Sun position
Sun position algorithm
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Several tests were performed to compare the calculations of the routines in star.h / star.c with those given in examples in section B of the Astronomical Almanac (various years).
The 1987 Astronomical Almanac uses a fictitious star for its example calculations of stellar reduction. The catalog position of the star (given on page B40 of the Almanac) is
14 39 36.087, -60°50′07.14″, J2000,, -49.486 s/cy, +69.60″/cy, 0.752″, -22.2 km/s
The table below shows the results of converting this position to apparent coordinates (at the date shown in the table heading), using various approximations, and compared with the results from the Almanac itself.
Apparent coords at 1987-01-01 0h TT | RA | Dec |
---|---|---|
Almanac page B41 | 14:38:40.164 | -60°46′44.82″ |
Confirmation (see 1. below) | 14:38:40.1641 | -60°46′44.822″ |
No light deflection (see 2.) | 14:38:40.1652 | -60°46′44.820″ |
Simpler nutation (see 3.) | 14:38:40.1639 | -60°46′44.820″ |
IAU 2000 prec&nut | 14:38:40.1632 | -60°46′44.829″ |
Approx Earth (see 4.) | 14:38:40.1564 | -60°46′44.843″ |
All of the above (see 5.) | 14:38:40.1572 | -60°46′44.841″ |
The simplest calculation (see 5. below) gives a position error in RA of 0.0069 s and in Dec of 0.019″, giving a total angular position error on the sky of 0.054″.
The same star appears on page B40 of the 1990 Astronomical Almanac. Likewise, the table below compares the calculations here with the results from the Almanac itself.
Apparent coords at 1990-01-01 0h TT | RA | Dec |
---|---|---|
Almanac page B41 | 14:38:54.112 | -60°47′32.78″ |
Confirmation (see 1. below) | 14:38:54.1120 | -60°47′32.780″ |
No light deflection (see 2.) | 14:38:54.1131 | -60°47′32.778″ |
Simpler nutation (see 3.) | 14:38:54.1119 | -60°47′32.779″ |
IAU2000 prec&nut | 14:39:54.1109 | -60°47′32.784″ |
Approx Earth (see 4.) | 14:38:54.1046 | -60°47′32.790″ |
All of the above (see 5.) | 14:38:54.1056 | -60°47′32.789″ |
The simple calculation (see 5. below) gives a position error in RA of 0.0064 s and in Dec of 0.010″, giving a total angular position error on the sky of 0.048″.
The 2007 Astronomical Almanac introduced a very slightly different fictitious star for its example calculations on page B68. This one has a catalog position of
14 39 36.4958, -60 50 02.309 ICRS, J2000.0, -3678.06 mas/yr, 482.87 mas/yr, 0.742″, -21.6 km/s
Again, the table below compares the calculations here with the results from the Almanac itself.
Apparent coords at 2007-01-01 0h TT | RA | Dec |
---|---|---|
Almanac page B68 | 14:40:03.4343 | -60°51′37.770″ |
Nutation IAU2000B (see 6. below) | 14:40:03.4342 | -60°51′37.770″ |
No light deflection (see 7.) | 14:40:03.4353 | -60°51′37.769″ |
Approx Earth (see 8.) | 14:40:03.4265 | -60°51′37.784″ |
All of the above (see 9.) | 14:40:03.4276 | -60°51′37.782″ |
Nutation IAU1980 with precision 0 | 14:40:03.4400 | -60°51′37.784″ |
All above and Nutation 1980 | 14:40:03.4334 | -60°51′37.796″ |
All above and simpler Nutation 1980 | 14:40:03.4336 | -60°51′37.796″ |
The simple calculation (see 9. below) gives a position error in RA of 0.0067 s and in Dec of 0.012″, giving a total angular position error on the sky of 0.051″. Or if we use 1980 nutation, 0.0009s and 0.026″,
These three results show very small position errors.
Test conditions