Interval between two sun sights

The focus of this webpage centers around day planning for the sun’s Line of Position (LOP), emphasizing the time interval between two sun sights to achieve a precise running fix when utilizing a sextant for sun observation.

Interval between two sun sights, image interval between first and second LOP

The self-instruction website systematically guides users through the process, utilizing eight identical exercises to aid them in determining a LOP at any time of the day.

Additionally, I added a page on how to calculate the Local Apparent Noon sight, which depends on a single moment of the day.

Furthermore, there is also a page on how to calculate the time of this single moment of the noon sight

In exploring the time interval between the first and the second LOP, the goal is to delve into and consider specific elements.

Light house at seashore of Dwarka. Author image: Sneha G Gupta

Interval between two sun sights:

the intersection angle between two LOP’s

In order to determine a position, it is necessary for two LOPs to intersect at an angle, with an angle closer to 90° being preferable. This, in turn, necessitates the use of distinct azimuths in the observations.

In fact, considering a 60°angle between the crossing of two LOPs is still good, and 30° is acceptable, but it will increase the uncertainty area.


Checking out the ocean under the stars. Author image: Daniel Ramirez Honolulu, USA

How to plan the time interval and what to know about the tropics, mid and high latitudes.

A little reminder:

Declination of the Sun throughout the year

The declination of the sun is increasing from the winter solstice to the summer solstice  ( -23° 26’ au 23°26’ )

and decreasing of the sun from the summer solstice to the winter solstice.( 23°26’ au -23°26’ )

Passing through the equinoxes where the declination is 0°

So the tropics (torrid zone) are between 23.5° N and 23.5° S.

Tropics: The Sun’s declination determines the boundaries of the tropical zones.

Interval between two sun sights, image tropic of cancer and tropic of capricorn
Archives of Pearson Scott Foresman, donated to the Wikimedia Foundation

Where is the sun?

In tropical regions, the sun’s position at local apparent noon can shift between north and south, leading to occasional confusion. For a simplified explanation, please see the details below.

Interval between two sun sights, image sun in the north or south on hemisphere north
Hemisphere North: L = Latitude observer and D = Declination of the sun
Interval between two sun sights, image sun in the north or south on hemisphere south
Hemisphere South

Dayplanning for the Interval between two sun sights

This table can be used to find the time between a normal sight with the sextant and the local apparent noon sight to obtain a change in azimuth of 60°

Interval between two sun sights,the time between a normal sight with the sextant and the local apparent noon sight to obtain a change in azimuth of 60°

In general, if possible we take a LOP of the sun in the morning and then intersect it with the noon sight.


Example 1:

D.R. Latitude = 40° N; Declination is 20°N (from the nautical almanac).

The best time for observation is 1 hour and 55 minutes before or after local apparent noon.

Interval between two sun sights, image of transferred LOP

Example 2:

D.R. Latitude = 15° N; Declination is 20° S (from the nautical almanac).

The best time for observation is 3 hours and 50 minutes before or after local apparent noon.


Further down on this page, I explain how to plan the day using two lines of position without relying on the local apparent noon sight latitude.


What is a apparent noon sight:

Calculating this local apparent noon sight is straightforward without any formula, and we design it on the map as a latitude.

In fact, you can execute the local apparent noon sight only at the moment when the sun culminates during the day

Interval between two sun sights, image of local apparent noon and sun's path

Indeed, this local apparent noon sight has two main problems: first, it will disrupt your dinner with the appetizer, and second, the clouds in the sky can hide the sun at that very special moment.

In general, if possible we take a LOP of the sun in the morning and then intersect it with the noon sight.

You can also take the noon sight and then intersect later in the afternoon with a normal line of position (LOP).

After mastering the LOP calculated with our formulas, you should also focus on mastering this latitude noon sight.

Interval between two sun sights:

Day planning with two Sun LOPs for a good running fix, without specifically relying on the local apparent noon latitude.

Day planning in the tropics

We should focus our attention when the latitude of the observer closely matches the sun’s declination (refer to the pictures below).

Interval between two sun sights, image differnce declination and latitude

When the declination is equal to the latitude, the azimuth will not change. We call this day a “zero shadow day”.

In simpler terms, during a zero shadow day, an object on the ground will not cast a shadow around solar noon because the Sun is directly overhead

On this day, there will be no crossing angles between two Lines of Position (LOPs) obtained from celestial navigation sights

This day the azimuth will not change in the morning and then flip over 180° at the solar noon and will become steady again on the opposite direction

On the other hand, when there is a small but substantial difference between latitude and declination, then the sun’s azimuth changes slowly for most of the morning and most of the afternoon, switching rapidly from east to west around local apparent noon.

“In this case, you need to take sights before, near to, and after local apparent noon”—that is to say, close sights around local apparent noon.

this statement is quoted from Bowditch.

Interval between two sun sights:

Day planning at high latitudes

On the contrary, at high latitudes, the sun steadily moves throughout the day, changing its azimuth by 15° per hour.

Here, we can choose an interval of at least 3 hours but preferably not more than 8 hours to achieve a good running fix.

Take care in this case that the sun is high enough above the horizon to take an accurate sight.

How to gain a brief understanding of the azimuthal change:

Keep in mind that the most crucial factor is the difference between the latitude of the observer and declination of the sun. In the table below, you will find:

Δ L/D (Difference in Latitude and Declination)

1 Average change in azimuth between 5 and 3 hours before local apparent noon

2 Average change in azimuth between 3 and 1 hour before local apparent noon

3 Average change in azimuth within the hour preceding local apparent noon.

Being able to calculate the local apparent noon time is necessary for using this table, even if you do not use the local apparent noon latitude.

Interval between two sun sights, table of delta latitude and declination to obtain change in azimuth
The change in azimuth averages tends to be slightly greater at high latitudes and slightly smaller at low latitudes, as indicated in the table

The table is quite compact, so the actual change in the azimuth of the sun may differ from the values presented in this table. However, it provides a general idea for planning your day when chasing the sun or ensuring a clear, visible horizon.

Interval between two sun sights:

Here are four examples without the noon sight latitude

example 1:

 you navigate at 35°N latitude

The declination that day is about 5°N

one of the many possibilities:

Δ L/D = 30°

First sight at 3h before apparent local noon

Second sight 2,5 hours later

changement in azimuth = 18 + 18 + 27/2 ≈ 50° 


example 2:

 you navigate at 15°N latitude

The declination that day is about 10°N

Δ L/D = 5° (The difference is small; referring to tropical conditions).

In this case, you need to take sights before, near to, and after local apparent noon


example 3:

you navigate at 15°N latitude

The declination that day is about 15°S

Δ L/D = 30°

one of the many possibilities:

First sight at 3h before apparent local noon

Second sight 2,5 hours later

changement in azimuth = 18 + 18 + 27/2 ≈ 50°


example 4:

you navigate at 45°N latitude

The declination that day is about 15°S

Δ L/D = 60°

This day the average changement in azimuth is ≈15°

Here, we can select a time frame of at least 3 hours, but preferably no more than 8 hours, to attain a reliable running fix.



Dark clouds on the sea of Hualien. Author image: Tzuhsun Hsu