Telescope Reviews: Re: Full Moon Tonight

Hi Curt and Jim!
Thanks so much for the most interesting discussions on this issue!

To wrap things up a bit, I would like to make one proposition to ponder upon.

This is about the case of Moon illusion, with regard to the presence of airmass.

We know the following:

(1) The reflected sunlight from the rising / setting Moon near the horizon has to travel through a complex, layered airmass of (roughly) 40 times the reference height (8,4 km) of the troposphere, which results into a distance of at least 336 km.

(2) To understand the behavior of airmass (as a system of troposphere), a complex model involving integral calculations is required. This probably brings us somewhat away from euclidian geometrics or simple laws of reflection – introducing complexity and even chaos to the atmospheric system of airmass.

(3) The airmass has an effect on the rising / setting Moon (known as an optical distortion of the Moon’s image, in a way Curt pointed out and Jim stated: “So it’s not difficult to imagine very bizarre effects from atmospheric refraction, but for the mild bending experienced in the Earth’s actual atmosphere, the goldfish bowl shaped part of the celestial sphere that we actually see at any one time differs only very slightly from the perfect hemisphere that it looks like. So, as I tried to show with the cosine formula, the theoretical distortion in the horizontal diameter of the rising Moon is extremely slight”

(4) Details on the effect of airmass of the troposphere are somewhat known regarding the mechanism of extinction as the loss of signal strength of the beam of light. In this respect three sources of attenuation have been recognized. Rayleigh scattering is caused by air molecules. Mie scattering is caused by aerosols and molecular absorption is primarily caused by ozone.

(5) According to Wikipedia (on airmass), the relative contribution of each of these sources of optical distortion varies with elevation above sea level, and the concentrations of aerosols and ozone cannot be derived simply at all. On this it is further noticed as follows: “At very high zenith angles, airmass is strongly dependent on local atmospheric conditions, including temperature, pressure, and especially the temperature gradient near the ground. In addition low-altitude extinction is strongly affected by the aerosol concentration and its vertical distribution. Many authors have cautioned that accurate calculation of airmass near the horizon is all but impossible.” – On this, one shoud of course note that a high zenith angle means observing near the horizon (zenith angle is at zero on the zenith and grows toward the horizon until reaching 90 degrees at the horizon).

We are thus dealing with a complex, ever-changing system: the humidity, air pressure and temprerature form various layrers of air(mass), plus the convections (due to winds and temperature differences) on the troposphere have a factor to play on their part.

This complex system can be (to some extent) derived into a model through integral calculations. Yet, the nearer we get to the point where the troposphere meets the Earth's surface, the more complex the case is. Observing the rising or setting Moon near the horizon, the situation is most complex.

The troposphere forms (complex) layers of airmass that have been observationally proven to act like refractional lenses – as was staed in Jim referring to Les Cowley’s site (fata morgana -effects on the horizon, etc.).

Would it, then, be plausible to propose that in the case of Moon illusion, the Snell's law of refraction could be applied – even to some extent – if any? Thus, one would gain a means for elaborating the “standard” distortion that occurs due to airmass – and is “additioned” by special conditions on the troposphere due to weather phenomena.

The Snell’s law is applicable in physics and optics and has to do with a beam of light passing through various plane-parallel layers of tempered "surfaces".

Now, would this apply to airmass at all? We know the airmass is layered and very thick towards the horizon. Observing the rising or setting Moon, the airmass is reaching onto a distance over 336 km, until – with respect to “the optical path of Moonlight” - it exits the troposphere at tropopause, along the tangential line of sight. This arimass has the most complex nature. So, would this mean one should take into consideration the (relative) opticall thickness of layered troposphere – to play a role in creating the Moon illusion for that part?

On the mentioned Wiki page it is stated: "In optics and physics, Snell's law (also known as Descartes' law or the law of diffraction), is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves, passing through a boundary between two different isotropic media, such as water and glass. The law says that the ratio of the sines of the angles of incidence and of refraction is a constant that depends on the media. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material.”

I happened to find a patent application that elaborates on Snell’s law in developing diver’s glasses – fighting the deformation effect of angular magnification and perspective distortion by the transition effect from various materials into others – as in looking into water and seeing the bottom magnified – or in the case of looking through a diver’s glasses and getting one’s sight diverted.

On the mentioned patent page it is stated as follows (the citation is several paragraphs long):

--- citation starts---

“A well-known phenomenon that creates angular magnification and perspective distortion is caused by the medium transition from water to air through a plane-parallel layer of tempered glass or plastic (see Human Underwater Vision: Physiology and Physics by J. S. Kinney, pg. 83-106). Such transitions are common in diver face-masks or flat optical windows used to protect a camera and electronic parts of cameras from the water environment. This effect is also visible looking down into still water and can be seen to be a function of the change in medium rather than the material of the optical window.

--- /there is the formula described on the page in this section/---

The window material turns out to be unimportant and the net effect of Snell's law in the transition from water to air is that there is a paraxial angular magnification of about 1.34 and binocular triangulation is subverted. This makes objects look nearer than they would look if they were perceived through air (i.e., perspective distortion). The magnification problem is particularly acute when attempting to view objects off-center in the optical system. There is an angle at which objects can no longer be seen from the air side of the window. Theoretically it is over 48 degrees but practically it is less than 45 degrees. Reports of 50-degree or greater fields of view result from slight motions of the head. Light having incidence angles greater than the value of somewhere between 48 and 49 degrees is totally reflected at the interface.“

---citation ends---

It is stated in the previous citation, that the net effect of Snell’s law regarding transition from water to air results into a paraxial angular magnification of about 1.34.

What if this complex system of thick airmass (when observing on horizon) would somehow have the same kind of paraxial effect as the transition between layers or air takes place?

Naturally, this would only be a very small fraction of the phenomenon observed regarding (layered plane-parallel) glas. So, the paraxial effect would observing the Moon be times X smaller? Could this then be counted in when one sums up the effect(s) of the airmass in observing – and especially regarding Moon illusion?

Maybe there is a crucial factor in play there that I am missing completely in this.

Perhaps air is so much different a case - even being layered and convected – that gas-to-gas –optical transition is not in any case at all the same thing as with surfaces like water and glass?

But if this is not the case, wouldn’t it actually be interesting, that under the altitude of 10 degrees from the horizon, the rising or setting Moon would be effected by paraxial angular magnification - due to layered airmass of the troposphere.

The 10 degrees limit comes from the paraxial approximation being “fairly accurate for angles under about 10°, but is inaccurate for larger angles” (as stated on the Wiki page on this).

Be well all!

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Share - and you shall have it all

Timo Keski-Petäjä

CtheMoon

Observation shelter KuuMaja (MoonHut)

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