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    Re: Lunars at Cusco, Peru
    From: Frank Reed
    Date: 2024 Jun 9, 23:44 -0700

    Unfortunately, it looks like you're "double-dipping" on altitude here. I gather you're using a barometric pressure that is actual "at altitude" while normal weather air pressures are given as reduced to sea level. And the app, when you enter an observer altitude in km corrects both for the small change in parallax and also adds the relatively larger correction for pressure altitude. That's a design choice.

    How much difference should observer altitude make in terms of parallax --a pure geometric shift?

    Normal parallax when the Moon is "at the horizon", or as we know it in the oldie english of celestial navigation, "horizontal parallax" is very nearly equal to the radius of the Earth, R, divided by the distance to the Moon, r. And that ratio is about 1/60 on average. That is an angle as a "pure number" as some sciences (like physics) and schools of math call it, or it's an angle "in radians" as engineering and some other schools of math call it. We can convert any angle expressed as a pure number (so long as it is less than about 1/10, as this one is) to minutes of arc by multiplying by 3438. That gives 57.3 as the approximate average "HP" for the Moon. That is, the average shift in the Moon's position when it is at the horizon (the maximal case) is about 57.3 minutes of arc for an observer at "sea level".

    But what would that number be for an observer at some altitude besides sea level, let's say at N km above sea level? It's exactly the same math. We still want the ratio of R/r, but now R is bumped up by some "N" kilometers. Do the math and you find, nearly enough, it's N · 0.009', or 0.9 minutes of arc for every 100km altitude above sea level. Or for anything less than 10km, it's below a tenth of a minute of arc and therefore insignificant for manual sextant observatons. But if you're in orbit? Then it's a concern. :)

    Effect on the Moon's SD (semi-diameter)? Much smaller. Really nothing at all for any observer on the Earth's surface, even on the highest mountain (see PS). To increase the Moon's SD by even a tenth of a minute of arc, we would need an observer altitude of 2000km or higher. And again, that's insignificant. And this time insignificant even in LEO (Low Earth Orbit).

    Frank Reed

    PS: for parallax and semi-diameter enhancement, like this, the highest mountain is Chimborazo after all. :)

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