NASA の機関である JPL(Jet Propulsion Laboratory) が惑星探査用に編纂・発行している月・惑星の暦の最新版 DE430 のバイナリ形式のデータを C++ で読み込んでみました。

過去には Ruby, Python, Fortran95 で行っています。

0. 前提条件

  • Debian GNU/Linux 10.8 (64bit) での作業を想定。
  • GCC 9.2.0 (G++ 9.2.0) (C++17) でのコンパイルを想定。

1. 天文暦バイナリデータについて

当ブログ過去記事を参照のこと。

また、天文暦データには各種バージョンが存在するが、日本の国立天文台が現在使用している DE430 を当方も採用する。

2. ソースコードの作成

ここでは、実行部分のみ掲載。(全てのコードは GitHub リポジトリとして公開している)

jpl_read_430.cpp
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/***********************************************************
  JPLEPH(JPL の DE430 バイナリデータ)読み込み
  : データの読み込みテストのため、対象日時・天体番号は定数で設定している
       1: 水星 (Mercury)
       2: 金星 (Venus)
       3: 地球 - 月の重心 (Earth-Moon barycenter)
       4: 火星 (Mars)
       5: 木星 (Jupiter)
       6: 土星 (Saturn)
       7: 天王星 (Uranus)
       8: 海王星 (Neptune)
       9: 冥王星 (Pluto)
      10: 月(地心) (Moon (geocentric))
      11: 太陽 (Sun)
      12: 地球の章動(1980年IAUモデル) (Earth Nutations in longitude and obliquity (IAU 1980 model))
      13: 月の秤動 (Lunar mantle libration)

    DATE        AUTHOR       VERSION
    2020.12.23  mk-mode.com  1.00 新規作成

  Copyright(C) 2020 mk-mode.com All Rights Reserved.

  ----------------------------------------------------------
  引数 : 天体番号(1-13) ユリウス日
         * ユリウス日無指定なら現在(システム日時)と判断。
         * 天体番号も無指定なら太陽(11)と判断。
***********************************************************/
#include "jpl.hpp"

#include <cstdlib>   // for EXIT_XXXX
#include <iomanip>
#include <iostream>
#include <string>

int main(int argc, char* argv[]) {
  static constexpr unsigned int kNoSun = 11;         // 天体番号(太陽)
  static constexpr double       kJd0   = 2458849.5;  // 2000-01-01 UTC
  namespace ns = jpl_read_430;
  unsigned int astr = kNoSun;  // 天体番号
  double       jd   = kJd0;    // ユリウス日
  unsigned int i;

  try {
    if (argc > 1) {
      // 天体番号取得
      astr = atoi(argv[1]);
      if (astr < 1 || astr > 13) {
        std::cout << "[USAGE] ./jpl_read_430 [ASTR_NO [JULIAN_DAY]]"
                  << std::endl
                  << "        !!! ASTR_NO must be between 1 and 13 !!!"
                  << std::endl;
        return EXIT_FAILURE;
      }
      // ユリウス日取得
      if (argc > 2) { jd = atof(argv[2]); }
    }

    // バイナリファイル読み込み
    ns::Jpl o_jpl(jd);
    o_jpl.read_bin();

    // 結果出力
    // (単に取得した情報を確認するためだけのものなので、
    //   視認性は考慮していない)
    std::cout << "---" << std::endl;
    std::cout << " Astro No. : " << astr << std::endl;
    std::cout << "Julian Day : " << std::fixed << std::setprecision(1)
              << jd << std::endl;
    std::cout << "=== TTL" << std::endl;
    for (i = 0; i < 3; ++i) {
      std::cout << o_jpl.ttls[i] << std::endl;
    }
    std::cout << "=== CNAM" << std::endl;
    for (i = 0; i < 800; ++i) {
      std::cout << o_jpl.cnams[i] << std::endl;
    }
    std::cout << "=== SS" << std::endl;
    for (i = 0; i < 3; ++i) {
      std::cout << o_jpl.sss[i] << std::endl;
    }
    std::cout << "=== NCON" << std::endl;
    std::cout << o_jpl.ncon << std::endl;
    std::cout << "=== AU" << std::endl;
    std::cout << o_jpl.au << std::endl;
    std::cout << "=== EMRAT" << std::endl;
    std::cout << std::fixed << std::setprecision(14)
              << o_jpl.emrat << std::endl;
    std::cout << "=== NUMDE" << std::endl;
    std::cout << o_jpl.numde << std::endl;
    std::cout << "=== IPT" << std::endl;
    for (i = 0; i < 13; ++i) {
      std::cout << "["
                << o_jpl.ipts[i][0] << ", "
                << o_jpl.ipts[i][1] << ", "
                << o_jpl.ipts[i][2] << "]" << std::endl;
    }
    std::cout << "=== CVAL" << std::endl;
    for (i = 0; i < o_jpl.ncon; ++i) {
      std::cout << std::scientific << o_jpl.cvals[i] << std::endl;
    }
    std::cout << "=== Record Index" << std::endl;
    std::cout << o_jpl.idx << std::endl;
    std::cout << "=== Julian Day (start, end)" << std::endl;
    std::cout << std::fixed << std::setprecision(1)
              <<  o_jpl.jds[0] << ", " << o_jpl.jds[1] << std::endl;
    std::cout << "=== COEFF" << std::endl;
    std::cout << std::fixed << std::setprecision(14);
    for (auto& v_0 : o_jpl.coeffs[astr - 1] ) {
      for (auto& v_1 : v_0) {
        for (auto& v_2 : v_1) {
          std::cout << v_2 << std::endl;
        }
        std::cout << "-" << std::endl;
      }
    }
    //for (i = 0; i < 13; ++i) {
    //  std::cout << o_jpl.coeffs[i].size() << std::endl;
    //}
  } catch (...) {
      std::cerr << "EXCEPTION!" << std::endl;
      return EXIT_FAILURE;
  }

  return EXIT_SUCCESS;
}

3. ソースコードのビルド(コンパイル&リンク)

  • リポジトリMakefile があるので、それを使用して make するだけ。(リビルドする際は make clean をしてから)
  • 上記の Makefile 内では別途個別にインストールした c++92 コマンドを使用しているが、通常は c++ であるので注意。
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$ make

4. 準備

5. 動作確認

  • 第1引数に天体番号(1-13)、第2引数にユリウス日を指定して実行。
  • 単に取得した情報を確認するためだけのものなので、視認性は考慮していない。
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$ ./jpl_read_430 11 2459276.125
---
 Astro No. : 11
Julian Day : 2459276.1
=== TTL
JPL Planetary Ephemeris DE430/LE430
Start Epoch: JED=  2287184.5 1549-DEC-21 00:00:00
Final Epoch: JED=  2688976.5 2650-JAN-25 00:00:00
=== CNAM
DENUM
LENUM
TDATEF
TDATEB
JDEPOC
CENTER
CLIGHT
BETA
GAMMA
AU
EMRAT
GM1
GM2
GMB
GM4
GM5
GM6
GM7
GM8
GM9
GMS
XS
YS
ZS
XDS
YDS
ZDS
X1
Y1
Z1
XD1
YD1
ZD1
X2
Y2
Z2
XD2
YD2
ZD2
XB
YB
ZB
XDB
YDB
ZDB
X4
Y4
Z4
XD4
YD4
ZD4
X5
Y5
Z5
XD5
YD5
ZD5
X6
Y6
Z6
XD6
YD6
ZD6
X7
Y7
Z7
XD7
YD7
ZD7
X8
Y8
Z8
XD8
YD8
ZD8
X9
Y9
Z9
XD9
YD9
ZD9
XM
YM
ZM
XDM
YDM
ZDM
XC
YC
ZC
XDC
YDC
ZDC
PHI
THT
PSI
OMEGAX
OMEGAY
OMEGAZ
PHIC
THTC
PSIC
OMGCX
OMGCY
OMGCZ
ASUN
J2SUN
J3SUN
J4SUN
RE
J2E
J3E
J4E
J5E
J2EDOT
K2E0
K2E1
K2E2
TAUE0
TAUE1
TAUE2
TAUER1
TAUER2
ROTEX
ROTEY
DROTEX
DROTEY
AM
K2M
TAUM
LBET
LGAM
IFAC
COBLAT
KVC
PSIDOT
J2M
C22M
J3M
C31M
S31M
C32M
S32M
C33M
S33M
J4M
C41M
S41M
C42M
S42M
C43M
S43M
C44M
S44M
J5M
C51M
S51M
C52M
S52M
C53M
S53M
C54M
S54M
C55M
S55M
J6M
C61M
S61M
C62M
S62M
C63M
S63M
C64M
S64M
C65M
S65M
C66M
S66M
J7M
J8M
J9M
C71M
S71M
C72M
S72M
C73M
S73M
C74M
S74M
C75M
S75M
C76M
S76M
C77M
S77M
C81M
S81M
C82M
S82M
C83M
S83M
C84M
S84M
C85M
S85M
C86M
S86M
C87M
S87M
C88M
S88M
C91M
S91M
C92M
S92M
C93M
S93M
C94M
S94M
C95M
S95M
C96M
S96M
C97M
S97M
C98M
S98M
C99M
S99M
MA0001
MA0002
MA0003
MA0004
MA0005
MA0006
MA0007
MA0008
MA0009
MA0010
MA0011
MA0012
MA0013
MA0014
MA0015
MA0016
MA0017
MA0018
MA0019
MA0020
MA0021
MA0022
MA0023
MA0024
MA0025
MA0026
MA0027
MA0028
MA0029
MA0030
MA0031
MA0032
MA0034
MA0035
MA0036
MA0037
MA0038
MA0039
MA0040
MA0041
MA0042
MA0043
MA0044
MA0045
MA0046
MA0047
MA0048
MA0049
MA0050
MA0051
MA0052
MA0053
MA0054
MA0056
MA0057
MA0058
MA0059
MA0060
MA0062
MA0063
MA0065
MA0068
MA0069
MA0070
MA0071
MA0072
MA0074
MA0075
MA0076
MA0077
MA0078
MA0079
MA0080
MA0081
MA0082
MA0083
MA0084
MA0085
MA0086
MA0087
MA0088
MA0089
MA0090
MA0091
MA0092
MA0093
MA0094
MA0095
MA0096
MA0097
MA0098
MA0099
MA0100
MA0102
MA0103
MA0104
MA0105
MA0106
MA0107
MA0109
MA0110
MA0111
MA0112
MA0113
MA0114
MA0115
MA0117
MA0118
MA0120
MA0121
MA0124
MA0127
MA0128
MA0129
MA0130
MA0132
MA0134
MA0135
MA0137
MA0139
MA0140
MA0141
MA0143
MA0144
MA0145
MA0146
MA0147
MA0148
MA0150
MA0154
MA0156
MA0159
MA0160
MA0162
MA0163
MA0164
MA0165
MA0168
MA0171
MA0172
MA0173
MA0175
MA0176
MA0177
MA0181
MA0185
MA0187
MA0191
MA0192
MA0194
MA0195
MA0196
MA0198
MA0200
MA0201
MA0203
MA0205
MA0206
MA0209
MA0210
MA0211
MA0212
MA0213
MA0216
MA0221
MA0223
MA0224
MA0225
MA0227
MA0230
MA0233
MA0236
MA0238
MA0240
MA0241
MA0247
MA0250
MA0259
MA0266
MA0268
MA0275
MA0276
MA0283
MA0287
MA0303
MA0304
MA0308
MA0313
MA0322
MA0324
MA0326
MA0328
MA0329
MA0334
MA0335
MA0336
MA0337
MA0338
MA0344
MA0345
MA0346
MA0347
MA0349
MA0350
MA0354
MA0356
MA0357
MA0358
MA0360
MA0362
MA0363
MA0365
MA0366
MA0369
MA0372
MA0373
MA0375
MA0377
MA0381
MA0385
MA0386
MA0387
MA0388
MA0389
MA0393
MA0404
MA0405
MA0407
MA0409
MA0410
MA0412
MA0415
MA0416
MA0419
MA0420
MA0423
MA0424
MA0426
MA0431
MA0432
MA0433
MA0442
MA0444
MA0445
MA0449
MA0451
MA0454
MA0455
MA0464
MA0465
MA0466
MA0469
MA0471
MA0476
MA0481
MA0485
MA0488
MA0489
MA0490
MA0491
MA0498
MA0503
MA0505
MA0506
MA0508
MA0511
MA0514
MA0516
MA0517
MA0521
MA0532
MA0535
MA0536
MA0545
MA0547
MA0554
MA0566
MA0568
MA0569
MA0584
MA0585
MA0591
MA0593
MA0595
MA0596
MA0598
MA0599
MA0602
MA0604
MA0618
MA0623
MA0626
MA0635
MA0654
MA0663
MA0667
MA0674
MA0675
MA0680
MA0683
MA0690
MA0691
MA0694
MA0696
MA0702
MA0704
MA0705
MA0709
MA0712
MA0713
MA0735
MA0739
MA0740
MA0747
MA0751
MA0752
MA0760
MA0762
MA0769
MA0772
MA0773
MA0776
MA0778
MA0780
MA0784
MA0786
MA0788
MA0790
MA0791
MA0804
MA0814
MA0849
MA0895
MA0909
MA0914
MA0980
MA1015
MA1021
MA1036
MA1093
MA1107
MA1171
MA1467




































































































































































































































=== SS
2287184.5
2688976.5
32.0
=== NCON
572
=== AU
149597870.7
=== EMRAT
81.30056907419062
=== NUMDE
430
=== IPT
[3, 14, 4]
[171, 10, 2]
[231, 13, 2]
[309, 11, 1]
[342, 8, 1]
[366, 7, 1]
[387, 6, 1]
[405, 6, 1]
[423, 6, 1]
[441, 13, 8]
[753, 11, 2]
[819, 10, 4]
[899, 10, 4]
=== CVAL
4.30000000000000e+02
4.30000000000000e+02
2.01303292004380e+13
2.01303291910070e+13
2.44040050000000e+06
0.00000000000000e+00
2.99792458000000e+05
1.00000000000000e+00
1.00000000000000e+00
1.49597870700000e+08
8.13005690741906e+01
4.91248045036476e-11
7.24345233264412e-10
8.99701139019987e-10
9.54954869555077e-11
2.82534584083387e-07
8.45970607324503e-08
1.29202482578296e-08
1.52435734788511e-08
2.17844105197418e-12
2.95912208285591e-04
4.50250878464055e-03
7.67076427091007e-04
2.66057917766978e-04
-3.51749536075523e-07
5.17762640983340e-06
2.22910217891203e-06
3.61762716560282e-01
-9.07819721567660e-02
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3.36749397200576e-03
2.48945205576834e-02
1.29463004097041e-02
6.12751940835072e-01
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1.09520684235282e-02
1.56176842678677e-02
6.33110570297786e-03
1.20517414101385e-01
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1.68112683097838e-02
1.74830923073434e-03
7.58202897383129e-04
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1.44816530570476e-02
2.42463076836469e-04
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1.09201259423734e-03
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7.89439068290953e+00
4.59647805517127e+00
1.55869584283190e+00
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4.33581034174663e-03
1.92864631686016e-03
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2.21190391015615e-04
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2.64276984798006e-03
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5.12830031411853e-03
3.82392784201737e-01
1.29416700274878e+00
4.57372418599143e-05
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2.29944860189922e-01
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4.11019464886527e-01
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2.29648796522997e-01
6.96000000000000e+05
2.11060885327268e-07
0.00000000000000e+00
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6.37813630000000e+03
1.08262545000000e-03
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3.35000000000000e-01
3.20000000000000e-01
3.20000000000000e-01
6.40000000000000e-02
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7.36321902280419e-03
2.53529786333887e-03
5.67542033228935e-03
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2.76899155744835e-04
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1.73800000000000e+03
2.40590000000000e-02
9.58305472733067e-02
6.31021319348873e-04
2.27731714800919e-04
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2.46239047891981e-04
1.63656165337095e-08
0.00000000000000e+00
2.03215684649526e-04
2.23827405905600e-05
8.45970269745946e-06
2.84807411955929e-05
5.89155515553186e-06
4.84494206197706e-06
1.68447439627839e-06
1.67561781341146e-06
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1.57892027892457e-06
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7.42216083840529e-07
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7.11995379673533e-07
1.71078866734304e-07
1.53997504249045e-08
2.87362576163343e-07
2.14447043192185e-08
5.26521107201468e-10
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1.40047655617234e-13
3.10444819893871e-14
3.61753831714794e-15
3.85475018780881e-14
3.74873628455203e-16
8.31241921267337e-16
2.13643444257141e-15
5.89425652970691e-16
1.07784100424073e-15
1.23580078729412e-14
1.33153625545997e-15
1.93177578518292e-16
1.79700489450745e-15
1.10064567957507e-15
4.67830741835090e-15
3.41158682619381e-15
2.08150639646974e-16
2.00892773665113e-16
1.03564484013119e-15
9.19980747763091e-17
2.52944287204100e-16
1.20262444348346e-15
1.89533176041978e-16
1.89390166752538e-15
7.23984152236621e-17
1.63734395226108e-16
3.88800389854579e-16
2.92627274429453e-16
1.97584236512452e-15
1.48201901643753e-16
6.34328047364860e-15
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1.15639547136458e-16
5.73458156633686e-17
1.74595572627050e-15
1.37206175961378e-16
4.55859924880692e-16
1.41442289208981e-16
3.59349348076176e-16
1.10318518229683e-16
1.50793337119652e-15
1.00446598396309e-16
3.43334441285917e-16
6.22510183873803e-17
1.55860000000000e-16
1.45216789548422e-16
5.57648047680854e-16
1.56785041404748e-16
8.21450000000000e-16
3.61865469702973e-16
1.46557349756319e-16
5.40012140874342e-17
1.48698562934496e-16
3.67820000000000e-16
4.83520000000000e-16
2.11243836059995e-15
7.37998534437523e-17
2.29797581279715e-16
6.34077834952170e-17
1.87801229589893e-17
9.90000118979590e-19
5.55346562874691e-17
9.07080484411450e-16
1.15342108493159e-16
1.35581713067349e-16
2.29555939063746e-15
7.68088477470000e-17
2.28615933395781e-16
8.06351842900558e-17
6.53992577244024e-17
2.70714167365278e-16
3.22840000000000e-16
8.45943072895968e-16
2.41931605646407e-16
3.34070052970452e-16
3.67379607992342e-17
1.91515627988508e-16
5.48467242911317e-16
3.64149739778329e-16
1.48589708382529e-16
1.29879292391702e-16
1.11871833145008e-16
3.41769850174724e-16
1.97353139110484e-16
3.41067697975349e-16
5.19812697945750e-15
2.93765207953148e-16
6.96000000000000e-17
1.08862665088002e-16
1.81244939644586e-16
9.31594859406562e-16
7.25386164346611e-17
1.09756310328225e-15
1.94849861155713e-16
2.81235774586577e-17
2.74856688034015e-16
6.26740000000000e-16
8.59780218818313e-17
6.11232197266831e-17
2.17605956141595e-17
1.17169915406794e-17
2.00383935095216e-17
5.01889934520749e-17
2.22111336158284e-16
3.83508917087800e-16
6.15306415407552e-17
6.91187747327401e-17
2.15014674336123e-16
6.42603995331864e-17
4.63868801607939e-16
1.44979767976933e-17
1.66437787258822e-16
1.69956695263314e-16
3.59530000000000e-16
1.20495494885782e-16
9.09429441579076e-17
1.43837480044679e-16
1.59234708844923e-16
9.95816201002552e-17
1.04361036125066e-16
4.76375353165425e-16
9.45370522582010e-17
1.49386680301336e-16
1.11777344239748e-16
8.89506728492704e-16
5.25616867849366e-15
2.91750035064825e-16
1.54560085386599e-16
5.02042422129257e-16
1.42681578483330e-16
8.59762026371732e-17
7.13824339752935e-17
1.18928144393177e-16
6.21574606623669e-16
1.79893748114765e-16
4.99820481258925e-17
5.81679210057328e-17
2.08180128309057e-16
1.97251539856938e-16
2.52061449253389e-16
1.95761609064233e-16
3.05671194466365e-16
4.77435477387998e-17
1.48574053476563e-16
1.63082309665981e-16
1.58301988046999e-16
2.15815568176360e-16
1.75589918332470e-15
1.21964875174107e-16
2.26710334145991e-16
4.55595956637724e-16
1.03549725015276e-16
3.78647503308948e-16
3.36297549276104e-16
4.11726826839954e-17
1.53529788855662e-16
1.25837659264500e-16
7.61714098728427e-17
6.46776721323746e-17
2.87164048267020e-16
9.54912821588765e-17
6.24856870846376e-17
1.11528013303482e-16
=== Record Index
5377
=== Julian Day (start, end)
2459248.5, 2459280.5
=== COEFF
-1036100.40018406498712
-7849.11334081224504
17.10702605395267
0.09730442395558
0.01121604993384
-0.00129075146622
-0.00001611395246
0.00002629052926
-0.00000391315055
0.00000006405643
0.00000007589683
-
783683.54256980703212
-6857.32945135365026
-20.62397390316596
-0.05383368124948
0.00612662989230
0.00079952613240
-0.00019132203588
0.00001428233056
0.00000159062294
-0.00000057009603
0.00000005915065
-
358424.17231651901966
-2698.57789202705499
-9.29764421978406
-0.03799708951343
0.00194972112477
0.00056068433433
-0.00010046138992
0.00000490429087
0.00000125537527
-0.00000031118322
0.00000002372284
-
-1051656.97095572808757
-7706.10759445215717
18.70221558069586
0.13625317278718
-0.00199875401109
-0.00011348732842
0.00001925394554
-0.00000200451535
0.00000017079249
-0.00000000853570
-0.00000000026007
-
769803.21015249157790
-7022.98002249968158
-20.60362860438559
0.04883023850386
0.00409171451518
-0.00024136948819
0.00001180983535
-0.00000012020640
-0.00000008038291
0.00000001534029
-0.00000000174257
-
352951.77522372710519
-2773.95111812624191
-9.45720768401200
0.01030056188949
0.00224556637289
-0.00011565627618
0.00000438276075
0.00000014331115
-0.00000006057559
0.00000000909285
-0.00000000091059
-

JPL バイナリデータの読み込みができれば、そのデータを利用した天体の正確な位置計算が可能になります。

以上、