Daily Almanac Data

Selected date: Saturday 7 Dec 2019 UT1
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Aries, Sun and Moon

AriesSun
d = -0.3' SD = 16.2'
Moon
SD = 14.9'
UT1GHAGHAdecGHAvdecdHP
0 75° 28.6'182° 13.5'S 22° 32.6' 60° 30.4'15.9'N 0° 44.7'11.8'54.4'
1 90° 31.0'197° 13.2'S 22° 32.9' 75° 05.4'15.9'N 0° 56.5'11.8'54.4'
2105° 33.5'212° 13.0'S 22° 33.2' 89° 40.3'15.9'N 1° 08.2'11.8'54.5'
3120° 36.0'227° 12.7'S 22° 33.5'104° 15.2'15.9'N 1° 20.0'11.8'54.5'
4135° 38.4'242° 12.4'S 22° 33.8'118° 50.1'15.9'N 1° 31.8'11.8'54.5'
5150° 40.9'257° 12.2'S 22° 34.0'133° 24.9'15.8'N 1° 43.6'11.8'54.5'
6165° 43.3'272° 11.9'S 22° 34.3'147° 59.7'15.8'N 1° 55.4'11.8'54.5'
7180° 45.8'287° 11.6'S 22° 34.6'162° 34.5'15.8'N 2° 07.2'11.8'54.5'
8195° 48.3'302° 11.4'S 22° 34.9'177° 09.3'15.8'N 2° 19.0'11.8'54.5'
9210° 50.7'317° 11.1'S 22° 35.2'191° 44.1'15.7'N 2° 30.8'11.8'54.6'
10225° 53.2'332° 10.8'S 22° 35.5'206° 18.8'15.7'N 2° 42.6'11.8'54.6'
11240° 55.7'347° 10.6'S 22° 35.8'220° 53.5'15.7'N 2° 54.4'11.8'54.6'
12255° 58.1' 2° 10.3'S 22° 36.0'235° 28.2'15.7'N 3° 06.2'11.8'54.6'
13271° 00.6' 17° 10.0'S 22° 36.3'250° 02.9'15.6'N 3° 18.0'11.8'54.6'
14286° 03.1' 32° 09.8'S 22° 36.6'264° 37.5'15.6'N 3° 29.7'11.8'54.6'
15301° 05.5' 47° 09.5'S 22° 36.9'279° 12.1'15.6'N 3° 41.5'11.8'54.6'
16316° 08.0' 62° 09.2'S 22° 37.2'293° 46.7'15.5'N 3° 53.3'11.8'54.7'
17331° 10.5' 77° 09.0'S 22° 37.4'308° 21.2'15.5'N 4° 05.0'11.7'54.7'
18346° 12.9' 92° 08.7'S 22° 37.7'322° 55.7'15.5'N 4° 16.8'11.7'54.7'
19 1° 15.4'107° 08.4'S 22° 38.0'337° 30.2'15.4'N 4° 28.5'11.7'54.7'
20 16° 17.8'122° 08.2'S 22° 38.3'352° 04.6'15.4'N 4° 40.3'11.7'54.7'
21 31° 20.3'137° 07.9'S 22° 38.5' 6° 39.0'15.4'N 4° 52.0'11.7'54.7'
22 46° 22.8'152° 07.6'S 22° 38.8' 21° 13.3'15.3'N 5° 03.7'11.7'54.8'
23 61° 25.2'167° 07.4'S 22° 39.1' 35° 47.6'15.3'N 5° 15.4'11.7'54.8'

Planets

Venus
v = -0.9' d = 0.3'
Jupiter
v = 1.9' d = 0.0'
Saturn
v = 2.2' d = 0.0'
Mars
v = 0.8' d = -0.5'
UT1GHAdecGHAdecGHAdecGHAdec
0150° 31.3'S 24° 21.4'164° 26.6'S 23° 18.2'145° 20.9'S 22° 03.8'216° 02.6'S 14° 46.8'
1165° 30.4'S 24° 21.2'179° 28.5'S 23° 18.2'160° 23.0'S 22° 03.8'231° 03.5'S 14° 47.4'
2180° 29.4'S 24° 20.9'194° 30.3'S 23° 18.2'175° 25.2'S 22° 03.7'246° 04.3'S 14° 47.9'
3195° 28.5'S 24° 20.7'209° 32.2'S 23° 18.2'190° 27.4'S 22° 03.7'261° 05.1'S 14° 48.4'
4210° 27.6'S 24° 20.4'224° 34.0'S 23° 18.2'205° 29.6'S 22° 03.7'276° 06.0'S 14° 48.9'
5225° 26.7'S 24° 20.1'239° 35.9'S 23° 18.2'220° 31.8'S 22° 03.6'291° 06.8'S 14° 49.5'
6240° 25.8'S 24° 19.9'254° 37.7'S 23° 18.2'235° 34.0'S 22° 03.6'306° 07.6'S 14° 50.0'
7255° 24.8'S 24° 19.6'269° 39.6'S 23° 18.2'250° 36.1'S 22° 03.6'321° 08.5'S 14° 50.5'
8270° 23.9'S 24° 19.3'284° 41.4'S 23° 18.2'265° 38.3'S 22° 03.5'336° 09.3'S 14° 51.1'
9285° 23.0'S 24° 19.1'299° 43.3'S 23° 18.2'280° 40.5'S 22° 03.5'351° 10.1'S 14° 51.6'
10300° 22.1'S 24° 18.8'314° 45.1'S 23° 18.2'295° 42.7'S 22° 03.5' 6° 11.0'S 14° 52.1'
11315° 21.2'S 24° 18.5'329° 47.0'S 23° 18.2'310° 44.9'S 22° 03.4' 21° 11.8'S 14° 52.6'
12330° 20.3'S 24° 18.2'344° 48.8'S 23° 18.2'325° 47.1'S 22° 03.4' 36° 12.7'S 14° 53.2'
13345° 19.4'S 24° 18.0'359° 50.7'S 23° 18.2'340° 49.2'S 22° 03.4' 51° 13.5'S 14° 53.7'
14 0° 18.4'S 24° 17.7' 14° 52.5'S 23° 18.2'355° 51.4'S 22° 03.3' 66° 14.3'S 14° 54.2'
15 15° 17.5'S 24° 17.4' 29° 54.4'S 23° 18.2' 10° 53.6'S 22° 03.3' 81° 15.2'S 14° 54.7'
16 30° 16.6'S 24° 17.1' 44° 56.2'S 23° 18.2' 25° 55.8'S 22° 03.3' 96° 16.0'S 14° 55.3'
17 45° 15.7'S 24° 16.9' 59° 58.1'S 23° 18.2' 40° 58.0'S 22° 03.2'111° 16.8'S 14° 55.8'
18 60° 14.8'S 24° 16.6' 74° 59.9'S 23° 18.2' 56° 00.2'S 22° 03.2'126° 17.7'S 14° 56.3'
19 75° 13.9'S 24° 16.3' 90° 01.8'S 23° 18.2' 71° 02.3'S 22° 03.2'141° 18.5'S 14° 56.8'
20 90° 13.0'S 24° 16.0'105° 03.6'S 23° 18.2' 86° 04.5'S 22° 03.1'156° 19.3'S 14° 57.4'
21105° 12.0'S 24° 15.7'120° 05.5'S 23° 18.2'101° 06.7'S 22° 03.1'171° 20.2'S 14° 57.9'
22120° 11.1'S 24° 15.4'135° 07.3'S 23° 18.2'116° 08.9'S 22° 03.1'186° 21.0'S 14° 58.4'
23135° 10.2'S 24° 15.2'150° 09.2'S 23° 18.2'131° 11.1'S 22° 03.0'201° 21.8'S 14° 58.9'

Navigational stars with magnitude ≤ 1.5 and Polaris

magSHAdecmagSHAdecmagSHAdec
Fomalhaut+1.2 15° 19.1'S 29° 31.2'Spica+1.0158° 26.8'S 11° 15.7'Betelgeuse+0.5270° 56.2'N 7° 24.5'
Deneb+1.2 49° 28.8'N 45° 21.3'Acrux+0.8173° 04.7'S 63° 12.1'Capella+0.1280° 27.4'N 46° 00.9'
Altair+0.8 62° 04.2'N 8° 55.4'Regulus+1.4207° 38.7'N 11° 52.2'Rigel+0.2281° 07.5'S 8° 10.8'
Vega+0.0 80° 36.4'N 38° 48.3'Pollux+1.2243° 22.0'N 27° 58.5'Aldebaran+0.9290° 43.9'N 16° 32.8'
Antares+1.1112° 21.2'S 26° 28.3'Procyon+0.4244° 54.8'N 5° 10.4'Polaris+2.0315° 24.7'N 89° 20.9'
Rigil Kent-0.0139° 46.3'S 60° 54.7'Adhara+1.5255° 08.7'S 28° 59.9'Achernar+0.5335° 23.0'S 57° 08.5'
Arcturus-0.1145° 52.0'N 19° 04.8'Sirius-1.4258° 29.5'S 16° 44.6'
Hadar+0.6148° 42.1'S 60° 27.7'Canopus-0.6263° 53.7'S 52° 42.3'

Lunar distances

Lunar distance of celestial bodies east of the moon

UT1PolluxProcyonAdharaSiriusBetelgeuseCapellaRigelAldebaran
0 99° 55.8'100° 00.4' 90° 15.7' 86° 54.1' 74° 08.0' 72° 05.5' 64° 18.7' 55° 44.0'
1 99° 25.9' 99° 31.9' 89° 57.3' 86° 31.1' 73° 39.1' 71° 38.5' 63° 53.5' 55° 14.1'
2 98° 56.1' 99° 03.3' 89° 38.9' 86° 08.2' 73° 10.3' 71° 11.5' 63° 28.3' 54° 44.2'
3 98° 26.3' 98° 34.8' 89° 20.6' 85° 45.2' 72° 41.5' 70° 44.5' 63° 03.2' 54° 14.3'
4 97° 56.4' 98° 06.2' 89° 02.2' 85° 22.3' 72° 12.6' 70° 17.5' 62° 38.1' 53° 44.4'
5 97° 26.5' 97° 37.6' 88° 43.8' 84° 59.3' 71° 43.7' 69° 50.5' 62° 13.0' 53° 14.4'
6 96° 56.6' 97° 09.0' 88° 25.4' 84° 36.4' 71° 14.8' 69° 23.5' 61° 47.9' 52° 44.4'
7 96° 26.7' 96° 40.4' 88° 07.0' 84° 13.4' 70° 46.0' 68° 56.5' 61° 22.8' 52° 14.4'
8 95° 56.8' 96° 11.7' 87° 48.5' 83° 50.4' 70° 17.1' 68° 29.6' 60° 57.8' 51° 44.4'
9 95° 26.8' 95° 43.0' 87° 30.1' 83° 27.5' 69° 48.1' 68° 02.6' 60° 32.8' 51° 14.4'
10 94° 56.8' 95° 14.3' 87° 11.7' 83° 04.5' 69° 19.2' 67° 35.6' 60° 07.9' 50° 44.4'
11 94° 26.8' 94° 45.6' 86° 53.3' 82° 41.5' 68° 50.3' 67° 08.6' 59° 43.0' 50° 14.3'
12 93° 56.8' 94° 16.9' 86° 34.8' 82° 18.6' 68° 21.4' 66° 41.6' 59° 18.1' 49° 44.3'
13 93° 26.8' 93° 48.1' 86° 16.4' 81° 55.6' 67° 52.4' 66° 14.7' 58° 53.2' 49° 14.2'
14 92° 56.7' 93° 19.4' 85° 58.0' 81° 32.6' 67° 23.4' 65° 47.7' 58° 28.4' 48° 44.0'
15 92° 26.7' 92° 50.6' 85° 39.5' 81° 09.6' 66° 54.5' 65° 20.8' 58° 03.6' 48° 13.9'
16 91° 56.6' 92° 21.7' 85° 21.1' 80° 46.7' 66° 25.5' 64° 53.8' 57° 38.9' 47° 43.8'
17 91° 26.5' 91° 52.9' 85° 02.7' 80° 23.7' 65° 56.5' 64° 26.9' 57° 14.1' 47° 13.6'
18 90° 56.3' 91° 24.0' 84° 44.2' 80° 00.7' 65° 27.5' 63° 59.9' 56° 49.5' 46° 43.4'
19 90° 26.2' 90° 55.2' 84° 25.8' 79° 37.8' 64° 58.5' 63° 33.0' 56° 24.8' 46° 13.2'
20 89° 56.0' 90° 26.3' 84° 07.4' 79° 14.8' 64° 29.4' 63° 06.1' 56° 00.3' 45° 43.0'
21 89° 25.8' 89° 57.3' 83° 49.0' 78° 51.9' 64° 00.4' 62° 39.2' 55° 35.7' 45° 12.7'
22 88° 55.6' 89° 28.4' 83° 30.5' 78° 28.9' 63° 31.4' 62° 12.3' 55° 11.2' 44° 42.4'
23 88° 25.3' 88° 59.4' 83° 12.1' 78° 06.0' 63° 02.3' 61° 45.4' 54° 46.8' 44° 12.1'

Lunar distance of celestial bodies west of the moon

UT1SunVenusJupiterSaturnFomalhautAltair
0119° 22.4' 90° 19.2'103° 04.8' 85° 30.0' 41° 50.7' 77° 04.8'
1119° 49.8' 90° 46.0'103° 34.2' 85° 59.7' 42° 17.8' 77° 30.2'
2 91° 12.9'104° 03.6' 86° 29.4' 42° 44.8' 77° 55.6'
3 91° 39.8'104° 33.0' 86° 59.1' 43° 12.0' 78° 21.0'
4 92° 06.7'105° 02.5' 87° 28.8' 43° 39.2' 78° 46.5'
5 92° 33.6'105° 31.9' 87° 58.6' 44° 06.5' 79° 11.9'
6 93° 00.6'106° 01.4' 88° 28.3' 44° 33.8' 79° 37.4'
7 93° 27.5'106° 30.9' 88° 58.1' 45° 01.2' 80° 03.0'
8 93° 54.5'107° 00.4' 89° 27.9' 45° 28.7' 80° 28.5'
9 94° 21.5'107° 29.9' 89° 57.8' 45° 56.2' 80° 54.1'
10 94° 48.5'107° 59.4' 90° 27.6' 46° 23.8' 81° 19.7'
11 95° 15.6'108° 29.0' 90° 57.4' 46° 51.5' 81° 45.4'
12 95° 42.6'108° 58.6' 91° 27.3' 47° 19.2' 82° 11.1'
13 96° 09.7'109° 28.2' 91° 57.2' 47° 46.9' 82° 36.8'
14 96° 36.8'109° 57.8' 92° 27.1' 48° 14.7' 83° 02.5'
15 97° 03.9'110° 27.4' 92° 57.1' 48° 42.6' 83° 28.2'
16 97° 31.0'110° 57.1' 93° 27.0' 49° 10.5' 83° 54.0'
17 97° 58.2'111° 26.8' 93° 57.0' 49° 38.5' 84° 19.8'
18 98° 25.4'111° 56.5' 94° 27.0' 50° 06.5' 84° 45.6'
19 98° 52.6'112° 26.2' 94° 57.0' 50° 34.5' 85° 11.5'
20 99° 19.8'112° 56.0' 95° 27.1' 51° 02.7' 85° 37.4'
21 99° 47.0'113° 25.7' 95° 57.1' 51° 30.8' 86° 03.3'
22100° 14.3'113° 55.5' 96° 27.2' 51° 59.1' 86° 29.2'
23100° 41.6'114° 25.3' 96° 57.3' 52° 27.3' 86° 55.1'

Explanation

The almanac data was calculated using Python and Skyfield.

Greenwich Hour Angle (GHA) and declination (dec)

For celestial navigation Universal Time (UT1) is used. An explanation of UT1 and other astronomical times can be found here. A table with recent values for the difference between UT1 and UTC, and a 90 day prediction, can be found here. The GHA of Aries was calculated using Greenwich Apparent Sidereal Time:
from skyfield.api import load
ts = load.timescale()
t = ts.ut1(year, month, day, hour, minute, second)
gha_aries = pi * t.gast / 12. # GHA of Aries
For the calculation of the GHA and declination of a celestial body its position is required. Positions and coordinates are explained here. From NASA's Navigation and Ancillary Information Facility (NAIF) the following ephemerides were used: de421.bsp, jup310.bsp, sat375.bsp.
ephem = load_file('de421.bsp')
earth = ephem['Earth']
moon = ephem['Moon']
ra, dec, dist = earth.at(t).observe(moon).apparent().radec(epoch = t) # Right Ascension, declination, and distance
gha_moon = gha_aries - ra.radians # GHA of Moon
For the calculation of the apparent position the positions of the Earth, Sun, Jupiter, and Saturn are required. Since the ephemerides of Jupiter and Saturn do not contain all required positions, the segments of ephemeris de421.bsp were added. This is discussed here.

Increments to GHA (v) and declination (d)

For the sun the v value was not calculated. If needed anyway, the v value of the sun can easily be found by inspection, as it is equal to the hourly GHA increase minus 15°. For the planets a daily v value is given. It was calculated by taking the average over the day of the hourly GHA increase minus 15°. For the planets and the sun a daily d value is given, which was calculated by taking the average over the day of the hourly change in declination. For the moon hourly v and d values are shown. The v value of the moon is equal to the hourly GHA increase minus 14°19'.

Semi Diameter (SD) and Horizontal Parallax (HP)

The SD of the sun and the moon is given for each day at the start of the day. For the moon hourly values of the HP at the start of the hour are given. For the calculation of SD and HP the volumetric mean radius was used that can be found on the NASA website.

Lunar distance

The lunar distance of a celestial body is shown if the following requirements are met:
  1. The angle between the celestial body and the moon is less than 120°. With a sextant this is more or less the maximum angle that can be measured.
  2. In case of the lunar distance of the sun, the angle between the sun and the moon is larger than 40°. Otherwise the moon is not visible.
  3. The angle between the celestial body and the sun is at least 10°. Otherwise the celestial body might not be visible.
  4. The angle between the sun and the moon is at least 10°. This is because the moon is hardly visible during New Moon.
  5. The sun is not in between the celestial body and the moon. This is tested by looking at the GHA. The rationale behind this requirement is that the lunar distance of stars and planets can only be determined if the sun is below the horizon and the moon is above the horizon.
  6. The rate of change of the angle between the celestial body and the moon is at least 15' of arc per hour of time. If less, accurate time determination using the lunar distance becomes more difficult due to increasing sensitivity to measurement errors. The cutoff value is chosen to be half the right ascension rate of the moon, which is about 30' of arc per hour of time.
  7. The error that is made by linear interpolation of the lunar distance is ≤ 0.1' of arc. When the moon passes a celestial body close by, the lunar distance changes nonlinearly over time. As a consequence, a linear interpolation is not very accurate anymore. A quadratic interpolation yields more accurate results. The celestial body is not shown if the maximum difference between a linear and a quadratic interpolation is > 0.1' of arc. For a further explanation, click here.