A World where if You look far enough You’ll see Yourself…

I was reading up on the Flying Dutchman last night, which I can’t help but feel is the coolest thing ever (to the point that if I got an alt I’d style myself “Willem van der Decken”, i.e. its legendary captain), and I came across another freaky and rather more scientifically described phenomenon: not a mirage, technically speaking, but rather an optical illusion produced by atmospheric refraction, the best-known type being “looming”.

Objects on Horizon may be further than they appear

Looming, as Wikipedia describes, is “an abnormally large refraction of the object that increases the apparent elevation of the distant objects and sometimes allows an observer to see objects that are located below the horizon under normal conditions”. Landscape features normally too far to see can be magnified and appear closer than they actually are; for example, in the Great Lakes Canadian shorelines over 50 miles away can become visible under looming conditions and appear to be as little as 6 miles away. Cliffs and mountains especially can appear to shimmer, change elevation, appear and disappear over or under the horizon, and (most freakily) change shape, depending on the exact atmospheric conditions.

Looming is particularly common in the polar regions, due to large ice sheets creating uniformly low temperatures near the surface compared to the surrounding air. Many a shoreline has been charted in vivid detail in the Arctic and Antarctic only to find that the true coast is many miles beyond where it appeared to be, or even was altogether nonexistent.

Even further than you might think is possible…

Freaky stuff if you ask me. What’s even freakier is that our own planet is amateur hour when it comes to the sort of looming an alien planet might produce. William Jackson Humphreys in 1920 calculated that at on a planet 5.7 times the radius of the Earth, and under certain temperature and pressure conditions that would be eminently habitable (i.e. a shirt-sleeve environment!), looming would be so extreme the horizon would appear flat and images from all the way around the planet would be refracted and appear directly ahead of you, including yourself! Yes, you could peer at the horizon and see your own back in the distance. Here’s what he wrote in “Physics of the Air”, pages 447-448:

If, now, the density of the air at the place in question decreases with increase of elevation, as it nearly always does, the upper portion of the wave front will travel faster than the lower, and the path will be bent down towards the earth along a curve whose radius depends upon the rate of this density decrease. For example, let the corrected height of the barometer be 760 mm., the temperature 17 °C., and the rate of temperature decrease with elevation 5 °C. per kilometre; conditions that not infrequently obtain at sea level. On substituting these values in the density elevation equation, it appears that the density gradient would be such that if continuous the limit of the atmosphere would be reached at an elevation of about 10 kilometres. Hence, under these circumstances, the velocity of light at an elevation of 10 kilometres would be to its velocity at the surface in the ratio of 1,000,276 to 1,000,000, approximately, since the refractive index of the lower air would be 1.000,276, about. The radius of curvature, r, therefore, is closely given in kilometres by the equation,

r r + 10 = 1 , 000 , 000 1 , 000 , 276

Hence, r = 36,232 kilometres, or approximately 5.7 times the radius of the earth.

It is conceivable, therefore, that the size of a planet and the vertical density gradient of its atmosphere might be such that one’s horizon on it would include the entire surface—that he could look all the way round and, as some one has said, see his own back.

Earth-like, but in one crucial respect utterly alien. How is this not a well-known effect among worldbuilders, writers, and artists? It’s one of the cooler facts I’ve encountered; and this is real physics!

Yes, real Planets with flat and ghostly Horizons might be out there, waiting for us to discover…

5.7 times the Earth’s radius is rather large for a terrestrial planet. Just to equal Earth’s surface gravity such a world would have to weigh in at 32.3 Earth masses. For perspective, that’s more massive than Jupiter’s solid core is thought to be! Such solid masses aren’t unheard of, though; there’s a whole category of extrasolar planets called “mega-Earths”, which a 32-Earth-mass rocky planet wouldn’t look too out of place in. Large and massive, but plausibly so.

Where credibility starts to get a bit strained is the aspect of such a planet’s density. The more massive the terrestrial planet, the denser it is, and hence the greater the surface gravity. These mega-Earths likely all have densities far higher than Earth, with gravity too high for human habitation. To equal Earth’s surface gravity on Looming World, a planet 5.7 times Earth’s radius weighs in at 32.3 Earth masses; that works out to a density of 0.97 grams per cubic centimeter. For reference, Earth’s density is 5.51 grams per cubic centimeter, so despite being much more massive than Earth it would have to be only a fifth as dense. Tough.

Not impossible, though; water’s density is 1 gram per cubic centimeter, about the same as Looming World’s needs to be. To get a surface gravity of 1g the density needs to be 0.97 grams per cubic centimeter, i.e. less dense than water. There might be a mass range, perhaps 50% greater, where the density would be more like 1.5 grams per cubic centimeter, and the surface gravity around 1.5 times Earth, where a planet could be made of mostly water plus some rock, of the requisite size, and still be in the habitable range.

It might get easier if ammonia is introduced into the global oceans; liquid ammonia is 0.68 grams per cubic centimeter, so considerably less dense than water, so if the water of this world were more like antifreeze fluid it would help considerably. Arguably this is starting to grade out of the habitable range, though.

I’m thinking such a world would need to be predominately liquid; if there are large bubbles in the crust forming pockets of light gas somehow that would help out a lot. Think like a cross between Naboo and that asteroid from “Armageddon”: an object that is in large measure hollow. Such “rubble pile” structures are common in asteroids, but it would be unexpected in an object dozens of times more massive than the Earth.

Unexpected, but like I said, not impossible. It’s the sort of discovery that would bend known science a bit but not come remotely close to breaking it, and in all honestly I’m getting “hot Jupiter” vibes from this idea: a hypothetical sort of object that defies the usual models, but later turns out to actually exist in large numbers, leading to a revision of the models, i.e. the sort of discovery that might be waiting for us out there, somewhere. An expedition to such a world might make for an interesting science fiction story…


Featured image for this post courtesy of Brocken Inaglory. CC-BY-SA 3.0.

2 Replies to “A World where if You look far enough You’ll see Yourself…”

    1. Well, looming can magnify images, so if the effect were strong enough your back might be easily visible with the naked eye. Doesn’t seem very likely, I will admit; even on such a planet as that it might not be the sort of thing that happens every day. Still cool, though.

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