Tangents

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							                                                   Data


l (I)         l (II)         Tangents                   V          V           V           sin(l)
        322             -5                              Tangent                              -0.087156
        327              0                                                                           0
        330              3                                                                    0.052336
        335              8        2.05                 21.370863                            0.1391731
        340             13        2.06                 21.475111                            0.2249511
        345             18        7.03    -2.2         73.286422   -22.93458                  0.309017
        350             23       12.58    -2.6         131.14412   -27.10451                0.3907311
        355             28        9.16    -3.2         95.491269    -33.3594                0.4694716
          0             33        8.28    -3.7         86.317435    -38.5718                  0.544639
          5             38        7.54      -4         78.603075   -41.69924                0.6156615
         10             43        6.66      -4         69.429242   -41.69924                0.6819984
         15             48        5.36    -4.4         55.876987   -45.86917                0.7431448
         20             53        4.92    -4.7          51.29007   -48.99661                0.7986355
         25             58        3.25    -5.8         33.880636    -60.4639                0.8480481
         30             63        2.93      -6         30.544696   -62.54887                0.8910065
         35             68        1.11    -5.8          11.57154    -60.4639                0.9271839
         40             73        0.69      -6         7.1931196   -62.54887                0.9563048
         45             78           0    -6.6    -2.4         0   -68.80375   -25.01955    0.9781476
         50             83               -6.93    -3.9             -72.24394   -40.65676    0.9925462
         55             88                  -7    -3.8             -72.97368   -39.61428    0.9993908
         60             93                -7.3    -4.2             -76.10112   -43.78421    0.9986295
         65             98                        -4.8                         -50.03909    0.9902681
         70            103                -9.2    -5.1             -95.90826   -53.16654    0.9743701
         75            108                -9.2    -4.9             -95.90826   -51.08157    0.9510565
         80            113                  -9    -4.7              -93.8233   -48.99661    0.9205049
         85            118                -8.6    -4.3             -89.65338   -44.82669    0.8829476
         90            123                -9.5    -4.3              -99.0357   -44.82669    0.8386706
         95            128                -9.5    -4.8              -99.0357   -50.03909    0.7880108
        100            133               -8.78    -4.3             -91.52984   -44.82669    0.7313537
        105            138                -8.4    -3.7             -87.56841    -38.5718    0.6691306
        110            143                -7.4    -3.7              -77.1436    -38.5718      0.601815
        115            148                        -3.1                         -32.31691    0.5299193
        120            153                        -2.2                         -22.93458    0.4539905
        125            158                        -2.2                         -22.93458    0.3746066
        130            163                        -1.5                         -15.63722    0.2923717
        135            168                        -1.1                         -11.46729    0.2079117
        140            173                       -0.65                         -6.776127    0.1218693
        145            178                                                                  0.0348995
        147            180                          0                                 0      -2.07E-13
        150            183                                                                   -0.052336
        155            188                       0.64                          6.6718791     -0.139173
        160            193                       0.91                          9.4865781     -0.224951
        165            198                       1.33                          13.864999     -0.309017
        170            203                 1.1    2.2           11.467292      22.934584     -0.390731
        175            208                 1.4    3.8           14.594735      39.614282     -0.469472
        180            213         0.8     2.6    4.5 8.3398488 27.104509       46.91165     -0.544639
        185            218                 2.7    5.2            28.14699      54.209017     -0.615661
        190            223         1.4     3.5    5.8 14.594735 36.486839      60.463904     -0.681998



                                                  Page 1
                          Data


195   228    1.6   3.8   6.3   16.679698   39.614282    65.67631   -0.743145
200   233    2.1   4.6   6.9   21.892103   47.954131   71.931196   -0.798636
205   238   1.95   5.5   7.9   20.328382   57.336461   82.356007   -0.848048
210   243    1.8   6.3   8.8    18.76466    65.67631   91.738337   -0.891007
215   248    1.8   5.9   8.5    18.76466   61.506385   88.610894   -0.927184
220   253    1.7         8.6   17.722179               89.653375   -0.956305




                         Page 2
                                                   Data


DW       DW           DW      r          r               r   q         q            q




          -8.835461                          11.867698                  0.0978093
          -8.258178                          11.556004                  0.0684222
          -8.459206                           11.66267                  0.1850627
          -8.431054                          11.647614                   0.259141
           -8.06319                           11.45439                  0.3368381
          -7.278897                          11.063104                  0.4280713
          -7.347983                          11.096494                  0.5039264
           -7.30362                           11.07503                  0.5648197
          -8.487825                          11.678016                  0.5993389
          -8.357171                          11.608285                  0.6495595
          -7.763383                          11.301591                  0.7409243
          -7.786528                          11.313241                  0.7775256
          -8.373913   -3.045059                     9.3406268
                                             11.617174                  0.7856243 1.190308
          -8.665057   -4.876439                     10.015119
                                             11.773956                  0.7868338 1.1045204
          -8.692638   -4.718861                     9.9532765
                                             11.789028                  0.7924747 1.1258074
           -9.07209   -5.219559                     10.152472
                                             12.000375                  0.7740245 1.0998281
                      -6.015578                     10.486111                     0.9161507
          -11.71798   -6.495837           13.714818 10.698224           0.6394803 1.0316939
          -12.00523   -6.394089           13.930886 10.652572           0.6107291 1.0085537
          -12.13404   -6.336664           14.030004 10.626979            0.583708 0.9719035
          -12.08794   -6.043972           13.994374 10.498417           0.5585788 0.9345887
          -14.05792   -6.363059           15.698224 10.638727           0.4653842 0.8895406
          -14.96168   -7.559586           16.626938 11.200031           0.4094517 0.7981122
          -14.89896   -7.296757           16.558952 11.071717           0.3800856 0.7414474
          -15.57964   -6.862459           17.327878 10.866014           0.3303489 0.6902693
          -15.26011   -7.630054            16.95822 11.234941           0.3027016 0.5958722
                      -7.260071                      11.05404                     0.4144508
                      -6.014019                     10.485436                     0.3722335
                      -7.288467                     11.067717                     0.2882897
                      -6.367146                     10.640549                     0.2329079
                      -6.566027                     10.729946                     0.1634922
                      -6.619235                     10.754118                      0.095336
                              0
                              0
                              0
                      -5.707075                     10.354237                           -0.113147
                      -5.020446                     10.072311                           -0.188721
                      -5.341438                     10.202173                           -0.257259
          -3.493845   -6.987689           9.4973684 10.92454            -0.352861        -0.32435
          -3.700903   -10.04531           9.5714721 12.578748           -0.424661       -0.343322
-1.822931 -5.924524   -10.25398 8.9388889 10.446841 12.710098 -4.254836 -0.467256        -0.41359
          -5.442654   -10.48215           10.243818 12.856888           -0.529204       -0.461086
-2.547614 -6.369035    -10.5544 9.1728272 10.641391 12.904081 -4.566625 -0.592912        -0.52109



                                                  Page 3
                                                       Data


-2.671994   -6.345985    -10.52098   9.2142155   10.631125   12.882206   -4.723677    -0.6555 -0.572202
-3.263319   -7.148223    -10.72234   9.4162043   11.000494   13.015122   -4.859595 -0.69251 -0.621808
-2.853665      -8.0488     -11.561   9.2753437   11.446961   13.599547    -5.02962 -0.705729 -0.647313
-2.507151   -8.775029    -12.25718    9.159443   11.834283   14.126091   -5.197565 -0.716113 -0.668358
-2.409326   -7.897235    -11.37737   9.1272452   11.369303    13.46714   -5.350712 -0.786065 -0.719645
-2.206183                -11.16069   9.0611014                13.31418   -5.505479            -0.647681




                                                      Page 4
                                           Data


r            q            velscale  10.424811
Tangent      Tangent      rsun (km)        8.4
                          pi        3.1415927
                          Wsun (km/s/kpc) 30
 1.169054       1.43117   Vsun (km/s)     254
1.8895889    1.3439035
2.5957428    1.2566371
3.2821415    1.1693706
3.9435611    1.0821041
4.5749679    0.9948377
5.1715564    0.9075712
5.7287862    0.8203047
6.2424165    0.7330383
6.7085383    0.6457718
 7.123604    0.5585054
7.4844548    0.4712389
7.7883444    0.3839724
   8.03296    0.296706
8.2164398    0.2094395




                                          Page 5
                                                                Tangents


r              q          f              x              y
    1.182971    1.43117       0.139626       1.171459       0.164638
    1.912084   1.343904       0.226893       1.863077       0.430125       9
    2.626644   1.256637       0.314159       2.498087       0.811678       8
    3.321215   1.169371       0.401426       3.057194       1.297702       7
    3.990508   1.082104       0.488692        3.52341        1.87343       6
    4.629432   0.994838       0.575959       3.882568       2.521369
                                                                           5
    5.233123   0.907571       0.663225       4.123757       3.221832
                                                                           4
    5.796986   0.820305       0.750492       4.239647       3.953535
    6.316731   0.733038       0.837758       4.226718       4.694246       3
    6.788402   0.645772       0.925025       4.085362       5.421459       2
    7.208409   0.558505       1.012291       3.819875       6.113077       1
    7.573555   0.471239       1.099557       3.438322       6.748087       0
    7.881063   0.383972       1.186824       2.952298       7.307194
                                                                               0   2   4   6
     8.12859   0.296706        1.27409        2.37657        7.77341
    8.314255    0.20944       1.361357       1.728631       8.132568




                                                                 Page 6
                                                          Plot


r               q             x             y
    11.867698    0.0835309     0.9901675     11.826319                                    20
    11.556004      0.051265    0.5921594     11.540822
     11.66267    0.1635762     1.8992385     11.506988
    11.647614      0.233756    2.6979721     11.330837
     11.45439    0.3086011     3.4789976     10.913277
    11.063104    0.3986709     4.2946282     10.195511                                    15
    11.096494    0.4705422     5.0308137     9.8905559
     11.07503    0.5278633     5.5783668      9.567555     Perseus arm
    11.678016    0.5536974     6.1407187      9.933158
    11.608285    0.6007563       6.561775    9.5757705                                    10
    11.301591      0.691305    7.2052518     8.7069114
                                                                  Orion spur
    11.313241    0.7248522        7.50096     8.469063                                   Sun
    11.617174    0.7280339     7.7301053     8.6720352
    11.773956    0.7263758     7.8198448      8.802049
                                                                                           5
    11.789028    0.7311045     7.8714431      8.776193
    12.000375    0.5919067     6.6955414     9.9588518
    13.714818    0.5685651     7.3843795     11.557127
                                                                                     Galactic
    13.930886    0.5411358       7.175937    11.940499
                                                                                     center
    14.030004    0.5167249     6.9313173     12.198272                                      0
    13.994374    0.4954553     6.6533765     12.311583     -15            -10   -5              0
    15.698224    0.3990121        6.09889    14.465054
    16.626938       0.34463    5.6173852     15.649282
    16.558952    0.3207822     5.2211861     15.714264                                    -5
    17.327878    0.2745277     4.6974555     16.679007
     16.95822    0.2538808     4.2592652     16.414624
    9.4973684     -0.345436     -3.215876    8.9363385
    9.5714721     -0.414937     -3.858565    8.7592552
    10.446841     -0.448992     -4.534528    9.4114045                                   -10
    10.243818     -0.509477     -4.996121    8.9428511
    10.641391     -0.566783     -5.713588    8.9774224
    10.631125     -0.626033     -6.229147    8.6150183
    11.000494     -0.656194     -6.711462    8.7159137
    11.446961     -0.661911      -7.03559    9.0295837
    11.834283     -0.665547     -7.307547    9.3085993
    11.369303     -0.735859     -7.631348     8.427548

    9.6182777   1.1591921     8.8149609     3.8480814
    10.444715   1.0612643     9.1179532     5.0946055
    10.368062   1.0824073      9.155931     4.8647346
    10.615608   1.0889618      9.406982     4.9193324
    11.034457   0.8676595     8.4172786     7.1350308
    11.303535    0.982857     9.4055071     6.2694778
    11.245438   0.9627421     9.2298188     6.4241981
    11.212912   0.9293913     8.9844121     6.7089294
    11.050009   0.8967567      8.633446     6.8968328
    11.227839   0.8537021     8.4626305     7.3789061
    11.948922   0.7608686     8.2393878     8.6538555
    11.782701   0.7090081     7.6714957     8.9431652



                                                         Page 7
                                                   Plot


11.517945   0.6630668    7.0897185    9.0773869
11.994288   0.5697615    6.4700931    10.099546
11.759867    0.393068    4.5043137     10.86304
11.033605   0.3572961    3.8589192    10.336787
11.777533   0.2737654     3.184156    11.338935
11.230154   0.2231406    2.4851595    10.951728
11.343964   0.1564248    1.7672494    11.205461
11.374805   0.0911951    1.0358894    11.327538
10.868266   -0.109062    -1.182971    10.803693
10.515764   -0.182847    -1.912084    10.340466
10.677665   -0.248545    -2.626644    10.349554
11.593059   -0.309753    -3.533831    11.041334
13.788586   -0.318042    -4.311786    13.097084
13.969138     -0.38317   -5.222538    12.956153
14.172039   -0.425333    -5.847727    12.909329
14.237527   -0.480432    -6.580044    12.625775
14.207156   -0.527068    -7.146222    12.279039
14.392101   -0.571475    -7.784304    12.105254
15.217161   -0.589483    -8.459702     12.64893
 15.97749      -0.6038   -9.071611    13.152417
15.028521   -0.654993      -9.15468   11.918402
14.811857   -0.580915      -8.12859   12.382129

9.1358831    -4.24894    8.1721917    -4.084072
9.4159093   -4.555306    9.2999786    -1.473006
9.4657063   -4.709966    9.4656785    -0.022935
 9.709841   -4.840791    9.6299069    1.2433447
9.5393946   -5.010524    9.1185734     2.802083
9.3998224   -5.178028       8.39907   4.2204601
9.3611556   -5.329192    7.6361904    5.4147788
9.2818681   -5.482669    6.6617429    6.4633008

                         1.1714588    0.1646378
                         1.8630774    0.4301253
                         2.4980873    0.8116778
                         3.0571942    1.2977019
                         3.5234097    1.8734302
                         3.8825682    2.5213693
                         4.1237568    3.2218319
                         4.2396472     3.953535
                         4.2267181     4.694246
                         4.0853622    5.4214588
                         3.8198747    6.1130774
                         3.4383222    6.7480873
                         2.9522981    7.3071942
                         2.3765698    7.7734097
                         1.7286307    8.1325682

      8.4           0            0          8.4



                                                  Page 8
                                              Plot


8.4   0.098175    0.823344     8.3595517
8.4    0.19635   1.6387587     8.2385964
8.4   0.294524   2.4383913     8.0382988
8.4   0.392699   3.2145408     7.7605881
8.4   0.490874   3.9597326     7.4081386
8.4   0.589049      4.66679    6.9843447
8.4   0.687223   5.3289036     6.4932878
8.4   0.785398    5.939697      5.939697
8.4   0.883573   6.4932878     5.3289036
8.4   0.981748   6.9843447        4.66679
8.4   1.079922   7.4081386     3.9597326
8.4   1.178097   7.7605881     3.2145408
8.4   1.276272   8.0382988     2.4383913
8.4   1.374447   8.2385964     1.6387587
8.4   1.472622   8.3595517      0.823344
8.4   1.570796           8.4   -8.71E-13
8.4   1.668971   8.3595517     -0.823344
8.4   1.767146   8.2385964     -1.638759
8.4   1.865321   8.0382988     -2.438391
8.4   1.963495   7.7605881     -3.214541
8.4    2.06167   7.4081386     -3.959733
8.4   2.159845   6.9843447       -4.66679
8.4    2.25802   6.4932878     -5.328904
8.4   2.356194    5.939697     -5.939697
8.4   2.454369   5.3289036     -6.493288
8.4   2.552544      4.66679    -6.984345
8.4   2.650719   3.9597326     -7.408139
8.4   2.748894   3.2145408     -7.760588
8.4   2.847068   2.4383913     -8.038299
8.4   2.945243   1.6387587     -8.238596
8.4   3.043418    0.823344     -8.359552
8.4   3.141593   -1.73E-12            -8.4
8.4   3.239767   -0.823344     -8.359552
8.4   3.337942   -1.638759     -8.238596
8.4   3.436117   -2.438391     -8.038299
8.4   3.534292   -3.214541     -7.760588
8.4   3.632467   -3.959733     -7.408139
8.4   3.730641     -4.66679    -6.984345
8.4   3.828816   -5.328904     -6.493288
8.4   3.926991   -5.939697     -5.939697
8.4   4.025166   -6.493288     -5.328904
8.4    4.12334   -6.984345       -4.66679
8.4   4.221515   -7.408139     -3.959733
8.4    4.31969   -7.760588     -3.214541
8.4   4.417865   -8.038299     -2.438391
8.4   4.516039   -8.238596     -1.638759
8.4   4.614214   -8.359552     -0.823344
8.4   4.712389          -8.4    2.61E-12
8.4   4.810564   -8.359552      0.823344



                                             Page 9
                                            Plot


8.4   4.908739   -8.238596   1.6387587
8.4   5.006913   -8.038299   2.4383913
8.4   5.105088   -7.760588   3.2145408
8.4   5.203263   -7.408139   3.9597326
8.4   5.301438   -6.984345      4.66679
8.4   5.399612   -6.493288   5.3289036
8.4   5.497787   -5.939697    5.939697
8.4   5.595962   -5.328904   6.4932878
8.4   5.694137    -4.66679   6.9843447
8.4   5.792311   -3.959733   7.4081386
8.4   5.890486   -3.214541   7.7605881
8.4   5.988661   -2.438391   8.0382988
8.4   6.086836   -1.638759   8.2385964
8.4   6.185011   -0.823344   8.3595517
8.4   6.283185   3.519E-12           8.4

                        0           8.4




                                           Page 10
                         Plot




       Outer arm




Tangents


 5          10     15




                        Page 11

						
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