How do they measure height of Mointains before electronic/GPS systems were avaiable?
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shadows and movement of the sun maybe? they used shadows in two cities at the same sun position to discover the circumference of the earth
Point by poin. A simple bubble to set a level and then a theodolite with a surveying stick can be used to determine the elevation angle. Mostly simple triangle geometry – just done repeatedly. So point A to B, then B to C then C to D etc etc. Finally add all the elevations and you have the total height.
You can take some basic surveying measurements and use high school level math to get a pretty decent estimate.
The answer is trigonometry which is really hard to ELI5. But they use 2 points on the ground with a known distance between them, then measure the angle from the top of the mountain to each of those points. With those 3 values and some trigonometry they calculate the height.
Triangulation. You measure the distance between two points by conventional means, and then measure the horizontal and vertical angles to a third point (like the peak of a mountain) from both of these points. From that you can then calculate distances and heights.
This can get quite precise; the height of Mount Everest was first measured in 1854, 99 years before someone actually managed to climb it, and the measurements were performed from more than 100km away (Nepal didn’t trust Great Britain enough to let their surveyors into the country), and the calculated height was only around 10 meters less than modern GPS measurements.
Wikipedia has an interesting part about measuring Mount Everest before digital instruments:
In 1802, the British began the Great Trigonometrical Survey of India to fix the locations, heights, and names of the world’s highest mountains. Starting in southern India, the survey teams moved northward using giant theodolites, each weighing exactly 500 kg (1,100 lb) and requiring 12 men to carry, to measure heights as accurately as possible. They reached the Himalayan foothills by the 1830s, but Nepal was unwilling to allow the British to enter the country due to suspicions of their intentions. Several requests by the surveyors to enter Nepal were denied.
The British were forced to continue their observations from Terai, a region south of Nepal which is parallel to the Himalayas. Conditions in Terai were difficult because of torrential rains and malaria. Three survey officers died from malaria while two others had to retire because of failing health.
Nonetheless, in 1847, the British continued the survey and began detailed observations of the Himalayan peaks from observation stations up to 240 km distant. Weather restricted work to the last three months of the year. In November 1847, Andrew Scott Waugh, the British Surveyor General of India, made several observations from the Sawajpore station at the east end of the Himalayas. Kangchenjunga was then considered the highest peak in the world, and with interest, he noted a peak beyond it, about 230 km away. John Armstrong, one of Waugh’s subordinates, also saw the peak from a site farther west and called it peak “b”. Waugh would later write that the observations indicated that peak “b” was higher than Kangchenjunga, but closer observations were required for verification. The following year, Waugh sent a survey official back to Terai to make closer observations of peak “b”, but clouds thwarted his attempts.
In 1849, Waugh dispatched James Nicolson to the area, who made two observations from Jirol, 190 km away. Nicolson then took the largest theodolite and headed east, obtaining over 30 observations from five different locations, with the closest being 174 km from the peak.
Nicolson retreated to Patna on the Ganges to perform the necessary calculations based on his observations. His raw data gave an average height of 9,200 m (30,200 ft) for peak “b”, but this did not consider light refraction, which distorts heights. However, the number clearly indicated that peak “b” was higher than Kangchenjunga. Nicolson contracted malaria and was forced to return home without finishing his calculations. Michael Hennessy, one of Waugh’s assistants, had begun designating peaks based on Roman numerals, with Kangchenjunga named Peak IX. Peak “b” now became known as Peak XV.
In 1852, stationed at the survey headquarters in Dehradun, Radhanath Sikdar, an Indian mathematician and surveyor from Bengal was the first to identify Everest as the world’s highest peak, using trigonometric calculations based on Nicolson’s measurements. An official announcement that Peak XV was the highest was delayed for several years as the calculations were repeatedly verified. Waugh began work on Nicolson’s data in 1854, and along with his staff spent almost two years working on the numbers, having to deal with the problems of light refraction, barometric pressure, and temperature over the vast distances of the observations. Finally, in March 1856 he announced his findings in a letter to his deputy in Calcutta. Kangchenjunga was declared to be 8,582 m (28,156 ft), while Peak XV was given the height of 8,840 m (29,002 ft). Waugh concluded that Peak XV was “most probably the highest in the world”. Peak XV was calculated to be exactly 8,839.2 m high, but was publicly declared to be 29,002 ft (8,839.8 m) in order to avoid the impression that an exact height of 29,000 feet (8,839.2 m) was nothing more than a rounded estimate. Waugh is sometimes playfully credited with being “the first person to put two feet on top of Mount Everest”.
Same way they do it with GPS
Good ol trigonometry.
Just instead of using theodolites as the measurement points we use a few satellites and a base station.
Alternatively you can use photogrammetry from pictures taken of the mountains as well. For heights you can use comparisons to objects of known dimensions or use the shadow it casts if you know longitude/latitude and time.
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