Quick Answer
To estimate distance without GPS, one can use dead reckoning, triangulation, or the "method of intersections" based on celestial navigation, or by measuring the shadow of an object at known intervals during the day.
Dead Reckoning Techniques
Dead reckoning is a simple method of estimating distance traveled by tracking the direction and speed of travel. It involves measuring the distance traveled per unit time, called the “pace” or “speed,” and multiplying it by the elapsed time. For example, if you travel at 5 kilometers per hour for 2 hours, you can estimate the total distance traveled as 10 kilometers.
Triangulation and the Method of Intersections
Triangulation involves using two or more known reference points to determine an unknown position. By measuring the angles and distances between reference points, you can use trigonometry to calculate the unknown distance. The “method of intersections” is similar, but involves using the intersection of two lines (e.g. latitudes and longitudes) to determine a position. For example, if you know your latitude and the latitude of a nearby reference point, and you also know the longitude of a nearby reference point, you can use the “method of intersections” to estimate your longitude.
Celestial Navigation
Celestial navigation involves using the position of the sun, moon, or stars to estimate your position. By measuring the angle between the sun or a star and the horizon, you can use the altitude to estimate your latitude. By measuring the time of day and the angle between the sun and a reference point (e.g. a nearby mountain), you can use the “method of shadows” to estimate your longitude. For example, if you know the time of day and the angle between the sun and a reference point, and you also know the latitude of the reference point, you can use the “method of shadows” to estimate your longitude.
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