Knowing your latitude will help you understanding climate and weather, what you can plant in a garden, and can help you recognize historical and cultural contexts. Although unlikely, it is possible for some event to cause a temporary shutdown of current GPS technologies. In an extended outage, here are three methods to determine your latitude without using modern technology:
Using the Sun at Noon
1. At solar noon (when the sun is at its highest point in the sky), stick a vertical pole into the ground and mark the tip of its shadow on the ground[4][7].
2. Draw a line connecting the base of the pole and the shadow tip. This line points north-south[4].
3. Measure the angle between the north-south line and the sun’s rays using a quadrant or sextant. This angle is your latitude[4][7].
4. To get an accurate reading, adjust for the sun’s declination (seasonal tilt). For example, in May add about 11.7° to your measurement[4].
Using the Sun at Noon at the Equinox
To find your latitude using only an obelisk and the sun, you can follow these steps:
1. Choose a day near the equinox (March 21 or September 23) when the sun’s declination is close to 0°. This will simplify the calculations.
2. Erect a vertical obelisk or stick at a location where the ground is level. Make sure the obelisk casts a shadow.
3. At solar noon, when the sun reaches its highest point in the sky, measure the length of the obelisk’s shadow. Let’s call this length “s”.
4. Also measure the height of the obelisk. Let’s call this length “h”.
5. Calculate the angle between the obelisk and the tip of its shadow using the tangent function:
`angle = arctan(s/h)`
6. This angle is equal to 90° minus your latitude. So your latitude is:
`latitude = 90° – angle`
For example, if the obelisk is 10 feet tall and its shadow is 15 feet long at solar noon on an equinox day, then:
– `angle = arctan(15/10) = 56.3°`
– `latitude = 90° – 56.3° = 33.7°`
So if you performed this measurement and calculation, you would be at a latitude of approximately 33.7° north or south of the equator.
This method works because at the equinoxes, the sun is directly overhead at the equator. The angle between the vertical obelisk and its shadow is therefore equal to the latitude. Some error may occur due to the sun’s declination not being exactly 0°, but this can be minimized by choosing a day very close to the equinox.
Declination Factors by Month
Calculation: The declination angle can be calculated using the equation:
where δ is the declination angle and is the day of the year with January 1 as n=1.
Example for January 1st:
=
−23.45 * sin(360 * 285 / 365)
−23.45 * sin(284.93°)−23.45 * (−0.9945)
Example for January 30th:
Plugging in n=30 for January 30:
δ= =
−23.45 * sin(360 * 314 / 365)
−23.45 * sin(310.96°)
−23.45 * (−0.8795)
=20.59°°.
The key factors are the Earth’s 23.5° tilt on its axis and its revolution around the sun over the course of a year. This causes the sun’s declination to vary from +23.5° to -23.5° throughout the seasons. Knowing the declination for a given date is crucial for accurately determining latitude using the sun’s position.
Sine Values to Memorize
- 0°: sin 0° = 0
- 30°: sin 30° = 1/2
- 45°: sin 45° = √2/2
- 60°: sin 60° = √3/2
- 90°: sin 90° = 1
- 180°: sin 180° = 0
- 270°: sin 270° = -1
- 360°: sin 360° = 0
So, in the above example, you wanted to know the sin of 310.96 degrees. This is between 270 and 360, so you know it will be between those values on the number line. There are 90 degreess between those two angles and 311 is 41 degrees away from 270, or just less than 1/2 of 90 degrees. Therefore, if you have memorized the above values, you could roughly estimate that the sin of 310.96 degrees (call it 311), will be less than -0.5, and it is −0.8795. For determining your latitude, the -0.5 adjustement gives you -11.725 degress to subtract, while using the −0.8795 gives you a latitude adjustment of -20.6. You can see that this is a difference of 8.88 degrees (-20.6 minus -11.7 ).
The length of 1 degree of latitude is approximately 69 miles (111 km). Therefore, a span of 8.88 degrees of latitude would be approximately: 8.88 degrees × 69 miles/degree = 612.72 miles.
Clearly, if you can have access to a calculator or accurate sin tables, you will be much better able to determine your latitude if the Internet were no longer available.
Using the North Star
1. Locate the North Star (Polaris) by first finding the Big Dipper (Ursa Major) constellation. The North Star is about 4 “dipper blade-lengths” from the end of the dipper’s handle[4][7].
2. Measure the angle between the North Star and the horizon using a quadrant or sextant. This angle is your latitude[4][7].
3. The North Star’s elevation above the horizon is equal to your latitude[7].
Using a Map
1. Obtain a detailed map with latitude lines (parallels) clearly marked[8].
2. Locate your position on the map and count the number of degrees latitude between your location and the nearest parallel line[8].
3. Use a map ruler to precisely measure the distance to the parallel line and determine your latitude[8].
The key is that latitude lines are parallel to the equator, so your latitude is the angle between your location and the equator. Using the sun, North Star, or map, you can measure this angle to determine your latitude without modern instruments[4][7][8].
Citations
[1] https://www.wikihow.com/Read-Latitude-and-Longitude-on-a-Map
[2] https://www.ancientportsantiques.com/ancient-measures/latitude/
[3] https://www.youtube.com/watch?v=ircLt-qvl3M
[4] https://www.open.edu/openlearn/society/politics-policy-people/geography/diy-measuring-latitude-and-longitude
[5] https://www.jqjacobs.net/geodesy/ancient_monument_latitudes.html
[6] https://www.youtube.com/watch?v=X4W0D5FkN64
[7] https://wonderdome.co.uk/determine-coordinates-latitude-longitude/
[8] https://www.wikihow.com/Determine-Latitude-and-Longitude
[9] https://worldbuilding.stackexchange.com/questions/171721/without-modern-electronics-how-could-you-determine-your-longitude-latitude-an
[10] https://www.researchgate.net/figure/Recommended-average-day-and-declination-for-each-month_tbl2_360085738
[11] https://www.sciencedirect.com/topics/engineering/solar-declination
[12] https://www.researchgate.net/figure/Average-days-of-each-month-and-obtained-values-of-declination-angle_tbl1_281772907
[13] https://sciencepickle.com/earth-systems/sun-earth-connection/earths-illumination-patterns/declination-latitude-and-earth-illumination/
[14] https://www.pveducation.org/pvcdrom/properties-of-sunlight/declination-angle
