Computer Ephemeris for 2020 from DE200/LE200.

Elements of the Annular Solar eclipse - 21 Jun 2020.

2020 Jun  21  6h43m 7.53s   Min(gamma) = 0.12141   t = time -  6h40m

Geocentric coordinates of the Sun:
Right ascension =   60132.805 + t *    10.404
Declination     =  232609.727 + t *    -0.379 + t * t * -0.022
Parallax        =       8.653
Radius          =    1544.218 + t *    -0.003

Geocentric coordinates of the Moon:
Right ascension =   60127.213 + t *   221.037 + t * t *  0.110
Declination     =  233253.090 + t *   254.194 + t * t * -3.903
Parallax        =    5631.064 + t *     1.388 + t * t * -0.001
Radius          =    1524.003 + t *     0.379

Contacts of the eclipse:
Begin Semishadow eclipse:   3 47.21
Begin Partial    eclipse:   4 48.92
Phase Maximum of eclipse:   6 41.14
End   Partial    eclipse:   8 33.52
End   Semishadow eclipse:   9 35.19

Besselian elements
 time     x        y         sind     cosd      ue       ui      mu
 3  20  -1.79256 -0.05414  0.39773  0.91750  0.55222  0.00627  2293235.
 3  30  -1.70411 -0.04539  0.39773  0.91750  0.55221  0.00626  2320235.
 3  40  -1.61566 -0.03664  0.39773  0.91750  0.55221  0.00625  2343234.
 3  50  -1.52720 -0.02791  0.39773  0.91750  0.55220  0.00624  2370234.
 4   0  -1.43873 -0.01918  0.39773  0.91750  0.55219  0.00623  2393233.
 4  10  -1.35026 -0.01046  0.39773  0.91750  0.55218  0.00622  2420233.
 4  20  -1.26178 -0.00175  0.39773  0.91750  0.55217  0.00621  2443232.
 4  30  -1.17330  0.00695  0.39773  0.91750  0.55216  0.00620  2470232.
 4  40  -1.08482  0.01564  0.39773  0.91750  0.55215  0.00619  2493231.
 4  50  -0.99633  0.02432  0.39773  0.91750  0.55213  0.00618  2520231.
 5   0  -0.90784  0.03300  0.39773  0.91750  0.55212  0.00617  2543230.
 5  10  -0.81934  0.04166  0.39773  0.91750  0.55211  0.00615  2570230.
 5  20  -0.73084  0.05032  0.39773  0.91750  0.55209  0.00614  2593229.
 5  30  -0.64234  0.05897  0.39772  0.91750  0.55208  0.00613  2620229.
 5  40  -0.55383  0.06761  0.39772  0.91751  0.55206  0.00611  2643228.
 5  50  -0.46532  0.07624  0.39772  0.91751  0.55205  0.00609  2670227.
 6   0  -0.37681  0.08486  0.39772  0.91751  0.55203  0.00608  2693227.
 6  10  -0.28829  0.09347  0.39772  0.91751  0.55201  0.00606  2720226.
 6  20  -0.19977  0.10208  0.39772  0.91751  0.55200  0.00604  2743226.
 6  30  -0.11126  0.11067  0.39772  0.91751  0.55198  0.00603  2770225.
 6  40  -0.02273  0.11926  0.39772  0.91751  0.55196  0.00601  2793225.
 6  50   0.06579  0.12784  0.39772  0.91751  0.55194  0.00599  2820224.
 7   0   0.15431  0.13641  0.39772  0.91751  0.55192  0.00597  2843224.
 7  10   0.24284  0.14497  0.39772  0.91751  0.55190  0.00595  2870223.
 7  20   0.33137  0.15352  0.39772  0.91751  0.55188  0.00593  2893223.
 7  30   0.41990  0.16206  0.39772  0.91751  0.55186  0.00591  2920222.
 7  40   0.50843  0.17059  0.39772  0.91751  0.55184  0.00588  2943222.
 7  50   0.59696  0.17912  0.39772  0.91751  0.55181  0.00586  2970221.
 8   0   0.68549  0.18763  0.39772  0.91751  0.55179  0.00584  2993220.
 8  10   0.77402  0.19614  0.39771  0.91751  0.55176  0.00581  3020220.
 8  20   0.86255  0.20464  0.39771  0.91751  0.55174  0.00579  3043219.
 8  30   0.95108  0.21312  0.39771  0.91751  0.55172  0.00576  3070219.
 8  40   1.03961  0.22160  0.39771  0.91751  0.55169  0.00574  3093218.
 8  50   1.12814  0.23007  0.39771  0.91751  0.55166  0.00571  3120218.
 9   0   1.21667  0.23853  0.39771  0.91751  0.55164  0.00568  3143217.
 9  10   1.30520  0.24698  0.39771  0.91751  0.55161  0.00566  3170217.
 9  20   1.39373  0.25542  0.39771  0.91751  0.55158  0.00563  3193216.
 9  30   1.48225  0.26386  0.39771  0.91751  0.55155  0.00560  3220216.
 9  40   1.57078  0.27228  0.39771  0.91751  0.55152  0.00557  3243215.
 9  50   1.65930  0.28069  0.39771  0.91751  0.55149  0.00554  3270215.
10   0   1.74782  0.28910  0.39771  0.91751  0.55146  0.00551  3293214.

time       x'       y'
  4    0.008847    0.000872
  5    0.008849    0.000867    Tan(fi) =  0.00457494
  6    0.008851    0.000862    Tan(fe) =  0.00459784
  7    0.008853    0.000856    Mu'     =  0.00436306
  8    0.008853    0.000851
  9    0.008853    0.000846