I'm posting this with the hope that others will compare their results with mine, using software they've written or own, with the ultimate goal that by June 7, as accurate a transit path prediction can be made as is possible. Except for the latitude & longitudes, most of the values in my results were never intended to be extremely high precision (e.g., the angle of elevation, and azimuth). In fact, at 5:50:53, I report an elevation angle (of the ISS as it transits Venus) of 1.0°, while the Sun's elevation is given as 0.4°, and the Sun/Venus separation angle is 0.2°. Even allowing for rounding error, Venus (and hence the ISS as it transits Venus) could be no more than 0.7° in elevation, so there's at least half a Sun diameter of error in there, somewhere. If there's substantial disagreement with any of these results (that is, the latitudes & longitudes I compute), then I can post my intermediate results for further comparison; e.g., the ECI position of the ISS, the position of Venus, etc. The results that follow are based upon the TLE given below, posted by NASA's Mission Control Center on June 1 (the transit of Venus begins at about day-of-year 160.22); the calculations were performed at 1 second intervals. (Naturally, for comparisons to have any meaning, this TLE must be used.) 1 25544U 98067A 04159.51921885 .00020000 00000-0 20000-3 0 9074 2 25544 51.6331 15.0248 0005532 209.7910 150.2937 15.68809969 36809 An elevation of sea-level was used in these calculations; hopefully, I'll finish implementing my GTOPO30 Digital Elevation Model code by June 7, that will allow me to calculate the transit path using accurate elevation data. However, for the sake of comparison, an elevation of sea-level should be used. The Contact times below represent "as observed by a demon at the Earth's center." Since Venus is close to the Earth in size, moving from the Earth's center to the Earth's "edge" would cause Venus to shift by about a third of its diameter, relative to the disk of the Sun (which would also shift relative to the stars, by about 1/3 the amount of Venus' shift). Key times: see http://sunearth.gsfc.nasa.gov/eclipse/OH/transit04.html Contact 1 5:13:29 (ISS will be on the night side of the Earth at this moment) Contact 2 5:32:55 Venus is first entirely silhouetted against the Sun Greatest 8:19:44 " at the midpoint of its transit Contact 3 11:06:33 " begins to emerge from the Sun's disk Contact 4 11:25:59 end of the 2004 transit of Venus A - seconds elapsed since somewhat arbitrary program starting time of 5:12:54 ("Contact 2" minus 20 minutes and 1 second) B - UTC time (June 8) C - elevation angle of the ISS/Venus D - azimuth angle of the ISS ( + is East from North; - is W from N) E - range (miles) F - latitude for observing the transit G - longitude H - sun elevation angle I - sun/Venus separation angle A---- B------ C--- D----- E--- F------- G-------- H---- I---- ORBIT 1: The ISS is first seen transiting Venus as Venus transits the Sun 166 5:15:40 1.3 66.6 1296 -10.6179 16.6564 1.2 0.3 Contact 2; also represents (to 0.1°) the highest elevation for any ISS transit of Venus 1201 5:32:55 63.6 147.0 255 46.1773 81.6199 63.9 0.2 1431 5:36:45 60.0 -166.0 263 52.1930 103.2916 60.3 0.2 1560 5:38:54 55.0 -142.4 277 53.4559 117.4513 55.2 0.2 1663 5:40:37 50.0 -125.9 294 53.1848 129.0865 50.1 0.2 1757 5:42:11 45.0 -112.7 316 51.9433 139.4399 45.0 0.2 1842 5:43:36 40.0 -102.3 344 50.0574 148.2982 40.0 0.2 1922 5:44:56 35.0 -93.8 378 47.6828 156.0937 35.0 0.2 1999 5:46:13 30.0 -86.7 424 44.8977 163.1224 29.9 0.2 2070 5:47:24 25.0 -81.0 485 41.9138 169.3036 24.9 0.2 2135 5:48:29 20.0 -76.3 566 38.8051 174.9051 19.8 0.2 2192 5:49:26 15.0 -72.5 678 35.6822 -179.9041 14.8 0.2 2238 5:50:12 10.0 -69.2 837 32.6552 -174.9298 9.8 0.2 2269 5:50:43 4.9 -66.4 1068 29.7989 -169.8705 4.6 0.2 2279 5:50:53 1.0 -64.4 1314 27.7853 -165.7539 0.4 0.2 ORBIT 3: 11182 8:19:16 1.6 66.7 1274 -9.9868 -29.3634 1.3 0.2 11191 8:19:25 4.9 66.2 1075 -8.3539 -26.3397 4.7 0.2 Greatest transit of Venus 11210 8:19:44 8.4 65.9 906 -6.3542 -23.3779 8.3 0.2 11222 8:19:56 10.0 65.8 839 -5.3198 -22.0455 10.0 0.2 11267 8:20:41 15.0 65.9 681 -1.9698 -18.2882 14.9 0.2 11324 8:21:38 20.0 66.4 566 1.7759 -14.6744 20.0 0.2 11389 8:22:43 25.0 67.6 484 5.7591 -11.1737 25.0 0.2 11459 8:23:53 30.0 69.3 423 9.8626 -7.7359 29.9 0.2 11536 8:25:10 35.0 72.0 376 14.2285 -4.1223 35.0 0.2 11617 8:26:31 40.0 75.5 341 18.6881 -0.3574 40.0 0.2 11702 8:27:56 45.0 80.4 314 23.2314 3.6748 45.0 0.2 11795 8:29:29 50.0 87.2 292 28.0338 8.3043 50.1 0.2 11899 8:31:13 55.0 97.2 275 33.1626 13.9036 55.1 0.2 12030 8:33:24 60.0 114.2 262 39.1650 21.8632 60.2 0.2 12234 8:36:48 63.4 151.2 255 47.0528 37.0968 63.7 0.2 13294 8:54:28 0.8 -64.5 1325 27.3823 148.1378 0.4 0.2 ORBIT 4: 16690 9:51:04 1.8 66.7 1265 -9.6802 -52.3954 1.4 0.2 16699 9:51:13 4.9 66.2 1072 -8.0881 -49.4657 4.7 0.2 16729 9:51:43 9.9 65.9 843 -5.1485 -45.2990 9.8 0.2 16775 9:52:29 15.0 66.0 681 -1.7206 -41.4470 14.8 0.2 16832 9:53:26 20.0 66.5 566 2.0222 -37.8361 19.9 0.2 16897 9:54:31 25.0 67.7 484 6.0029 -34.3350 24.9 0.2 16968 9:55:42 30.0 69.5 423 10.1614 -30.8467 29.9 0.2 17044 9:56:58 35.0 72.1 377 14.4665 -27.2753 34.9 0.2 17125 9:58:19 40.0 75.7 341 18.9220 -23.5018 39.9 0.2 17210 9:59:44 45.0 80.6 314 23.4601 -19.4576 44.9 0.2 17211 9:59:45 45.0 80.7 314 23.5127 -19.4091 44.9 0.2 17304 10:01:18 50.0 87.5 292 28.3057 -14.7592 50.0 0.2 17409 10:03:03 55.0 97.7 275 33.4689 -9.0728 55.0 0.2 17541 10:05:15 60.0 115.0 262 39.4869 -0.9876 60.1 0.2 17742 10:08:36 63.2 151.5 256 47.1997 14.1343 63.6 0.2 17944 10:11:58 60.0 -167.3 263 52.2396 33.5070 60.4 0.2 18077 10:14:11 55.0 -142.8 277 53.4873 48.1278 55.4 0.2 18182 10:15:56 50.0 -125.9 295 53.1330 59.9764 50.3 0.2 18275 10:17:29 45.0 -112.8 316 51.8355 70.1724 45.3 0.2 18362 10:18:56 40.0 -102.1 344 49.8448 79.1689 40.2 0.2 18443 10:20:17 35.0 -93.6 379 47.3835 86.9762 35.2 0.2 18519 10:21:33 30.0 -86.7 424 44.5908 93.8316 30.2 0.2 18591 10:22:45 25.0 -80.9 484 41.5326 100.0236 25.2 0.2 18656 10:23:50 20.0 -76.3 565 38.4000 105.5577 20.2 0.2 18714 10:24:48 15.0 -72.5 679 35.2050 110.7819 15.1 0.2 18760 10:25:34 10.0 -69.3 838 32.1643 115.7207 10.0 0.2 18791 10:26:05 4.9 -66.5 1071 29.2954 120.7750 4.8 0.2 Lowest elevation at which my program "sees" a transit 18801 10:26:15 0.7 -64.4 1338 27.1613 125.1682 0.4 0.2 Contact 4, on ORBIT 5: 22385 11:25:59 23.5 67.4 506 5.0450 -58.5304 23.3 0.3 ------------------------------------------------------------------------- Subscribe/Unsubscribe info, Frequently Asked Questions, SeeSat-L archive: http://www.satobs.org/seesat/seesatindex.html
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