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    Low altitude observations
    From: Frank Reed
    Date: 2017 Nov 27, 08:59 -0800

    Bob Goethe, in the Pub249 discussion, you wrote:
    "Frank, I am intrigued by this statement:
    >a modern navigator should feel much more comfortable using stars as low as 1.5° altitude<
    Could you unpack this a bit for me?
    I have had some good results with low altitude shots...but wondered if they were just flukes."

    A century ago, there was some reason to be suspicious of refraction tables for low altitudes. The science was good, but the calculating tools could not produce accurate refraction tables below about 10° altitude. Furthermore, temperature and pressure corrections were not necessarily available. Avoiding low altitudes because of uncertainty of refraction became part of navigation lore, and many navigators today are still trained to think that low-altitude refraction is uncertain below 10, 15 or even 20°. That's just not so. There is still a danger zone where exotic refraction can become problematic, but that's below altitudes around 1°-2° (and the uncertainty in dip under the conditions that would cause uncertainty in refraction is a bigger concern). For altitudes above 1.5°, the published refraction tables are accurate and reliable --validated both by long-term observations at astronomical observatories and also by modern numerical integrations of atmospheric models. The only catch is that since the refraction values are large at these altitudes, it's important to consider the corrections for temperature and pressure (and altitude above sea level). Temperature and pressure variations away from standard values up to 5% are not unusual and even 10% isn't rare, and these impact the refraction in direct proportion. So if the standard refraction is 20.0' (as it is around 1.5° altitude), then we could expect the actual refraction would be in the range from 19.0' to 21.0' for common weather variability. That's +/-5%. If one minute of arc is not worth worrying about, then our results will be acceptable even if we ignore the temperature and pressure correction, right down to that very low altitude. But by including temperature and pressure, we can erase even that uncertainty.

    It's worth mentioning that you can do the temperature/pressure correction in your head! You need to know that standard pressure is about 1010 millibars and standard temperature is 10°C (mnemonic: 10-10-10). You also need to remember that you convert a Celsius temperature to kelvins by adding 273 which makes the baseline standard 283 kelvins. Then we just compare the actual pressure and temp to those absolute values and ask how much they differ in percentage terms. If the actual pressure is 1% higher than standard while the absolute temperature is 3% higher, then remembering that these two operate in opposite directions, the net is 2% thinner air yielding a 2% reduction in refraction. For example, if I have observed Venus under these conditions at 10°41' altitude, the tabulated refraction is 5.0', so the actual refraction would be 2% lower or 4.9'.

    Frank Reed
    Conanicut Island USA
    (current temp here is 47°F and pressure 29.90 inches Hg, which is quite close to the standard --even down at 1.5° altitude, the T/P correction would be only 0.2')

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