Monday, February 01, 2016

[pwtknnpy] ICRF in decimal

The International Celestial Reference Frame, now ICRF2, is a very impressive human achievement in science.  (Or perhaps better described as impressive engineering because there is no hypothesis being tested.)

Although its usefulness technically has limited scope in space and time, that scope is huge: any point in space where you don't get parallax on distant galaxies, and any point in time where the distant galaxies haven't done much proper motion.  I can think of no other human achievement which is so grand but limited in such a way.

I think merely the positions of quasars does not establish the 3 dimensional origin of the reference frame, e.g., the barycenter of the solar system, unless there is VLBI magic that I'm failing to understand.  The positions of the quasars are going to appear to be the same when viewed from any point in the solar system.  In order to establish an origin, I think one also needs a solar system model which can provide testable predictions of where planets and other bodies will appear in our sky (ephemerides) with celestial coordinates expressed relative to ICRF.  Such a model would be a reverse orrery for specifying time.

Below are the 295 defining sources of ICRF2 reexpressed in decimal right ascension and declination.  The original specification used a precision of 1 part in 36000*10^7 of an hour of right ascension, and 1 part in 3600*10^7 of a degree of declination.  The decimal conversions below provide precision of 1 part in 10000*10^7 of an hour for RA and 1 part in 1000*10^7 of a degree of D, which is less precise.  However, the smallest uncertainties in the source are 1 part in 132*10^7 of an hour of RA, and 1 part in 8.7*10^7 of a degree of D, which exceeds the precision.  (Incidentally, the angular resolution of the Hubble Space Telescope is 0.05 arc second, compared to the largest uncertainty in the ICRF2 defining sources of 0.0003101 arc second of declination, so ICRF2 is at least 160 times more precise than Hubble.)

The coordinates define the vertices of a polyhedron inscribed within a sphere which, if manufactured, would be an elegant way to store the information, but I don't think any manufacturing process can be precise to such tolerances.

An astronomer starting anew, given just these coordinates, would do a VLBI survey of thousands of extragalactic radio sources and align his or her measurements with this set, seeking approximate matching subsets.  I don't know how hard this computational geometry matching problem is, though I suspect it is easy.

      RA         Declination
 0.07657097329 -47.6054454972
 0.17527941718  10.9748623285
 0.18367964957 -26.2092713936
 0.22531394537  40.8603178067
 0.26974682077  -0.2534570393
 0.32938511650  73.4583381777
 0.37567811365   6.1345191891
 0.64023433120  41.6183334176
 0.84481038543  -9.4847806302
 0.85263939448 -42.4425814578
 1.04604510624  58.4030935003
 1.11252999125 -40.5722111748
 1.15429866833 -60.8301277691
 1.20161797709  22.7441073308
 1.22416855651  49.8066786595
 1.31590615741 -21.6917055552
 1.36155417872  11.8306703059
 1.55160071002 -52.0010960336
 1.61627633496  47.8580833457
 1.61909267492  31.3766264892
 1.69050893207  -9.4787983859
 1.91563607995  47.7240387703
 2.05927360234  72.5482409149
 2.08470148891  32.2083598483
 2.29693187551   1.7471386307
 2.40789672127   6.9898170943
 2.49304072044 -78.7960004992
 2.52941501509  13.3818656297
 2.60865817238 -29.8987611878
 2.61479048497 -61.6042176181
 2.63122379926  28.8024972286
 2.66263118549  -2.5780317783
 3.05978950626  47.2711876224
 3.06406426333 -62.1904305198
 3.11184987443  62.7172289345
 3.15100652782  10.4878724889
 3.16558309832 -60.9775155973
 3.18052220264  38.2482882978
 3.21721170085  41.3336620996
 3.42689287543  22.4001015520
 3.57045958711 -40.1403882893
 3.59831245601 -54.5069762980
 3.75178237340  14.8970995006
 3.81059571590 -27.8204348757
 4.02921279794  21.1746075100
 4.06493052732 -36.0838647524
 4.09277871932 -13.1371363079
 4.11639870433 -38.4411228769
 4.27681790317 -18.8523166746
 4.38772242438  -1.3425181676
 4.41301168359   0.6017581577
 4.49804465779  27.4105211928
 4.56050829443  29.0987436207
 4.65023740801 -45.3729341294
 4.72545422293  34.6851844506
 4.81879752802  11.3579434605
 4.83484450037 -81.0172864786
 4.95088311906 -23.4144500394
 5.02022496768  -1.9872934037
 5.02924189453  13.9353390049
 5.11221909109 -61.1613871650
 5.14510095889  84.5345955599
 5.15762696351  10.1957222332
 5.16732475828  18.0115504593
 5.27914615776 -62.1181636677
 5.30106236203  20.9145826361
 5.37622929967 -61.1325370901
 5.42538893059 -45.9651902399
 5.43796425296 -48.5102198742
 5.45908484666   3.5254212897
 5.55440716185  48.3813354617
 5.57660346934 -61.1019647391
 5.60789788200 -34.0198523375
 5.64732265339 -44.0858163657
 5.66176833084  14.5626560276
 5.66507818790 -28.6655410589
 5.79281914475  27.3657896019
 5.83599449527 -57.5401101473
 5.92522378097  39.8136569351
 5.99223142546  23.8983129912
 6.05253618382  17.7046696001
 6.77556277629  44.8546083677
 6.80391568631 -30.7387943563
 6.84016162645 -16.6277014421
 6.98833223174   8.2252648062
 7.00042376013  17.1560281917
 7.17947357689  47.5364285324
 7.36484679538  71.3434342848
 7.42133548924  14.4204851917
 7.43659312249  79.1919489468
 7.50530902061 -11.6868334753
 7.65500941581   1.6179494052
 7.70076359625  49.0043358150
 7.76502286698  -0.7382055152
 7.77385393853  25.8172596543
 7.81003035408  24.0066972310
 7.84779048200  12.5180078268
 8.04667554495  18.1636803877
 8.08838321346  61.7399167491
 8.13264960282   4.5429252784
 8.14435174543  49.8434806676
 8.14907001090  40.8791357949
 8.19075203108   1.7811722949
 8.25720690483  36.5875413588
 8.30444433464  42.3792819206
 8.43064954286   3.1568111314
 8.51446838631  24.1832834453
 8.61089312582 -20.2831955820
 8.91357636862  20.1085113572
 8.94494559670 -11.0873417195
 9.24386484213   2.7664574831
 9.37956062796 -39.9930745434
 9.38734803640  38.8277528160
 9.46439564332 -20.5808978897
 9.87556282404  35.2145564053
 9.97213101092  47.4188451207
 9.97248600865  32.4006137598
 9.97979030591  65.5652272385
10.10389147672 -50.3037418544
10.24640707127  23.0212696847
10.26753790769   5.2173170689
10.29052432699  61.2743046296
10.30305224746  35.7109557855
10.39542588888 -66.7801993757
10.41244710974  19.2056710069
10.55102996338  41.2683980327
10.55945119203   7.1905965843
10.61484433389 -37.7375182422
10.62113325966 -29.5674481485
10.69632823268  52.5578420324
10.73973959664  80.9109563966
10.74886423498   6.9272951820
10.80183905750 -19.1599240622
10.86355252081  21.3311982818
10.96987093878  81.2424097727
10.97489033541   1.5663399359
11.06450601992 -53.9501935081
11.07425387260  38.2088330734
11.23297085655  14.7074868324
11.43158664524  26.1722163011
11.45122012488 -18.9548449051
11.51480072554  38.2551519426
11.55557105325   0.6813436917
11.60682692581  -3.5081934637
11.76489560296 -69.9004993867
11.78286053230  39.9761956952
11.78371408383 -38.2030620611
11.79765389688  -7.4114280802
11.83867004835  24.2982875891
11.87144708760  -8.6842538562
11.98841818020 -66.5942853385
11.99217608604  29.2455074650
12.26298660031 -17.5292785973
12.29780054483  30.1168433108
12.37293045022   4.2210489388
12.39458159404  80.6678723442
12.47983991040  37.1033599620
12.65683009033   7.5047747968
12.71426918788  37.8500070124
12.76784225099  -7.5129373742
12.77966723192 -25.7970246639
12.91062655878  11.6849708833
12.91664484686 -71.6384546305
13.04790702102  57.8104470328
13.18316742482  32.5595693426
13.26888498332 -33.6497701405
13.45023925382  22.1806008258
13.48365136911 -56.1340738174
13.62771743824 -12.9568592394
13.72943321426  66.0404847503
13.73574435191  66.1032344124
13.88237081748 -44.2112187563
13.90191536726  -2.1008862346
13.95312360549 -15.4579963120
13.96538098096  76.7225141809
14.14902255566  -7.8740740056
14.32961038948  54.3874408854
14.32961493353  38.3634653035
14.41543260990 -68.1328040335
14.43028278231  14.4158060844
14.46563821260 -42.1053993331
14.57772037646  19.8668710615
14.76482674623 -16.4837830316
14.87768868053 -65.0342870442
14.90914232200 -40.2090317326
14.98315450334   4.2705057228
15.01351506164  47.8543161622
15.07360549484  10.4942218375
15.08513254421   3.4418924060
15.10264721327  37.5142034734
15.16747843462  57.0453821964
15.21403692359  -9.0999526633
15.22913705942 -10.2000734703
15.28244337873  19.5369422272
15.36378163329  43.6109078212
15.37713221909 -27.5029959493
15.82484356750   2.6169898388
15.84313034489   5.4529023406
15.96428721424  -0.0306704743
15.98063454539 -64.5415659464
15.99193683762   3.0800713564
16.12632287356 -33.5191425865
16.14616755154  10.4854932861
16.27517821106 -71.1420707062
16.27709911528   4.9924268749
16.32078461405  22.7966252996
16.40512139048 -68.1534712587
16.42969212225 -25.4606463330
16.48185828432 -61.8767771906
16.63707119363  57.3399941869
16.67489799217  39.7794523620
16.69034099028  22.9511202114
16.70218014041  68.9443768048
16.71592934811 -81.1430750469
17.01476501702 -26.1810348183
17.02912725384 -56.3655283203
17.06015034601 -62.2111133807
17.12622646417   1.8126942455
17.15954038702 -17.4814902701
17.32029124489  17.7517881392
17.45768077908  45.5110364846
17.55075160688 -13.0804300412
17.56130563283 -79.5988101926
17.57238292684  38.9642897429
17.65760847014  49.9176023447
17.66586918711  47.6328782102
17.73301559277  -3.8346157347
17.75978004745  17.3337288022
17.77056503811  62.4485384418
17.85911627033   9.6502023564
17.89513156786  28.8013719123
17.94808392673  15.5891184813
18.00687926701  38.8085270925
18.01268997678  78.4677829028
18.02564300586  44.0727500894
18.05652685194 -65.1268781137
18.16607548617 -45.8780594221
18.32927764403 -55.3557626051
18.39245941751  68.9646146089
18.40196343825  56.8504141214
18.48677843700 -58.2319893583
18.62464303833 -71.1454318303
18.70934491365  68.1570077178
18.80613571704  32.3173899286
18.82113119161  67.0949111938
19.18601469222 -20.1153080525
19.39227494852 -21.0759258485
19.41418220976 -29.2417002923
19.50171113735 -60.9358844866
19.52358799568  22.7253496169
19.62117148657 -39.9670980530
19.65740492986 -15.4286273384
19.67375783362 -69.1324920818
19.92853840788  51.5301517003
19.96661646519 -38.7517654885
20.01585845690 -17.8160201511
20.03622729324  47.4246593673
20.09863080562 -37.3948549593
20.18769748127 -15.7778482403
20.53194285309  12.3281500869
20.93787772743 -47.2465632350
21.02745393450   3.6920335994
21.14473115322  14.5075034216
21.15921905332 -41.1723903664
21.25817040432  29.5606574905
21.44186229579 -46.0966366731
21.48671552716 -15.6447336971
21.56953044345  -1.8881218864
21.65036368594  14.3933311693
21.78686961782 -75.6036735605
21.87356094431  17.5771652940
22.12881480670 -53.7760610341
22.20165730872  23.9279288409
22.38498071615 -34.9297715078
22.42979424806  -4.9503863217
22.49446787223  -8.5484542763
22.51013047359  69.7744658043
22.58701016031 -48.5996651391
22.65335442324 -57.0168998324
22.78442147857 -36.9628622118
22.81074603825 -32.5978299872
22.88538032594  19.7096190964
22.95480642291   7.7200840214
22.96832302356 -27.9725713174
23.06210128348 -68.1270674918
23.34579349942   5.2305423769
23.48825120841 -47.5053096779
23.60944030460 -41.2561066466
23.78885113739 -51.1766848564
23.90838755212 -15.2197813946
23.93352261274 -68.3342976968
23.96479613558 -53.1871359323
23.96968955767 -10.3357253670
23.99255022150  38.8450884151
23.99319209526 -31.5621734031

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