Dear Neville,
I'm glad we agree on those issues, below.
I have now had a look at your "Resolution of the planet Mars"-page
and have a few comments (I have only seen it in its recently corrected
form).
You talk about the "seeing" effect (blurring by the atmosphere) and state
that: "The response time of the cones in the fovea of the human eye make
this spreading almost completely non detectable."
The main reason that seeing is not seen as a widening of objects in the
sky, is that the "seeing disk" - the angular diameter of a point-source
(e.g., a star) broadened by seeing, is smaller than the diffraction limit
(a.k.a. the "Rayleigh resolution criterion") of our eyes. A clear night
at sea-level has seeing of about 3" (arcseconds) and the best observatories
in the world experience good seeing of about 0.3".
Seeing is caused by turbulence in the atmosphere, and this is what causes
stars to twinkle - they change brightness and colour in a random fashion on
a sub-second time-scale. With a telescope on a stable mount, you can also
see the star "jump" around in your field of view. This jumping around, fills
up the seeing disk in a few seconds - e.g., if you take a picture.
Stars twinkle because they are point-sources and all the light we see
passes through the same turbulence eddies.
Planets, on the other hand, are extended object, whether we resolve them
or not, and the light we see passes through different, neighbouring eddies
of turbulence. The twinkling therefore gets averaged out (to some extent)
and the (naked eye) planets appear as more steady lights, than the stars.
The point-spread function for the atmosphere + human eye, which you mention,
is overwhelmingly determined by the diffraction limit of our eyes.
In Fig.4 (attached), I have plotted intensity versus angular distance from
the centre of point-source (i.e., a source that is not resolved).
I have used a pupil diameter of 5mm (not fully dilated, which is more like
8mm), and I have shown the intensity for three objects with different
brightness. I have also plotted a sensitivity limit (dashed line) of the
human eye (the intensity axis is on an arbitrary scale, just demonstrating
the effect schematically). The part we see, is the part above the dashed
line. This means that the angular diameter of an object will increase with
its brightness. The central 20" is covered by a handful of photo-receptors
in the human eye, so we would (and do) see a difference in size between
the objects of different brightness, displayed here. Bear in mind that
this has nothing to do with the actual angular diameter of the objects,
which would have to be smaller than, say, 5", for the plot to be valid.
Conclusion: there is no problem with the size of Mars.
Regards,
Regner
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Quoting Neville Jones <njones@xxxxxxxxx>:
>
>
>
>
> -----Original Message-----
> From: art@xxxxxxxxxx
> Sent: Wed, 28 Nov 2007 01:40:04 +1100
>
> Okay, Jack.
> My previous posts on this subject still stand.
> I'll comment on a couple of the statements of Neville's that you included.
>
> Neville: Mars is not emitting visible light any more than the coin is.
> Regner: True. Both just reflect sunlight.
> BUT: Mars' surface area is some 1e17 (= 10^17 = 1 followed by
> 17 zeroes) times larger than a coin. The surface area of Mars'
> which is presented to the Sun is 1e17 times larger than for a
> coin. Granted the coin have a larger reflectivity (albedo)
> close to 1, and Mars' is about 0.15 - so that gives us a factor
> of 10. Also, Mars is farther from the Sun, than Earth is, so the
> sunlight will be diluted by the square of that factor = 2.3. To
> be generous I'll call those two a factor of 100 resulting in the
> coin still being 1e15 times dimmer than Mars.
> If we placed a coin next to Mars, Mars would be 1e15 brighter
> than the coin.
> Light that is emitted or reflected in all directions, will get
> diluted by the square of the distance. This means that if you
> look at a coin a meter away, glinting in the sunlight, it will
> be between 1e6 and 2e7 brighter than Mars, depending on the relative
> orbital positions of Mars and Earth.
> If you put the coin at between 970m and 4.7km away from you, Mars
> and the coin would be the same brightness - provided you catch the
> glint. The coin would now have an angular diameter between 0.88-4.25
> arcseconds - well below the resolution limit of your eye.
> Another point, of course, is that you wouldn't be able to see the
> coin because you would have to be on the dayside of Earth to get a
> reflection off the coin, which means the general daylight will
> completely outshine the coin seen at that distance - just as we
> can't see Mars in the daytime sky.
>
> Agreed.
>
> I agree with everything else that Neville says, except his statement that
> you can't see things that are below the resolution limit.
> I would like to add, though, that his statement is correct in sun-lit
> scenarios, where the contrast between objects is much lower than between
> the black Universe and a star or a planet, e.g., you will be able to see
> (not necessarily resolve - they might just be little dots) black letters
> on a white background at much larger distance than yellow letters on a
> white background.
>
> Agreed.
>
> My example with the airplane is good, since you know the size of the
> lights and approximate distance to the plane. I'll estimate the lights to
> be about 10cm in diameter, which means that planes more than 350m away will
> have lights that are below the resolution limit of your eye (I have used
> the 1 arcminute measure that Neville also prefers - the diffraction limit
> of 24" is too optimistic).
> I hope this helps.
>
> Regner
>
> Agreed. The whole issue is resolution. This is why the article needs slight
> modification/correction. Neville.
>
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>
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>
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>
>
>
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