So, Find Your Latitude by Hand: Determine Latitude at Night

This week, find your latitude on land, boat, or hyper-futuristic train

 

Overview

 

A well prepared chrononaut is never lost! At least not on Earth. Latitude is the simplest form of global navigation to determine and can be estimated by hand without the use of tools. Latitude measures the (angular) distance from the poles to the equator. Each line of latitude is an imaginary line that runs horizontal around the globe with the equator at the center.

 

Starting at 0° latitude at the equator, moving up or down the globe will gradually increase an observer’s latitude until reaching either pole at 90° North (90° N)  in the northern hemisphere or 90° South (90° S, often written as -90°) in the southern hemisphere. The angle between the poles and the horizon form the latitude of an observer. Due to the Earth’s tilt, the poles of the planet are not considered true north or south. The true pole that is corrected for the tilt is known as the celestial north pole or celestial south pole

 

History

 

The open ocean lacks distinctive landmarks besides the occasional whale. Historically this meant that celestial landmarks like the moon, planets, and stars were particularly useful in determining a sailor’s position. Stars and constellations remain useful navigation tools as they move predictably in the sky during the night.

 

Since the position of 90°N is directly in the center of the planet’s rotation, it will not move during the course of the night. All around a pole, the stars will appear to rotate counter-clockwise. By the 20th century, it was possible to find the position of 90°N in the night sky since the bright star Polaris was within a degree of the true north celestial pole, making it a pole star. A pole star is any star close to the pole that can be used as a bright landmark to find the position of the celestial pole, and it is close enough to the celestial pole that it will not appear to move. Instead the other stars will appear to rotate in a counterclockwise wheel around it.

 

By the 20th century, the position of the true southern celestial pole was considerably more difficult to find. Unlike the northern hemisphere, the southern hemisphere lacked a bright star near the pole. Instead, stars rotate around the starless southern celestial pole.

 

However, over large periods of time, the position of all stars will change. This is due to both an individual’s star proper motion as well as the Earth’s precession. Stars are not stationary in their position and while it tends to be exceptionally small, the proper motion of stars will gradually accumulate over a few thousand years and can dramatically change the night sky. In addition, the Earth does not move in a perfect orbit, instead it undergoes a wobble in its tilt, changing the position of the Earth’s axis in the sky and as a result, where the pole points in the night sky. This wobble is known as the precession of the equinoxes.

 

About ten thousand years after the first moon landing (in 13000 B.C.E) the night sky will have undergone some minor changes due to proper motion, but while the star Vega will only physically move a single degree, the entire axis of rotation will shift enough that its new position will sit within a few degrees of the new true celestial north as the new northern pole star.

 

Precession is a cycle where the wobble of the planet’s axis changes the orientation of the Earth’s axis and over time it will trace a circle in the night sky before it returns to its original position. One complete cycle of precession takes about 26 thousand years.

 

A Selection of Past and Future North Pole Stars

 

A Selection of Past and Future South Pole Star:

To find latitude, simply compare the apparent position of the celestial pole in the sky to the horizon. A bright pole star can make finding this position easier. The angular distance between the pole star and the horizon represents the observer’s latitude within a few degrees of accuracy

 

Northern Hemisphere: Find the Celestial North Pole in the 20th Century

 

By the 20th century, the northern pole star Polaris was within a single degree of true north, more than close enough for determining latitude. As a pole star, Polaris will appear as a fixed point in the northern sky because it is almost perfectly aligned with the Earth’s axis of rotation. Polaris historically has been one of the brightest stars in the Northern Hemisphere and its position can be accurately be found using pointer stars in the Big Dipper. The edge of the cup of the Big Dipper contains two stars—Dubhe and Merak—which point towards Polaris. Polaris is almost 30° from Dubhe, which is about five times the distance between Dubhe and Merak.

At the North Pole, Polaris will appear directly above an observer at an angle of 90°. Closer to the equator, Polaris will appear closer and closer to the horizon until it drops below as an observer moves into the Southern Hemisphere where it is no longer visible.

 

Southern Hemisphere: Find the Celestial South Pole in the 20th Century

 

Unlike the Northern Hemisphere, by the 20th century, there were no remarkably bright stars in the Southern Hemisphere to serve as a southern pole star. In its place is a southern “pit”—a dark section of sky with no particularly bright stars. This “pit” still represents the position of the true south that will be used to determine latitude. However, with the comparatively dimmer stars in the Southern Hemisphere, it requires some additional work to accurately determine its position. In the absence of a true southern pole star, two methods can be used to determine the position of the southern pole’s “pit”. Both methods make use of the Southern Cross, a relatively bright southern constellation. The first uses the Southern Cross along with two pointer stars. Both the pointer stars and constellations extend a theoretical line and where they intersect is the position of the southern pole.

The second method is simpler, but perhaps more prone to user error. This method only uses the Southern Cross, and extends a theoretical line through Gacrux (the top star of the Southern Cross) and Acrux (the bottom star of the Southern cross). The distance from Gacrux and Acrux is about 6° degrees so by extending a theoretical line out four times it will intersect the southern pole

 

Determine Latitude

 

Once the position of the pole has been found, the latitude of the observer is simply the angle between the horizon and the pole. The simplest way to perform this measurement is by hand*. The width of a finger is a good approximation for 1°, a palm or fist is 10°, and an extended hand is about 25°

The closer to the equator that an observation takes place, the closer to the horizon the pole stars will appear. At each pole, the celestial poles will appear directly overhead.

 

A more accurate reading can be made quadrant, sextant or just a level and protractor with a hanging bob. By aiming the bottom of the protractor until it points towards the pole star, the hanging bob (pulled by gravity) will read the angle for the latitude. Lastly, to account for the design, the latitude observed by the instrument needs to be minus 90°.

A more accurate method to determine this angle can be achieved with tools like a sextant. Accuracy remains paramount to all forms of measurement. For each 1° difference from the true latitude makes up 60 nautical mile on Earth (111.12 km)

 

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