Quote of the Day
Truth … is much too complicated to allow anything but approximation.
— John von Neumann. It took me a long time to accept that all models are wrong at some level, but that you can use them to produce useful results.
I often see popular descriptions of observatories that say things like the observatory "is above 40% of the Earth's atmosphere". I had not thought much about this kind of statement until I saw the Wikipedia's list of the world's highest-altitude observatories, which surprised me as to the height and remoteness of the largest telescopes. I cannot imagine trying to build on these locations (Figure 1 is an extreme example). In some respects, the construction challenges remind me of what builders must have gone through on some lighthouses.
In this post, I will look at the highest altitude observatories and compute the percentage of atmosphere that they are above.
The atmospheric pressure at a location is a measure of the weight of air above that location. We can determine the percentage of the air column below a given altitude by computing the ratio of p(h)/p(0), which represents the percentage of atmosphere above altitude h , and subtracting that ratio from 100%.
- %AtmoBelow(h) is the percentage of atmosphere below the altitude h.
- p(h) is the atmospheric pressure at altitude h.
- p(0) is the atmospheric pressure at sea level, h= 0.
In this post, I will:
- Verify some general statements about the amount of atmosphere below certain altitudes.
- Determine the amount of atmosphere below the world's highest observatories.
Atmospheric Pressure Curve Fit
To estimate the barometric pressure at different altitudes, I grabbed a table of pressures from the web and did a simple interpolation so that my function, p(h), is continuous (Figure 2).
Table 1 shows three examples of references to the percentage of atmosphere below that reference level. Note that the reference for Everest (marked in red) got their percentage number wrong by ~10%.
|Statement||Altitude (m)||Stated Air % Below||My Air % Below|
|Mauna Kea rises 9,750 meters from the ocean floor to an altitude of 4,205 meters above sea level, which places its summit above 40 percent of the Earth's atmosphere (Source).||4,205||40||40.8%|
|57.8 percent of the atmosphere is below the summit of Mount Everest (Source).||8,848||57.8||68.9|
|72 percent of the atmosphere is below the common cruising altitude of commercial airliners (about 10,000 m) (Source).||10,000||72||73.8|
Figure 3 shows how the calculation was performed using Equation 1.
World's Highest Observatories
The Wikipedia has a list of the highest observatories in the world. I used Equation 1 to find the percentage of atmosphere below each observatory in Table 2. The University of Tokyo Atacama Observatory is unbelievably high – that has to be a challenge for those who work there.
||Air % Below||Observatory Site||Location|
|University of Tokyo Atacama Observatory (TAO)||5,640||51.0%||Cerro Chajnantor||Atacama Desert, Chile|
|Chacaltaya Astrophysical Observatory||5,230||48.3%||Chacaltaya||Andes, Bolivia|
|James Ax Observatory||5,200||48.0%||Cerro Toco||Atacama Desert, Chile|
|Atacama Cosmology Telescope||5,190||48.0%||Cerro Toco||Atacama Desert, Chile|
|Llano de Chajnantor Observatory||5,104||47.4%||Llano de Chajnantor||Atacama Desert, Chile|
(NAOC Ali Observatory)
|5,100||47.4%||Shiquanhe, Ngari Plateau||Tibet Autonomous Region, China|
|Llano de Chajnantor Observatory||4,800||45.2%||Pampa La Bola||Atacama Desert, Chile|
|Large Millimeter Telescope Alfonso Serrano||4,580||43.6%||Sierra Negra||Puebla, Mexico|
|Indian Astronomical Observatory||4,500||43.0%||Hanle||Ladakh, India|
|Meyer-Womble Observatory||4,312||41.6%||Mount Evans||Colorado, United States|
|Yangbajing International Cosmic Ray Observatory||4,300||41.5%||Yangbajain||Tibet Autonomous Region, China|
|Mauna Kea Observatory||4,190||40.7%||Mauna Kea||Hawaii, United States|
|High-Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory||4,100||40.0%||Sierra Negra||Puebla, Mexico|
|Barcroft Observatory||3,890||38.3%||White Mountain Peak||California, United States|
|Very Long Baseline Array (VLBA), Mauna Kea Site||3,730||37.0%||Mauna Kea||Hawaii, United States|
|Llano del Hato National Astronomical Observatory||3,600||36.0%||Llano del Hato||Andes, Venezuela|
|Sphinx Observatory||3,571||35.7%||Jungfraujoch||Bernese Alps, Switzerland|
|Mauna Loa Observatory||3,394||34.3%||Mauna Loa||Hawaii, United States|
|Magdalena Ridge Observatory||3,230||32.8%||South Baldy||New Mexico, United States|
|Mount Graham International Observatory||3,191||32.5%||Mount Graham||Arizona, United States|
|Gornergrat Observatory||3,135||32.0%||Gornergrat||Pennine Alps, Switzerland|
|European Extremely Large Telescope||3,060||31.4%||Cerro Armazones||Atacama Desert, Chile|
|Haleakala Observatory||3,036||31.2%||Haleakala||Hawaii, United States|
Just a quick note to explain where some of these atmosphere percentage numbers come from. I became interested in this after watching the movie Everest, which did an excellent job showing the effect of high altitudes on people.
Wiki has a formula for air pressure based on height and other atmospheric factors,
which works up to 44,331 meters