and Vicinity

Northern Wyoming 


Time Measurement

Navigating by Astronomy
Time Measurement

Copyright © 2017 Travis N. Wood

Time cartoon
Early developments in time reckoning.


Our most basic concepts of time derive from astronomy.  But for convenience, civilization has made compromises with the science behind concepts. Days, months, seasons, and years originated in astronomical phenomena. But civilization invented 30-day months, 24-hour days, and 60-minute hours.

And civilization invented Daylight Saving Time, hour-long time zones, and time-zone boundaries that stray back and forth across our maps with the unpredictable whims of some city, state, or nation.

Our concepts of time are so overwhelmed by human tradition that it is not in our interest to abandon all tradition in the wilderness. We will not attempt 100-minute hours. However, the traditional concept of time zones can seriously handicap our efforts to find direction in the wilderness if we do not set some traditions aside in favor of a more scientific system of time reckoning.

Whatever its advantages in our working world, in the backcountry Daylight Saving Time is not to our advantage. And the blocked out wandering of time-zone boundaries on our maps can mislead us badly. Even hour-long time "zones" can interfere with accurate navigation. So in this discussion we have looked at how to convert our clock times to times much more useful to us, because precise use of astronomy can rely upon precise accounting of time.


In this discussion of time our goals are to work out a system of time:

  • 1) where the sun is directly south at noon, no matter what our location, and
  • 2) where bright stars, moon, and planets are directly south at predictable times.

With such a revised system of time we will be prepared to obtain the azimuth and altitude of virtually any celestial body when above the horizon. Unlike a magnetic compass focused on north, our focus first will be on the direction of south. But with a simple formula for finding "southing" times, we can then branch out to other directions.

In reaching the goals above we will also set aside some highly misleading "tricks" popularized by backpacking and survival sources. Using the hands on an analog watch to find direction is prone to very large error.  The method wrongly assumes that the sun is south at noon in civil time. But that is rarely the case. The system of time best adapted to wilderness navigation is not the system of time used in commerce. Which time system to use is not a question of right or wrong. It is a question of accuracy, usefulness, and efficiency.


Time Zones
Figure 1: Times Zones from North America to Greenwich

Civil Time consists of Standard Time in the cooler months and Daylight Saving Time in the warmer times of the year. Civil Time is the time we set our clocks to, and it is a human invention where the modern world has assigned the "zero hour" to be at the meridian of longitude passing through Greenwich, England (See Figure 1). That zero line of longitude we call the Prime Meridian. In Standard Time on an "average day," the sun appears to cross the Prime Meridian at noon.

From that starting point, Standard Time makes several compromises. First, it establishes a time "zone" from the meridian the sun crossed a half-hour before to the meridian the sun will cross a half-hour after the Greenwich southing. And all times within that zone are assigned the same hour and same minute of time. Thus, the Prime Meridian has become the center line of an hour time zone.

Secondly, the boundaries of each time zone depart widely from the lines of longitude upon which they are founded. And they do so in zigzagging lines. So the time zones of North America are displaced westward to include areas that strictly speaking would belong to another time zone. In Alaska, the time zone is displaced up to two hours westward.

Finally, for over half the year much of North America resorts to Daylight Saving Time. That causes a part of Alaska to be three hours displaced from the lines of longitude upon which standard time was founded. The result is that in late June in Nome, Alaska, the sun is directly south after 3 PM. Assuming it would be south at noon would result in a near 60° error in navigation. Yet civilized societies have their reasons for these compromises in time. But our purpose here is to reverse these compromises and revert to times where the sun is south at noon in whatever location we are.


There are 24 hours in a day and 360° in the circumference of the earth. So strictly speaking, each hour-long time zone would be 15° of longitude in width. If we assume a constant rate of the earth's rotation and revolution around the sun, then each degree of longitude would correspond to 4 minutes of time. With that information we can calculate when the sun will be south at our location if we simply know our longitude and the correct time at Greenwich, England, that is, Coordinated Universal Time (UTC).

There is no need for time zones to be an hour in length. Civilization has found that length of time convenient. But strictly speaking, a time zone could be a minute in length. And for our purposes in wilderness navigation, a minute-long time zone would be helpful. In the Northern Rockies at a latitude of 44° N, a minute-long time zone would be 12.5 miles East to West. Along the same latitude, one degree of longitude would be 50.0 miles East to West. Incidentally, the sun at this latitude appears to be traveling 750 miles per hour from East to West.

The problem for the backpacker, or other outdoors men and women, is that in that hour of time, especially on the longer days of summer, the sun may be traveling up to 38° of azimuth per hour, thus creating for that backpacker a huge miscalculation of direction if he relies upon the sun's direction at noon on a watch set to civil time.

In comparison, a minute-long time zone would result in less than a single degree of error in azimuth reckoning. And a four-minute-long time zone would result in, at most, less than 3° of azimuth imprecision. (See US Naval Observatory.) Such smaller errors are far more compatible with our interests in backcountry navigation. And they serve to accent the importance of accurate times if using a watch for navigation.


Mountain Time Zone
Figure 2: Mean Solar Time in the Mountain Time Zone

The discussion above may sound complicated. But it is not. To reset our watches, all we need are: 1) Universal Time or Standard Time, 2) the longitude of our location, and, as we will discuss later 3) an understanding of the sun's analemma.

In the chart and map to the right, it is officially noon everywhere in the Mountain Time Zone. That is our civil time, that is, Mountain Daylight Time in warmer months or Mountain Standard Time in cooler months. But on our chart, it is noon in Mean Solar Time only at the meridian of 105° west longitude, which passes about 15 miles west of Devil's Tower in the Black Hills Area.

Simply stated, we are dividing our longitude by 15° and subtracting the results from Universal Time. That yields the time of our locations in such a format that we can locate the sun at noon within a degree of azimuth.

As an example, suppose that we are backpacking the Teton Crest Trail. Our longitude west of Greenwich averages 110.8°. Dividing 110.8° by 15°, we find we are 7.39 hours, or 7 hours 23 minutes of time, west of Greenwich. So the sun will be south at our location 7 hr 23 m after it is south at Greenwich. Since Mountain Standard Time (MST) is 7 hours after Greenwich, we must subtract an additional 23 minutes from MST.

We know that on the "average day" of the year, the sun will be south at Greenwich at 12:00 PM Universal Time (UTC). And we set our watches to be at 4:37 AM for when it is noon, or 12:00 UTC at Greenwich. Thus, 7 hours and 23 minutes after the sun is south at Greenwich, the sun will be south at our location — at 12 noon by our watches. But that is only on an "average day." But what is an "average day"?  And what if our backpacking trip in the Tetons does not include any average sun days?


We are told early in our school years that a day is 24 hours long. That is true if we consider the average or mean position of the sun over an entire year. The time system which employs that average in the discussion above is called Mean Solar Time, and it works well for tracking the stars, planets, and moon — and sun on an "average day." But what we need now is Solar Time. We'll consider how to use Mean Solar Time in later sections. For now we have progressed from Daylight Saving Time back to Standard Time, adjusted Standard Time to our location, and now have Mean Solar Time to work with.

But we must make one more adjustment to find the actual position of the sun on any given day. That will provide for us a fourth system of time called simply Solar Time. It will no longer be simply the average solar time over a year. It will be Solar Time based upon the day of the year as well as our position within the time zone.


An average day is 24 hours long, but in terms of the sun's southing, very few days are average. In fact, there are only about four average days in the course of a year.  (Those are on or around April 17th, June 14th, September 3rd, and December 25th.)

The Sun's Analemma
Figure 3: The Sun's Analemma and Equation of Time

Throughout the rest of the year, the earth's tilt and elliptical orbit around the sun displace the southing of the sun as much as 15 to 16 minutes before or after noon — even after we have set our watches so precisely to our location. To understand what is happening in the skies above us, we must define "one day" to mean the period of time from when the sun is directly south at our location to when the sun is again south at the same location on the following day. One day is thus the period of time from the sun's meridian crossing to the next meridian crossing. That is, one day is from southing to next southing at the same location.

To make that final adjustment to our watches and arrive at Solar Time, we will follow the graph in Figure 3. It shows upon which dates the sun is south early and on which dates the sun is south late. And it provides the number of minutes.

Those adjustments will be applied to Mean Solar Time as we derived it above for the longitude of our position. The phenomenon involved is called the sun's analemma, and it has been known since ancient times and has been used in the making of sundials.

As noted, it is the earth's tilt and elliptical orbit around the sun which cause the analemma. The graph in Figure 3 used to decipher that phenomenon is called "The Equation of Time." And that graph and the analemma can both be tracked in detail at the US Naval Observatory. We will discuss the analemma further in our section on the sun. For now we simply need to know how to make this final adjustment to our watches in order to arrive at the Solar Time System for our position of longitude.


In finding a system of time most suitable to wilderness navigation, we have progressed through four time systems:

  • 1) Daylight Saving Time,
  • 2) Standard Time,
  • 3) Mean Solar Time, and
  • 4) Solar Time.

The first two systems are the conventions of civilization. They constitute our Civil Time. The last two systems are well established among scientists. Neither is something we have invented here.

To reset our watches we first drop Daylight Saving Time in favor of Standard Time. We then convert Standard Time to strict longitudinal lines corresponding to our wilderness locations. In doing so, we arrive at Mean Solar Time, which is suitable for navigating by the stars. From Mean Solar Time, we apply the Equation of Time to account for the sun's analemma. That gives us Solar Time by which we can navigate by the sun during daylight hours.

In Solar Time the sun will be directly south at noon. And if the sun rises seven hours before noon, it will set seven hours past noon. Moreover, if we know altitude and azimuth of the sun before noon, we can employ those same bearings for after noon.


Let's do a few exercises such we might do in planning a backpacking trip. We can then check our work against astronomy software or the US Naval Observatory. For software I have chosen WinStars2, a free download that is versatile and easy to use. At the US Naval Observatory, we can get accurate data from the page for "Altitude and Azimuth of the Sun or Moon During One Day" under the heading "Positions of Selected Celestial Objects."

And by all means, let's begin with precise time by going to the official time source and set our watches precisely to the second for our time zone. Remember, our purpose in this section is to employ an accurate time system. We'll use the azimuth of the sun to check our work. Later sections of this website will discuss how to arrive at altitudes and other useful information for sun, moon, stars, and planets.

To put longitude and analemma adjustments in perspective, we can think of the two changes like this: As our location moves west of the Mountain Time Meridian (left on map), the sun's southing will be later than its southing at the Mountain Time Meridian. But as we move left on the Equation of Time graph (The Figure 8) the effect will be opposite, and the sun's southing will be earlier. So if we move 14 minutes of time left on the map and also 14 minutes of time left on the Figure 8, the time factors will cancel each other, and the sun's southing at our location will be as if we applied neither adjustment. That is, we can expect the sun to south at noon Mountain Standard Time. For our location on that day Mountain Standard Time and Solar Time are equal.

Bighorn Mountains
Figure 4, Exercise 1:
Bighorn Mountains

Big Horn Mountains, Wyoming, Early Autumn.

Our planned location is near the Shell Creek Trailhead, October 1, 2016. Map coordinates are 44.55° N latitude, 107.5° W longitude. From the map in Figure 2 above we see that because of our longitude, the sun's southing will be delayed 10 minutes from Mountain Standard Time. But from the analemma graph in Figure 3 we see that for this date the sun's southing will be early by 10 minutes.

 In this example, the effects of longitude adjustment and sun's analemma cancel each other. So we find that a precise setting to Mountain Standard Time with no other adjustments will provide a sun's southing at noon Mountain Standard Time on that date and in that location.

We then go to the Naval Observatory and check to see when the sun will be at 180° azimuth on the given date at the given location. The data sheet we are provided shows that the sun's southing will be at between 11:59 AM and 12:00 PM MST. Our calculations are successful. Our precision is within one minute of time and within one degree of azimuth.

Using WinStars software to check our work, we are unable to detect any error in precision. The 180° line of azimuth appears to directly bisect the sun.

Wind River Range, Wyoming, Mid-Summer.

Wind River Range
Figure 5, Exercise 2:
Wind River Range

We'll be backpacking into the Wind Rivers by way of the Wind River Indian Reservation. We'll basecamp for a few nights at Little Milky Lake, 43.1424 N latitude, 109.462 W longitude. Date of arrival is August 18, 2017. We plan to explore the area off-trail for a couple days. How do we set our watches so that the sun will be south at noon?

Our watches are currently set precisely to Mountain Daylight Time.

  • 1) First, we'll return to Mountain Standard Time by subtracting one hour.
  • 2) Our location will be 4.46° further west of the Mountain Time Meridian, which is at 105° W longitude. For every 15° longitude west of Greenwich, the south's southing is delayed an hour. So an addition 4.46° longitude west will delay southing another 18 minutes of time beyond the 7 hours at the Mountain Time Meridian.
  • 3) From the analemma graph, we see that on August 18th, the southing will be delayed another 4 minutes.

Taking the three steps together, we set our watches back an hour and 22 minutes. Our calculations say that the sun will be south at 12:22 hours MST or 13:22 hours MDT. Now checking with the US Naval Observatory, and scrolling down the page to around 180° azimuth, we see again that our precision is less than a degree off and less than a minute off.

As we set off backpacking we will set our watches back 1:22 hours, for example, from 7:00 AM MDT to 5:38 AM Solar Time. Then at noon Solar Time, on our watches, we can expect the sun to be directly south.

Black Hills, South Dakota, Late Springtime

Black Hills
Figure 6, Exercise 3:
Black Hills

Our plan is for a three-day backpacking trip into Black Elk Wilderness, where we'll camp near 43.86° N latitude, 103.5° W longitude on June 4, 2017. Because we will be traveling from the Upper Midwest, our watches will be set to Central Daylight Time.

Following are the steps we would take to set our watches to Solar Time:

  • 1) From Central Daylight Time to Central Standard Time: subtract one hour.
  • 2) From Central Standard Time to Mountain Standard Time: subtract another hour.
  • 3) From Mountain Standard Time to Mean Solar Time: Because we will be 1.5° east of the Mountain Time meridian, to adjust for longitude, add 6 minutes.
  • 4) From Mean Solar Time to Solar Time by the Analemma graph on June 4th: add another 2 minutes.

Taking the steps altogether, we have subtracted 1:52 hours, one hour and 52 minutes. That is, in other words, we are subtracting 2 hours and adding 8 minutes. The further east, the earlier the sun's meridian crossing. The earlier the meridian crossing, the more time we add to set our watches to get Solar Time. To the west we subtract time from our watches, to the east we add time. For later southings, we subtract time from our watch. For earlier southings, we add time to our watch.

Now let's check our calculations against data from the Naval Observatory.  The parameters we input at the Naval Observatory (Form B - Locations Worldwide) must be for even hours, so we'll enter 7 hours west of Greenwich for Mountain Standard Time. Since that does not allow us to enter the 8-minute adjustment above, we expect the data to show the sun at 180° azimuth at 11:52 MST.

The data sheet we are provided shows that once again our precision is within one minute of time and within one degree of azimuth.


This page of the website is simply about systems of time and setting our watches for precision. Above we have tested these methods against data from the Naval Observatory — but only for the sun's southing (meridian crossing.) Following pages will branch out and demonstrate how to arrive at the altitude and azimuth for any time of day or night and for not only the sun but also for stars, moon, and planets.

In the end, we will not restrict ourselves to precision watches. We will free ourselves from computers. And we will learn methods than can be done entirely in the backcountry. Yet with us we hope to carry the insight we have gained here. It is worth understanding than when we discover a method to derive time from directions in the wilderness, it will be Solar Time or Mean Solar Time that we arrive at. And Solar Time, as we have seen, can be vastly different from the Standard Time or Daylight Saving Time that we are accustomed to finding on our watches.

Copyright © 2017 Travis N. Wood

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