Calculating the time of twilight
One commonly stated reason for learning celestial navigation is "to learn the stars." The satisfaction of knowing what's up there in the sky and putting that knowledge together with polished sextant skills to make a good star sight surely is what keeps celestial navigators coming back for more. What most budding celestial navigators don't realize, however, is that it isn't necessary to learn all the stars in the sky. You just need to know how to find a few stars twice each day during times of twilight, not the entire star catalog. Let's take a look at how to determine twilight, and in a subsequent Toolbox we'll review the different ways to come up with a list of visible stars to shoot. There are two types of twilight used by navigators, nautical twilight and civil twilight. Civil twilight is defined as that point in time when the center of the sun is 6° below the horizon. Nautical twilight is when the sun is 12° below the horizon. (A third type of twilight, called astronomical twilight, occurs when the sun is 18° below the horizon.) Astronomical definitions aside, what is it about the two twilights that makes them important for navigators? Basically, to make good star sights, the navigator needs two things: visible stars and a visible horizon. In the evening, a few minutes after sunset, civil twilight marks the time when the brightest stars first appear in the sky (some planets may become visible earlier). Nautical twilight follows, marking the time when the horizon disappears from view, sending the celestial navigator down below and bringing the star gazers out on deck. In the morning, some time before sunrise, nautical twilight is marked by a brightening sky, one with enough light from the approaching sun to make the horizon visible. By the time of civil twilight, just a few minutes before sunrise, the stars are all but washed out by an even brighter sky. The time span between the two twilights varies depending upon the latitude of the observer, but generally there's enough time to grab a good round of sights. The two twilights, along with times of sunrise, sunset, moonrise, and moonset are listed on the daily pages of the Nautical Almanac, with rising or morning phenomena at the top half of the page and evening or setting phenomena on the bottom half of the page (see excerpt from Nautical Almanac). For our exercise, let's assume we are interested in determining the best time to shoot morning stars. Since we want to be on deck with enough time to take a good round of sights, we need to find the time of nautical twilight, which occurs first in the morning. But, before diving into the calculation, we need to go to the chart and calculate a DR for around the time of sunrise. For our exercise, let's assume a DR position of 36° N, 68° W and a date of July 25, 1998. The twilight times given in the daily tables are all GMT, at the given degrees of latitude, at the Greenwich Meridian (0° longitude). Our first job is to interpolate for the DR latitude of 36° N. Looking at the table, under the column for nautical twilight, we find a time of 0401 for 35° N and a time of 0342 for 40° N. That's about 20 minutes difference for the 5° spread of latitude, roughly four minutes per degree (a rough calculation is fine for our purposes). Subtracting four minutes from 0401 (to interpolate for the degree from 35° N to 36° N) we get a time of 0357, the GMT time of nautical twilight at 0° longitude. Naut. twilight 35°N: 0401GMTNaut. twilight 36°N: 0357 GMTBut, what about the DR longitude, some 68° to the west of Greenwich? Remember that the sun appears to move from east to west, so nautical twilight at the DR longitude of 68° W will occur several hours later than 0357 GMT, when it occurs at Greenwich. To find out how much later, we turn to the first colored page in the back of the Nautical Almanac, the table for Conversion of Arc to Time (see excerpt). This complicated-sounding table does the simple job of taking longitude and converting it to time (and vice-versa), based on the fact that the sun takes one hour to travel 15° (360° around the earth divided by 24 hours of the day = 15° per hour). Of course, we all know the earth is doing the revolving, but for celestial navigators it's easier to think in Ptolemaic terms of the sun revolving around the earth. Looking through the table for our longitude of 68°, we find an equivalent time of four hours, 32 minutesthe length of time it takes the sun, or, in this case, twilight, to travel 68° to the west. Adding this amount of time to 0357 yields a time for nautical twilight of 0829 GMT. Nautical twilight at 36° N (from left): 0357 GMT Nautical twilight at 36° N, 68° W: 0829 GMT We'll want to set our alarm a few minutes earlier than the calculated time, to give us a chance to gather our equipment, and get our eyes adapted to the dark (unless the alarm is working on GMT, it will also be necessary to convert this GMT to a local timewe'll cover that in another story). Also, it's a good idea to double-check the DR before turning in and to recalculate twilight if necessary, since there is nothing more frustrating than getting out on deck too late and finding all the stars gone. And who wants to get up too early in the morning and have to wait around for the horizon to appear? So, we know when twilight will take place, but how do we know what stars to shoot? In the next issue we'll look at how to make up a good list of stars ahead of time to shoot at our morning twilight.