[Phys-L] judging angles (was: shape of the sky)

[John Denker <jsd@AV8N.COM>]

On 07/04/05 07:37, SSHS KPHOX wrote:

> I was told by my father that he had determined in college ( an
> astronomy major in 1928) that the moon actually subtends a smaller
> arc at rising than when over-head. I never repeated the analysis but
> it has made sense to me as it is further away and atmospheric
> refraction should flatten it a bit.

A bit, but not very much.

If you google for sunset images, and manage to find one
that is not hopelessly overexposed, you find that the
flattening is barely perceptible, maybe 10% or so, even
when the sun is rather low in the sky:
   http://www.quintaanita.com/sunset%20ocean.jpg

> make a small "telescope" with your hands
> and view the moon through this small tube. It will "shrink" to normal
> size. I wonder if this would be true for pilots as well.

A similar idea, but simpler and more quantitative, is to
compare the moon to a coin held at arm's length.   This
allows us to formulate two different questions:
  *) Do you think people overestimate the size of the moon
   near the horizon, or underestimate the size of the moon
   high overhead?
  *) What's your prediction:  How big is the moon, really?
    -- about the size of a US quarter at arm's length?
    -- substantially larger than a quarter?
    -- about the size of a dime?
    -- substantially smaller than a dime?

=======================

As to the psychophysical origins of the "moon illusion",
there are two parts to the question.

a) In general, why do people misjudge angular sizes, and

b) In particular, why do they systematically judge the
  horizon-moon to be larger than the overhead-moon?

I will blatantly duck question (b).  I don't know.  I've
heard lots of alleged explanations, none of which rise
above the level of Kiplingesque just-so stories.

   "We have more experience with object near the
   horizon."  "Objects on the horizon are more relevant,
   more important."  Blah blah blah.  Whatever.

As for question (a), people's innate ability to judge
angles is just terrible.  Some examples:

  -- You can see this on the ski slopes.  People are
   traversing along a trail, and they come across a
   much steep trail going off to the side.  You ask
   them "how steep" and they say something like 45
   degrees ... when in fact it's more like 15 or 20,
   as you can confirm by reference to a 45-45-90 triangle
   formed by your arm and ski-pole.

  -- You can see this with student pilots.  I can train
   'em to judge angles ("a thumb at arm's length subtend
   four degrees") but without a thumb or similar reference,
   the untrained eye is incapable of judging angles to any
   reasonable precision.  I want them to use a 4 degree
   approach slope, but without a reference they might be
   shallower than 2 degrees or steeper than 6 degrees and
   not see the difference.
     http://www.av8n.com/how/htm/landing.html#sec-thumb

  -- Of course there is the moon illusion itself.  Ditto sun.
   Also the constellations appear to shrink as they rise.

There are some things the eye does amazingly well.  But
judging angles (untrained and unaided) is not one of them.
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