Category Archives: Phenomena

Human Exposure To Vacuum: Part 1

The topic of explosive decompression generates a lot of nonsense, particularly in science fiction films and television series, but also scattered across the internet generally. We actually know quite a lot about what would happen if a human being were exposed to the vacuum of space—and it turns out not to be like the movies.

For this first part, I’m going to write a bit about basic physics and physiology, and discuss what that can tell us about the accuracy (or otherwise) of the common SF tropes we see in the movies. In the second part, I’ll move on to the evidence we have from actual vacuum exposures and explosive decompressions.

EXPLODING
Exploding, Outland
John Ratzenberger explodes in Outland

Will people explode when exposed to vacuum?
Absolutely not.

Liquid pressures aren’t an issue—when decompressed, the liquids in our tissues will expand only very, very slightly before their ambient pressure drops to zero. Gas pressures are the problem. Our bodies contain various gas cavities which are at the same pressure as the surrounding atmosphere. Most spacecraft and spacesuits aren’t pressurized to one atmosphere, but we can take that as the worst-case scenario for explosive decompression. So at the moment tissue pressures fall to zero, these gas cavities will press outwards against the surround tissue with one atmosphere of pressure—that’s 100 kilopascals, which is 100,000 newtons per square metre.

But skin and soft tissue is strong. Here’s film from Arthur C. Clarke’s World of Strange Powers (1985). The scientists are reproducing a traditional “hook-hanging” rite carried out at Kataragama, Sri Lanka:

The volunteer weighs 55 kilograms, and hangs from six slim hooks. With a generous allowance of 30 square centimetres for the total suspension area, that comes out to pressures of 180,000 newtons per square metre on the soft tissues the hooks supports. That’s almost twice our worse-case limit, and the skin doesn’t even stretch very far.

So no exploding.

FREEZING
Troy Garity freezes in "Sunshine"
Troy Garity freezes (and later shatters) in Sunshine

Will people freeze solid as soon as they are exposed to space?
Absolutely not.

Vacuum is a good insulator. At cool ambient temperatures, our bodies lose heat mainly by conduction and convection, which is why air temperature and wind speed are so important to the way we dress outdoors. In the absence of air, our skin will cool by radiation—the loss of energy at infrared wavelengths emitted by our warm bodies. Depending on skin temperature and clothing, we radiate at anything from 100 to several hundred watts. So that’s how fast we’ll lose heat.

Now, we’re made mainly of water, and water has a high specific heat capacity, around 4000 J/kg/ºC—which means a kilogram of water needs to lose 4000 joules to fall in temperature by one degree Celsius. So an 80-kilogram bag of water (that’s approximately me), is going to need to lose over 300,000 joules of energy before its temperature falls by one degree. (That’s neglecting the continuing metabolic production of energy in the meantime.) If I’m radiating at a generous 500 watts, and producing no internal energy, and receiving no energy from sunlight, that’s ten minutes of vacuum exposure before my temperature falls by just one degree Celsius.

There may be some local difficulties, though. We also cool by evaporation, which becomes significant when it’s hot enough to cause sweating. Water will evaporate from any moist surfaces exposed to vacuum, and it will take energy with it as it does so, driving down the temperature of the tissue it evaporates from. So on exposure to vacuum the eyes, nasal cavity, and probably mouth and respiratory tract are going to start cooling by evaporation. How cold they get will depend on how quickly water moves out of the tissues to replace what is lost from the surface.

But no-one is going to turn to ice crystals and shatter.

BREATH-HOLDING
Breath-holding detail, 2001
Keir Dullea holds his breath in 2001: A Space Odyssey

Should people hold their breath if about to be exposed to vacuum?
Not a good idea.

With the tissues equilibrated to an ambient zero pressure, the cardiovascular system will continue to work as usual—all its pressures are relative pressures (what engineers call “gauge” pressures). A blood pressure of 120/80 is telling you that the systolic pressure is 120 millimetres of mercury (mmHg)  above ambient, and the diastolic pressure 80 mmHg above ambient. That’s true at sea level with an ambient pressure of one atmosphere, at twenty metres down in the ocean with an ambient pressure of three atmospheres, on top of Everest with an ambient pressure of a third of an atmosphere, or in vacuum at zero atmospheres.

Trouble is, respiratory gas exchange works on absolute pressures. No matter what your tissue ambient pressure is, you still need to breathe a partial pressure of 160 mmHg of oxygen (21% of an atmosphere) to get a normal concentration of oxygen into your blood. This is fine when you’re breathing at one atmosphere of ambient pressure. It’s even fine on top of Everest—if you mix supplementary oxygen into a third of an atmosphere of breathing gas, you can easily get normal oxygenation while still balancing the pressure inside your lungs against the ambient pressure outside your body and in your tissues. There’s no resulting pressure gradient, and nothing gets squashed or stretched.

But in a vacuum, the pressure in your lungs (necessary for gas exchange) is not balanced by any external pressure. Holding air in your chest is going to cause pressure outwards, stretching the lungs; and inwards, compressing the heart and large blood vessels in the middle of your chest. And notice that even a standard 160 mmHg pressure of oxygen is a large pressure, exceeding the normal pressures of arterial blood. It’s enough pressure to squash your heart, which is not going to have a good effect on its ability to pump. This is why people can make themselves faint while trying too hard to blow up a balloon—the high pressure inside their chest interferes with the flow of blood through the heart. So trying to hold on to a lungful of oxygen in vacuum will make your blood pressure crash, and you’ll almost certainly pass out.

And that 160 mmHg is the smallest plausible pressure someone might find themselves trying to hold when suddenly exposed to vacuum. It’s the minimum operating pressure for spacesuits—most operate at around 240 mmHg. The Space Shuttle maintained an internal atmosphere at 530 mmHg during missions. These are pretty lethal pressures to try to hold in the lungs.

It’s not just the cardiovascular system that will suffer. The lungs themselves are not designed to support that sort of pressure differential. In the fifth edition of Diving and Subaquatic Medicine, Chapter 6, Edmonds et al. report that a person’s lungs will leak air into the surrounding tissue when subjected to a pressure gradient of 110 mmHg, even if the chest is prevented from expanding using a binder. If the chest is allowed to expand in response to the imposed pressure, the lungs start to leak at just 70 mmHg. (Admittedly, this is from a cadaver study, but it’s not the sort of test you can find volunteers for.) What’s going on here is that stretch is bad for your lungs, too—if your chest is blown up like a balloon, the lungs will burst at a lower pressure. This is bad news for anyone tempted to take a deep breath before entering vacuum—the extra stretch moves their lungs closer to the burst point. But that’s probably academic, since these experimental burst pressures are lower than the lowest spacesuit operating pressures.

So if you try to hold a lungful of air on decompression, not only will you squash your heart and cause your blood pressure to fall catastrophically, your lungs will leak—they’ll squeeze air into the lung blood vessels, sending showers of bubbles into your circulation; they’ll squeeze air into the tissues around your heart and then up into your neck; and they’ll squeeze air into the pleural cavities lining your chest, causing your lungs to deflate.

As an added extra, the air held in your middle ears will burst your eardrums.

So breath-holding on exposure to vacuum is a good way to incapacitate yourself. Is there another option?

EXHALING
Robin Tunney in "Supernova"
Robin Tunney exhales (albeit too late) in Supernova

Should people exhale on exposure to vacuum?
Better … but still not great.

If breath-holding will make you lose consciousness and pop your lungs, not breath-holding seems like the only viable alternative. If you can arrange to yawn just as the pressure drops, to open your Eustachian tubes and let the air out of your middle ears, then you’ll also prevent your eardrums bursting.

Exhaling gets rid of that abnormal pressure gradient in the chest, so there’s no interference with blood pressure, and no popped lungs. However, it takes time for the lungs to empty, so if decompression is very fast, lung injury could still occur while the pressure in the lungs remains transiently higher than the pressure in the surrounding tissues. Here’s a theoretical plot from the second edition of the Bioastronautics Data Book, showing that a 250 mmHg decompression (from 350 to 100 mmHg) over 0.3 seconds will produce a brief pressure gradient across the chest wall that reaches what we know to be potentially lung-popping levels:

Pressure differential across lung during decompression
Click to enlarge

Having exhaled to vacuum, there’s now no oxygen at all in the lungs. From the point of view of keeping oxygen circulating in the blood, this is a disaster. Venous blood, returning from the tissues, still contains a considerable residue of oxygen. This is normally topped up by oxygen diffusing from the lungs into the blood. Even if not much oxygen is added (for instance, if you’re holding your breath), at least some oxygen goes back to the tissues. But if there’s no oxygen in the lungs, the normal diffusion gradient is reversed—oxygen leaves the venous blood and diffuses into the space inside the lungs. So very little then gets sent back to the tissues. This means that tissue oxygenation fails abruptly and catastrophically—much faster than it does with simple breath-holding.

We’ve got some experience of how quickly things go badly wrong under this sort of hypoxic insult—some of it comes from pilots depressurizing at very high altitude, and some of it comes from people who have accidentally breathed gas containing no oxygen, usually in an industrial accident.

The USN Aerospace Physiologist’s Manual makes a prediction about how long a person might remain conscious and orientated enough to carry out simple tasks, once exposed to near-vacuum. This is based on the apparent convergence of a number of graphs generated by decompressing various hapless volunteers to various altitude-equivalents during the 1960s:

Time of Useful Consciousness (USN Aerospace Physiologist's Manual 4-28)
Click to enlarge

Somewhere around an altitude of 65,000 ft (with an air pressure of 43 mmHg, and a partial pressure of oxygen of just 9 mmHg) the period during which volunteers remain conscious enough to perform simple tasks converges on 12 seconds.

So a Time of Useful Consciousness (TUC) of 12 seconds following  exposure to vacuum is often quoted, but there are two caveats to it, neither of them encouraging. Firstly, this derived time applies to individuals at rest—that is, not trying to do urgent things in order to stay alive. Secondly, it derives from experiments involving non-abrupt decompression. As Paul W. Fisher reports in the USAF Flight Surgeon’s Guide:

These TUCs are for an individual at rest. Any exercise will reduce the time considerably. For example, usually upon exposure to hypoxia at FL 250 [an altitude of 25,000 ft], an average individual has a TUC of 3 to 5 minutes. The same individual, after performing 10 deep knee bends, will have a TUC in the range of 1 to 1.5 minutes.
[…]
A rapid decompression can reduce the TUC by up to 50 percent caused by the forced exhalation of the lungs during decompression …

Exercise not only increases the consumption of oxygen, it also increases the speed at which blood returns to the lungs and is depleted of its oxygen content. So (extrapolating the extrapolations!) if you’re explosively decompressed while exercising vigorously, it looks like you might end up with less than six seconds of useful consciousness. Which would be disappointing.

BOILING
Michael Ironside in "Scanners"
Michael Ironside‘s blood boils (well, not really) in Scanners

Will a person’s blood boil on exposure to vacuum?
Yes.

At body temperature, water has a saturated vapour pressure of 47 mmHg. Which means that if the ambient pressure falls below 47 mmHg, the water will evaporate into the gas phase throughout its bulk. Which is the definition of boiling—bubbles forming and expanding within the liquid. The altitude at which the atmospheric pressure drops below 47 mmHg (63,000 ft), and the water in human tissues is in danger of boiling, is called the Armstrong Limit—named for Harry Armstrong, one of the pioneers of aviation medicine.

You’ll find some places on the internet that claim a person’s blood won’t boil, because normal blood pressure (120 mmHg systolic, 80 mmHg diastolic, remember) is higher than that 47 mmHg critical value. In support of this claim, many cite physicist Geoffrey Landis’s otherwise excellent exposition on explosive decompression:

Your blood is at a higher pressure than the outside environment. A typical blood pressure might be 75/120. The “75” part of this means that between heartbeats, the blood is at a pressure of 75 Torr (equal to about 100 mbar) above the external pressure. If the external pressure drops to zero, at a blood pressure of 75 Torr the boiling point of water is 46 degrees Celsius (115 F). This is well above body temperature of 37 C (98.6 F). Blood won’t boil, because the elastic pressure of the blood vessels keeps it it a pressure high enough that the body temperature is below the boiling point …

Now, the fact that Landis gets the notation for arterial blood pressure reversed (his numbers should be written 120/75) is probably a hint that he’s not entirely at ease with the physiology of blood circulation. What he has forgotten about is the blood that’s not in the arteries, which at any given time amounts to about 90% of the blood volume—flowing through the capillaries, veins and lung blood vessels, all of which normally have pressures well below the critical value. The pressure in the central veins, in particular, is usually only a few millimetres of mercury above ambient. So although Landis writes “No” in answer to the rhetorical question “Would your blood boil?” what he really means is that ten percent of your blood wouldn’t boil, but the rest would. Which certainly seems more like a “Yes” to me.

It’s also sometimes claimed that, while the veins do run at low pressures normally, they will tightly contain any rise in pressure, preventing gas bubbles from forming. But veins are so-called capacitance vessels—they adjust their volume according to the volume of the circulating blood. They will reach their elastic limit if overfilled, but in healthy adults they’re continuously adjusting their volume at low pressure. It’s possible to infuse a litre or more of fluid into the veins of a healthy adult without the venous pressure shifting much over 15 mmHg. So there’s likewise room for a litre or more of gas to form in the venous side of the circulation without causing any major pressure rise in the system. This is a problem, because the amount of gas necessary to cause cardiac arrest in a human is estimated at 3-5 ml/kg—if a few hundred millilitres of gas gets into the heart chambers, it forms a compressible volume that stops the heart propelling liquid when it pumps. The heart continues beating, but it moves no blood.

Another variation on this optimistic theme is that the skin and subcutaneous tissues are tight enough to prevent gas expanding. (Presumably the people who make this claim have never thought seriously about the level of tissue stretchiness implied by a yawn or a clenched fist.) There’s a condition called subcutaneous emphysema, in which gas (usually air from a leaking lung) becomes trapped  under the skin. We know that even the relatively low pressures associated with a mechanical ventilator (around 20 mmHg) can squeeze gas out of an already injured lung and into the tissues—which shows that the tissues are unable to immediately generate the necessary counterpressure. Like the veins, the tissues eventually reach an elastic limit and oppose the entry of any further gas, but there is considerable, obvious distension before that happens. So, on exposure to vacuum, the surrounding tissues are not going to be able to prevent the veins expanding.

What happens within the tissues themselves is an interesting question. Dense tissues like tendon and ligament may well be able to contain any tendency for gas bubbles to form within their substance. The loose, soft tissue that lies under the skin (the region affected by subcutaneous emphysema) obviously doesn’t have the structural strength to prevent the spread of gas bubbles once they start forming, but there’s some evidence that it is tightly woven enough to suppress initial bubble formation, for a while.

The second edition of the US Naval Flight Surgeon’s Manual discusses a study in which the hands of volunteers were decompressed to very low pressures. Subcutaneous gas bubbles didn’t form at the Armstrong Limit; they didn’t even form at pressures equivalent to the boiling point of water at skin temperature, which is a little lower than the body’s core temperature. The highest pressure at which gas formation occurred was 20 mmHg; three people were decompressed to 5 mmHg, and all showed gas formation. But the onset of visible gas was delayed—it occurred “suddenly and manifested itself by marked swelling”, but after a lapse of between thirty seconds and over ten minutes of decompression time. Once swelling occurred, it could be rapidly abolished by recompression. But, strikingly, gas was generated much more readily when the hand was decompressed again. So this experiment suggests that it might be initially difficult for gas bubbles to form spontaneously in the tissues, but once they do they can spread rapidly. Other body gases (nitrogen, oxygen, carbon dioxide) will diffuse into these gas bubbles once they form, and will persist as tiny bubbles for some time after recompression has caused the water vapour to collapse back into the liquid phase. These tiny bubbles then form nuclei that will quickly re-expand with water vapour if the tissues are decompressed again.

Unfortunately, the Naval Flight Surgeon’s Manual is a little short on detail. It’s not clear if these volunteers’ hands were still being perfused with blood, or if they’d been isolated by tourniquet, for instance—which would make a significant difference to the tissue pressures. The study was reported in the first edition of NASA’s Bioastronautics Data Book (1964), but was dropped from the second edition of 1973, apparently superceded by more recent experiments which I’ll describe in my next post on this topic. So the pressures and timings in this report are interesting, but may not reflect what happens with total-body decompression.

OTHER THINGS

As if all the foregoing wasn’t enough, a few other problems may occur. If the atmosphere you’re breathing immediately before decompression contains nitrogen, some of that nitrogen will bubble out of solution, in the tissues and blood, as the ambient pressure falls. While this can be a major problem for aviators at altitude, it’s probably a relatively minor problem for those exposed to vacuum, given that water vapour bubbles will be forming. And the second edition of the Bioastronautics Data Book notes that, “The symptoms of decompression sickness are rarely observed during the first few minutes of exposure to low pressure.”

I’ve already mentioned the problem of air trapped in the middle ear. Other areas where air can be trapped, causing pain when the ambient pressure falls, are in the sinuses and under dental fillings. The USN Aerospace Physiologist’s Manual puts the experimental incidence of sinus problems on decompression at 1%, and of dental pain at 0.1%.

Finally, there’s the volume of gas that’s sitting in everyone’s stomach and intestines. This will expand as the ambient pressure falls. On slow decompression it generally causes cramping pain, burping and flatulence. But both the third edition of the USN Flight Surgeon’s Manual and the second edition of the Bioastronautics Data Book note that more rapid expansion of gut gas has the potential to intensely stimulate the vagus nerve, causing a profound fall in heart rate and blood pressure, leading to unconsciousness.

SUMMARY

So:
You won’t explode, but you may well swell up. You won’t freeze instantly, but your eyes, nose, mouth and airways will experience evaporative cooling. You shouldn’t try to hold your breath. You should breathe out and yawn as the pressure drops, but if decompression is explosive that may not protect your lungs from pressure injury. Your venous blood will boil, and there’s room in your venous circulation to generate enough gas to stop your heart moving blood. The gas in your gut may expand so rapidly it leads to a reflex slowing of your heart and rapid fall in blood pressure. You will have a maximum of 12 seconds of useful consciousness, but if you’re exerting yourself and/or the decompression has been explosive, your period of consciousness may well be considerably shorter.

For Part 2 of this topic, I’m going to look at the data we have from actual vacuum exposure, in humans and animals.


Note: Almost all pressures are quoted in an antique unit of measurement, the millimetre of mercury (mmHg). This is because the most familiar physiological pressure for most people is blood pressure, which is always quoted in millimetres of mercury, and also because a lot of the relevant literature dates back to a time when atmospheric gas pressures were quoted in millimetres of mercury.
If you want to convert, the following are equivalents, in round numbers: 1 atmosphere, 1000 millibars, 760 millimetres of mercury, 100 kilopascals, 15 pounds per square inch.

Nacreous

ˈneɪkriːəs

nacreous: pertaining to or resembling mother-of-pearl

Nacreous cloud
Source

Nacreous clouds are in the UK news at present, with multiple sightings in Scotland. There was an interesting divide in the BBC news coverage of the phenomenon this evening, with national newsreader George Alagiah intoning some twaddle about “forming at sunset” and “caused by refraction” in a sing-song voice, as if delivering a boring bedtime story. Whereas the BBC Scotland weather presenter, Gillian Smart, got the story right and had some nice pictures, too.

Nacreous clouds form in the low stratosphere, which is pretty high for a cloud. They’re present at all times of the day and night, but are more visible before sunrise and after sunset, when they are the first things to catch the sunlight, and the last to lose it, by virtue of their altitude. Their colours are due to diffraction, not refraction.

But this is a post about words, not natural phenomena.

Nacreous means “pertaining to nacre“. Nacre is the iridescent substance that lines many varieties of sea-shells, most notably those of pearl-forming oysters—it’s therefore commonly known as mother-of-pearl. The word comes to us from the Romance languages—it has analogues in French, Portuguese, Spanish and Italian—but its early origins remain obscure.

Nacre also provides the characteristic sheen on the surface of a pearl. And it’s interesting that a simple little world like pearl should also be a puzzle to etymologists. There are tentative links to Latin perula, a diminutive of perum, “pear”; or to a hypothesized diminutive pernula of perna, “leg of mutton” (from the shape of a mussel shell); or to  pilula, “globule”. Take your pick.

In Latin, a pearl is margarita, and in Greek, margarites.  Just as Pearl is a woman’s name in English, so Margarita is in Spanish. Margaret and Margery are its English-language equivalents. Margarita is also the Spanish word for “daisy”, though the connection between the pearl and the flower is obscure. The connection between the flower and the various cocktails called “daisies” is also obscure—at one time there was a Whiskey Daisy, a Gin Daisy and a Brandy Daisy, but the Tequila Daisy was the one that became most popular, and took the name margarita for itself.

Margarita also gave us the name for margaric acid, a mixture of fatty acids with a pearl-like lustre. Margarins were chemical derivatives of margaric acid, and margarine is a butter-like substance that took its name from the margarins, although chemically unrelated.

Something that looks pearly is margaritaceous, and something that produces pearls is margaritiferous.

Oyster comes from Latin ostrea and Greek ostreon. Something that resembles an oyster is ostracine, ostraceous or ostreaceous. The farming of oysters is ostreiculture.

An ostrakon (plural ostraka) is an archaeological find—a shard of pottery that has been used to jot down a note, something that was common practice in Ancient Greece. The Greeks called these pottery shards ostraka because of their curving resemblance to oyster shells. Votes were cast using ostraka, in particular when citizens voted for the banishment of one of their number. Such banishment was called ostrakismos—which gives us our word ostracism, meaning “exclusion”.

Crepuscular Rays

Crepuscular Rays © 2016 Marion McMurdo
Crepuscular rays over the Tay estuary. Click to enlarge
© 2016 The Boon Companion

Crepuscular rays are rays that occur during the crepuscule, which is a fine old word for “twilight”. They’re the rays of brightness and shadow that seem to fan outwards and upwards from the setting or rising sun when it is masked by cloud. What’s happening is that the shadow of the clouds is being projected across the sky above your head. Dust and moisture in the air up there is being illuminated, or cast into shadow, and we see bright and dark streaks across the sky as a result. So we only get crepuscular rays if there’s something in the air to be illuminated—on a dry day with little dust or smog, there’s no hope of a spectacular display of rays like the one above.

One striking thing about the image above is that there is a noticeable dark shadow framing the cumulus cloud. That implies that there is an illuminated surface somewhere above the visible cloud. There’s actually a thin layer of higher stratus cloud, on to which the shadow of the cumulus is being projected. The illuminated stratus also accounts for the beautiful golden yellow hue of the sky. Just a couple of minutes later, the lengthening shadow on the stratus is more evident:

Crepuscular Rays © 2016 Marion McMurdo
Click to enlarge
© 2016 The Boon Companion

In the daytime, a place to look for clouds casting shadows on other clouds is around the tops of towering cumulonimbus. Sometimes the rising tops of these clouds push upwards through a layer of cirrus, and the sun will project the shadow of the crown of the cumulonimbus downwards on to the thin layer of cirrus.

Crespuscular rays become less evident as they fan out from the sun. My diagram shows what’s going on:

Crepuscular ray visibility
Click to enlarge

The individual bright rays are delineated by cloud shadow. When you look towards the sun, you’re looking diagonally through each  shadow zone. The long sightline within the shadow makes it appear noticeably darker than the background sky. But as your gaze sweeps upwards, away from the sun, you begin to look through the shadows at right angles. The shorter sightline makes them progressively less evident, and its unusual to see crepuscular rays extend right overhead. But look what happens behind you in the diagram—your sightline is diagonal again and, although the shadow will have become more diffuse as light scatters into it from the surrounding air, there’s a possibility it may return to visibility behind you. So whenever you see crepuscular rays, you should turn around and check the sky in the opposite direction.

You may also see clouds in the sky behind you generating their own visible shadows. Just as perspective makes the crepuscular rays seem to radiate outwards from the sun in front of you, it makes these anticrepuscular rays behind you appear to converge on a point directly opposite the sun:

Anticrepuscular rays
Source
Click to enlarge

The same phenomenon that produces crepuscular rays is also responsible for the appearance of sunbeams shining downwards through the clouds:

Solar Rays
Click to enlarge
© 2017 The Boon Companion

Perspective again makes these beams appear to radiate from a central point, centred on the sun above the clouds.

Since these don’t happen at twilight, they shouldn’t really be called crepuscular rays, though they often are. The common word sunbeam seems as good as any; solar rays is a catch-all term that includes crepuscular rays; computer graphics artists call them god rays; and Marcel Minnaert, in his marvellous book Light and Color in the Outdoors, introduced me to the old expression “the sun drawing water”, from the old belief that water evaporated along the sunbeams.

New Year / Resolution

NASA LRO full moon
NASA Lunar Reconnaissance Orbiter image

Christmas Day’s full moon made me decide to make my first post of the New Year about a resolution—specifically, the resolution of the human eye. (See what I did, there?)

We’re so used to images of the full moon like the one above, it’s difficult to remember that, until the invention of the telescope in the 17th century, people had a very limited idea of what it actually looked like.

Here’s a 16th-century sketch of the moon by Leonardo da Vinci:

Leonardo da Vinci moon sketch
Taken from Reaves & Pedretti Leonardo Da Vinci’s Drawings of the Surface Features of the Moon (J. History Astronomy 18;1 55-7, 1987)

A very careful observer and excellent draftsman, using the naked eye, was apparently able to record very little surface detail.

Lest you think Leonardo was having a bad day, or perhaps just wasn’t that interested in the detail, here’s the best effort of the astronomer William Gilbert:

William Gilbert moon sketch
Taken from Kopal The Earliest Maps of the Moon (The Moon 1;1 59-66, 1969)

Pretty rubbish, eh? Although Leonardo and Gilbert both captured some of the larger dark shapes on the lunar disc, neither was able to produce much in the way of detail.

What was the problem? The size of the moon was the problem. Although it can occasionally seem huge in the sky, especially when rising or setting, it’s actually surprisingly small, in angular terms. It averages about 31 minutes of arc in diameter—just over half a degree. For comparison, your thumb at the end of your outstretched arm covers about a degree of the sky. So it’s easy to blot out the whole lunar disc with a finger at arm’s length.

Snellen chartNow, the average human eye can resolve detail down to one minute of arc. The row of letters on your optician’s Snellen chart that corresponds to normal 6/6 vision (or 20/20 if you’re in the USA) is five minutes of arc high, with the black lines and narrow white spaces subtending one minute at your eye.

Part of that resolution limit is due to something called diffraction limitation—when your pupil is small, light rays are scattered by the edge of the iris and end up converging to form a small disc, rather than a point, on the retina. When your pupil is large, diffraction limitation is less of an issue, but imperfections in the optics of your eye, especially around the edge of the lens, become a problem. So most people end up with one minute of arc being their best resolution.

Even if the optics of your eye were perfect, you’d hit another resolution problem, which is the density of photoreceptor cells in the retina. Even at their densest, in the central fovea, there are only a couple of hundred thousand per square millimetre, packed so tight that each is just two microns across—translating to a resolution of about 0.4 minutes of arc. So that’s as good a resolution as you’re going to get even with an excellent human eye.

(And that is why, although that Ultra HD 4K television screen may look jaw-droppingly marvellous when you’re peering at it from a metre away in the shop, it’s probably going to be a disappointment when you get it home—for most sizes of TV, at the usual viewing distances, those 4K pixels are smaller than your ability to resolve. If your eyes are already at their resolution limit with HD, Ultra HD is going to look exactly the same. See if you can get a salesperson to admit that.)

Anyway, back to the moon. In terms of visual resolution, it’s just 31 pixels across, like some rubbish little 32×32 icon from a prehistoric version of Windows. That’s why Leonardo and Gilbert produced the surprisingly poor sketch maps they did. What we actually see of the moon with the naked eye is nothing like the image at the top of this post, but more like this *:One-minute resolution moon

To be visible to the naked eye, at one-minute resolution, a lunar feature has to be about 110 km across. So Leonardo and Gilbert were easily able to pick out the distribution of lunar “seas” (dark lava plains) that give the “Man in the Moon” his face, but neither of them was able to record a single lunar crater. However, now that we know where to look, we can often pick out the bright patches of ejecta surrounding the craters Kepler, Aristarchus and Copernicus, superimposed as they are on dark lava plains. Tycho produces a bright splash in the south, discernible even against the paler rocks of the lunar highlands. The 110-kilometre crater Plato makes a dark-floored contrast with the surrounding pale highland terrain, but it’s right at the dubious edge of visibility for most people.Labelled moon

Now here’s the moon at half-minute resolution, right down at the limit imposed by the density of photoreceptors in our eyes:half-minute res full moonThere’s a great deal more detail—the dark-floored notch of Plato is now pretty evident, and the bright patch around Tycho now contains a central, circular crater.

Are there people who see this well? There are. When the planet Venus is at its closest to Earth it shows as a tiny crescent, one minute of arc across, which can easily be discerned with a small telescope but which most of us see as a simple point of light. Some people claim to be able to discern the crescent shape, however, and many of them can make a sketch of its orientation which convincingly matches the telescopic view.


* I took the original image, and downsized it so that the moon was 31 pixels across. Then I enlarged it, to produce an image of the correct resolution, but it was full of blocky artefacts around the edge of the moon. So I took the original again, and applied Gaussian blur until it smoothly degraded the resolution to match my blocky 31-pixel version.

Converging Rainbows

Double rainbow from reflected sun
Click to enlarge

A familiar pair of primary and secondary rainbows is always concentric, and the outer rainbow has its colours in the reverse order from the primary. But these two have their colours in the same order, and are converging to meet on the horizon. What’s going on there?

I was walking home from work a couple of months ago when I saw this pair of rainbows sticking up above the roofs of the houses like some sort of cosmic V-sign. I lurched to a halt, stared for a few seconds, and then broke into a jog—the sun was going to be setting soon, and I wanted to get a proper view of the pair. Once chez Oikofuge, I body-checked my way past the Boon Companion’s customary greeting (sorry, my love), grabbed a camera, and ran up the stairs to take this photograph looking out over our local river estuary. The photo provides a hint as to what’s causing the unusual rainbow.

Here’s a reminder of how a standard primary rainbow forms:

Formation of rainbow
Click to enlarge

It’s actually a bit of a Just-So story. Quite why a spherical raindrop chooses to turn an incoming ray of red light back on itself at an angle of  42½º (and a violet ray at 40½º) is rather complicated, and I’m working on a little programming project to try to explain it clearly—watch this space. But for now, we just accept that if you look directly away from the sun, towards what is called the antisolar point (handily marked by the shadow of your head), then every raindrop that happens to be at 42½º from your line of sight will be directing red light towards your eyes (and every raindrop at 40½º will be directing violet light towards you). In principle, then, a primary rainbow should form a complete circle in the sky, centred on the shadow of your head, and 42½º in angular radius. In practice, the parts below the horizon become progressively more difficult to see, because there are fewer and fewer raindrops along your line of sight as you shift your gaze downwards.

Notice that the antisolar point is always below the horizon, because the sun can only illuminate raindrops when it’s above the horizon. (D’oh!)

Now, look at how still the water is in my photo. (That’s unusual, hereabouts.) The rainbow-forming raindrops on the far side of the estuary are not just being  exposed to direct sunlight, they’re also being illuminated by light coming from the image of the sun reflected in the still water. Although I can’t see that extra “sun”, it’s nevertheless providing me with another antisolar point and an associated rainbow. This reflected antisolar point is precisely as far above the horizon as the real antisolar point is below it. So the two rainbows have to meet exactly at the horizon, as in my diagram:

How double rainbows form

What you’re seeing in my photo is the little V formed by those two rainbows coming together just above the horizon. (The V is noticeably narrower in the photograph than in the diagram, because the sun is lower and the antisolar points are closer together—but when I tried to reproduce the real situation in the diagram, it got less clear and harder to label properly.)

I stood and watch the display for a while. In theory, the angle of the V should get progressively narrower as the sun gets lower in the sky and the two antisolar points approach each other. And as the light of the setting sun gets redder, the associated rainbow should lose its bluer shades.

What actually happened was that the sun dropped below a bank of cloud, and the two rainbows winked out of existence.

  • I’ve now written some more on the topic of converging rainbows—you can find that post here.

Phenomena: Introduction

Hardly a week goes by without some phenomenon in the natural world attracting my attention—the behaviour of waves and clouds, light and shade, animals and plants. There’s a great deal of physics going on out there, hidden in plain sight. Sometimes I can puzzle out what I’m seeing, sometimes I can look it up, sometimes I just go away baffled.

At the turn of the millennium, I wrote a series of columns about this stuff in The Scotsman newspaper, entitled “Just Phenomenal”. You used to be able to find some of them on the newspaper’s website, and then for a while 26 of the original articles were archived behind a subscription wall at the now-defunct HighBeam Research. But now they’re all gone.

After that, I produced some similar articles and columns for Wanderlust magazine.

I enjoy researching these things, so I plan on blogging here about a few topics relating to natural phenomena. There will also be the inevitable book recommendations.