | 23 | 37 | 30.0 | 23.625000 |
923 rows × 21 columns
print(ephem.Date(ephem.Date(datetime.datetime(1584,11,23,13,26))+(584484.88-578883.06)))
1600/3/26 09:06:48
df2=df.iloc[:,[14,20]]
df2.set_index('Days since 1 AD', inplace=True)
plt.scatter(range(len(l)), -np.array(l)/3+1.1, marker='.', alpha=0.01)
plt.scatter(df2.index.values - df2.index.values[0],
np.radians(df2.iloc[:,0].values),
c=None, marker='.', alpha=.5)
plt.show()
後半のデータを修正･･･
import bisect
bisect.bisect(df2.index.values - df2.index.values[0], 3000)
249
x=np.concatenate([
df2.iloc[:268,0].values,
df2.iloc[268,0] * 2 - df2.iloc[268:,0].values])
plt.scatter(range(len(l)), -np.array(l)/3+1.1, marker='.', alpha=0.01)
plt.scatter(df2.index.values - df2.index.values[0],
np.radians(x),
c=None, marker='.', alpha=.5)
plt.show()
