Telescope Reviews: Re: Full Moon Tonight

Curt,

I believe that if you re-read my postings carefully you will see that we are finally saying the same thing. Normal atmospheric refraction moves the perceived directions of objects (terrestrial or celestial) along lines of constant azimuth (measured relative to the observer’s zenith).

The reason you’re reaching a different conclusion from me is that you’re thinking about light originating at or above the horizon (the great circle at 90° from the observer’s zenith) and being raised above that by refraction. The perceived horizontal angle between such objects is decreased by refraction, just as you say. And I see now that my own photo shows the Moon as it appears above the horizontal (and not at the lower angles one might see looking out, for example, over the ocean), and your reasoning certainly applies to it, since the light from which it is composed originated above the great circle of my horizon.

But I thought (perhaps incorrectly) that the discussion was about what we see when we look horizontally. When the Moon, or stars, or quasars, or spaceships appear at 90° from the observer’s zenith (what I would call horizontal) it is only because refraction has placed them there. In “reality” they are at the observed azimuth but on a little circle below the perceived horizon -- normally by about 0.5°, but possibly much more. That is the open lip of the inverted “goldfish” bowl I was trying to describe. As refraction slides the objects slide up to the equator along the lines of constant azimuth, the perceived horizontal spacing between them increases in exactly the same way you are describe it decreasing for objects starting above the equator and moving still higher.

In general, the amount of horizontal magnification or minification is the ratio of the diameter of the celestial circle (relative to the observer’s zenith) on which the light is perceived to the one on which it originates; and that, in turn is the ratio of Cosines of the two angles above or below the equator. If light is seen at the observer’s equator (offset angle = 0°), but due to refraction it is actually originating at -0.5°, the horizontal magnification will be M = Cos(0°)/Cos(-0.5°) = 1/0.99996 = 1.000 04 (as previously stated). Exactly the same formula applies to each of the cases you mention. For example, for light that originates on the equator, but (due to refraction) is seen 0.5° above it, the magnification is M = Cos(+0.5°)/ Cos(0°) = 0.99996/1 = 0.99996 (i.e., the horizontal diameter is reduced). And, as you say, this is an extremely small effect for the amounts of refraction normally encountered on Earth.

I must apologize again for not having expressed my thoughts (and what I was talking about) more clearly at the outset.

For those who are utterly confused at this point, in addition to the well-known strong vertical flattening, the theory of standard atmospheric refraction predicts an extremely slight apparent horizontal magnification of objects seen at or below the horizon, and an equally slight horizontal compression of objects seen above it. The dividing point between horizontal magnification and minification occurs at the altitude where the refractive bending causes light originating a slight bit below the celestial equator (defined relative to the observer’s zenith) to be perceived an equal angle above it. For the normal amounts of refraction encountered on Earth the effect is too small to be of practical significance, certainly for lunar observing.

-- Jim

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