Monday, March 2, 2015

Telling Time by the Stars


As is the case with tricks for finding directions from the stars, there is no exclusive way to tell time from the stars, so we are free to make up whatever method works. To make up generalized star clocks that work on any arbitrary day of the year, however, does require some background, to be reviewed here. It is much easier to make up specific clocks on the spot, using a correct watch to calibrate it for the present date, and then use it on following nights by applying a simple daily correction. This does not require special reference books and calculations.

To tell time from the Big Dipper, as one example of a generalized star clock, imagine its pointers as the end of clock hands whose pivot point is Polaris and imagine a 24-hour clock face printed backwards on the sky around Polaris as shown in Figure 1. Midnight (0000 hours or 2400 hours) is straight up from Polaris; 0600 hours is to the west of Polaris and 1800 hours to the east. In 24 hours, the pointers sweep counterclockwise once around this clock face.



When the clock hand points straight up from the horizon, the clock reads midnight; when the hands point east with the pointers lying parallel to the horizon the clock reads 1800, and so forth. To read the clock at any time of the night, estimate the hour and fraction of an hour from the relative orientation of the pointers on the imaginary clock face. That’s all there would be to it if the sun kept pace with the stars. But the sun does not keep pace with the stars, and our daily time keeping is based on the sun so we must make a correction for this.

 All star clocks are fast; they gain 4 minutes each day because we keep track of time relative to the location of the sun, and we are moving around the sun relative to the stars at a rate of about 1º per day (360º/365d). Thus when we make our daily 24h rotation from noon to noon (relative to the sun) we are then 1º farther along our orbit, so we have passed any stars overhead by 1º. At our daily rotation rate of 360º/24h this 1º is equivalent to 4 minutes.

If you look at the same star on successive nights at the same time, it will be 1º farther (more westward) along its path across the sky. Thus if you want to see it at the same place on successive nights, you have to look 4 min earlier. This is basically how new stars appear on the eastern horizon at sunset as the seasons progress—although that is a bit more complicated because the time of sunrise is also changing. (We learn star positions relative to Aries, so check out the value of GHA Aries on successive days at the same time and you will see it increases by about 1º.)

At a gain of 4 minutes per day, star clocks gain a whole day in one year, so all star clocks reset themselves on a particular date that depends on the particular star clock in use—and by star clock we mean any two stars with the same SHA so the line between them rotates around the pole. The Big Dipper star clock resets itself on March 8th so all corrections must be reckoned from that date. (Official scientific star time used by astronomers resets on the Vernal Equinox, March 21st; the shift to March 8th comes about because scientific star time does not use the Big Dipper pointers for a reference line.)

To tell time from the Big Dipper, we need to know how many days have passed since March 8th. The time we read directly from the star clock is then fast by 4 minutes for each of these days. As an example, suppose the date was September 22nd and the stars looked as they do in Figure 1, with the star clock reading 0830. September 22nd is 198 days past March 8th, so the clock is fast by 198 × 4 minutes, which equals 792 minutes, or 13 hours and 12 minutes. The first 12 hours of the correction just switches the time from AM to PM, so the correct time of night is 2030 - 0112, which equals 1918, or 7:18 local time.

Figuring the correction is a bit involved, but this preparation need only be done once, after which the results can be rearranged to be more convenient. On September 22nd, for example, you could make an equivalent new rule for reading this star clock: change the star clock time from AM to PM (or vice versa, later in the night) and then subtract 1 hour and 12 minutes. Each subsequent night, you would subtract an extra 4 minutes, because the clock is still gaining time each night.

The time you figure from the corrected star clock will be the proper standard time for your time zone to within, at worst, some 30 minutes. It would be exact only if you happened to be located right in the middle of a time zone, each of which is about 1 hour wide according to star time. Star clocks also do not know about daylight saving time, so when daylight saving time is in effect, you must add 1 hour to the final result. Corrections for both longitude (the time zone correction) and for daylight saving time can be made simultaneously if you calibrate the star clock with a known time. In the last example, if the uncorrected star clock read 0830 AM at a time you knew was 8:10 Pacific Daylight Time, the rule becomes much simpler: subtract 20 minutes tonight, and then 4 minutes less each subsequent night.

The final accuracy of the time obviously depends on how accurately the star clock itself is read, which requires an estimate of the angle between the clock hand and the horizon—similar to reading a stylish watch with no numbers on the dial. Sticks held in one line with the Pointers and one with the horizon can help with this. The angle found this way can then be transferred to a sketch of the clock or to the compass rose of a chart. Reading the clock by eye alone, however, is usually adequate. Note that in normal circumstances most people have an adequate sense of time even without a watch, but under a great deal of stress this is not the case at all. During long storms at sea, it is possible to even lose track of how many days have passed. This is not likely to happen in a routine cruising, but one could imagine getting caught in coastal waters at night without a safe harbor nearby. If the wind and seas began to build on top of this, one could easily muster enough stress to lose track of time. Without a watch, you could monitor the duration of the adventure with the stars.

(Note: A star clock resets when the common SHA of the two stars making up the clock hand leads to GHA = 0º 0' at 00 UTC. For the Big Dipper clock, Dubhe and Merak have SHA = 194º 4.2'±14.3', so we need the nearest date when  GHA Aries = 360º - 194º 4.2' = 165º 55.8' at 00 UTC. You can get rough estimate from the Planet Diagram, or interpolate the Almanac to find that this is March 8.)

Stargazing for orientation in time and space clearly requires some hands-on practice. It is not like learning the combination to a lock, that once memorized can be opened at will. It is more like learning to play a kazoo. You start by learning to play a few notes well, and pretty soon you are playing a fine tune. And the enjoyment to be had from exercising this skill can be just as rewarding. It is one way to get in a little more in tune with a dependable part of the environment.

The above is adapted from our book Celestial Navigation: A Complete Home Study Course.


1 comment:

David Burch said...

PS. It is either a sad or happy coincidence that the star clock resets on the day that daylight saving time changes, but there is no relationship between these events, other than maybe a nice way to remember the date... besides the day when a huge commercial aircraft disappeared from the sky without a trace.