Almanac Data Tables
Aries, Sun, and Moon
Navigational stars with magnitude ≤ 1.5
Lunar Distance Tables
Lunar Distance Tables with one-hour intervals for up to 5 celestial bodies, including Proportional Logarithms
Lunar Distance Tables with one-hour intervals for up to 7 celestial bodies
Which table which with Proportional Logarithms can be used with the Lunar Distance Tables?
Use this Proportional Logarithm Table
for one-hour intervals.
For which celestial bodies is the lunar distance shown?
On the page with almanac data the lunar distance is shown if the following requirements are met:
- 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.
- 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.
- The angle between the sun and the moon is at least 10°. This is because the moon is hardly visible during New Moon. See Steven Wepster's notes for the choice of this cutoff value.
- The GHA of the celestial body differs by more than 15° from the GHA of the sun. Otherwise the celestial body might not be visible. The cutoff value of 15° is quite arbitrary.
- 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.
- 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. Again the cutoff value of 40° is quite arbitrary.
- In case of a star, it is one of the 57 navigational stars and the magnitude is ≤ 1.5
- 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.
See also Steven Wepster's website
for rules to decide whether the lunar distance is practically relevant. On his website you can also find tables with lunar distances
with 3-hour intervals for the years 2007 to 2015 that are in the same format as the tables in the 19th century Nautical Almanac. The format of the lunar distance tables on this website is almost the same, except that the interval is 1 hour instead of 3 hours.
On the NavList community website
I asked a question
about when to display lunar distances. With a subject & author search for "lunar distance" you can easily find replies to this question. I thank the other community members for their suggestions!
How are the celestial bodies in the Lunar Distance Tables selected?
For each day, a celestial body was selected if the requirements mentioned in the previous question were met at 0:00 UTC. The selected celestial bodies were then assigned a score using a weighted sum of the following parameters:
- The lunar distance.
- The absolute value of the change of the lunar distance between 0:00 UTC and 1:00 UTC.
Two celestial bodies, A and B, have the same score if the lunar distance of A is 10° larger than that of B, and the change of lunar distance of A is 1' of arc larger than that of B. The celestial bodies with the highest scores were selected, where at least one celestial body with increasing and decreasing lunar distance was selected.
What do the '+' and '-' sign in front of the names of the celestial bodies in the Lunar Distance Tables mean?
The '+' or '-' sign in front of the name of the celestial body indicates whether the lunar distance is increasing or decreasing with time, respectively. The '+' or '-' sign also indicates whether the celestial body is west or east of the moon, respectively.
Why is the lunar distance in the Lunar Distance Tables not always shown for all hours of the day?
When the moon passes a celestial body close by, the lunar distance changes nonlinearly. As a consequence, a linear interpolation of the lunar distance is not very accurate anymore. If the maximum error that is made by using a linear interpolation exceeds 0.1' the lunar distance is not shown. For an explanation, click here