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Today (June 30th) is asteroid day.  For this auspicious (yet anxious-making) holiday, I have been saving two asteroid-related miniature stories ripped from the headlines.

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First, we return to the dwarf planet Ceres, the largest object in the asteroid belt.  We need to revisit the bright spots upon the dwarf planet’s surface.  Ever since the New Horizons spacecraft began to approach the little world, these glistening spots have fascinated the astronomy community.  Initially scientists thought that the spots were composed of hydrated magnesium sulfate (a substance quite similar to the Epsom salts sold for bathing and foot-soaking), however it now seems like the shiny patches are made of something else entirely.  According to astronomers, the particular chemical in these glistening patches actually turns out to be sodium carbonate–a salt formed from carbon.  On Earth, this chemical usually forms in evaporitic conditions–when water evaporates from a lake, sea, or hot springs.  This seems to indicate that the geology of Ceres is more complicated than initially thought—instead of a big ice crystal which has always been the same, the miniature planet has undergone changes: surface water evaporated to leave these mysterious chemical deposits.  Hopefully finding out about Ceres’ past can teach us more about how planets form (or don’t form).

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Second, we turn our eyes back closer to Earth to take in the newly discovered “second moon” a tiny asteroid about the size of the great pyramid of Giza which seems to be orbiting Earth.  This new asteroid, called 2016 HO3, is not really a true moon but a quasi-satellite: it sometimes loops around our planet because Earth and the little rock both orbit the sun on a similar circuit.  The asteroid orbits the sun in 365.93 days (just slightly longer than Earth’s orbit of 365.24 days). Thus, for the next few hundred years it will act like a true moon as our orbits converge. The rock is about 40 meters (130 feet) across by 100 meters (328 feet) wide.  It is a bit strange to think about it up there hidden in the darkness, but it is a fairly comforting asteroid day story.  2016 HO3 is never destined to hit Earth.  The really bad asteroids seem to be the ones we don’t know about (so it is time to keep our eyes on the skies and learn more).

surface_area_largeToday features a short but vivid post borrowed from the futurist/science fiction/space blog io9 (which in turn took it from XKCD). Above is a map of all the surfaces of the solar system’s planets and moons flattened out and stitched together. The map was created by Randall Munroe and it does a superb job of explaining the relative size of rocky objects in the solar system. For obvious reasons the gas giants (and the sun!) have been excluded, but so too have small rocks and dust. For fun (um, I hope), the mapmaker also included an area equivalent to all human skin–which, distressingly, seems to be about the size of Hainan.

Russian concept art for a cloud colony in the upper atmosphere of Venus, (proposed in 1970s)

Russian concept art for a cloud colony in the upper atmosphere of Venus, (proposed in 1970s)

This map also emphasizes my most ardent fantasy of solar system colonization: I don’t really want to set up shop on Umbiel or Ceres, but I have a long-lasting interest in colonizing Venus. Sadly most of the rest of humankind is having trouble grasping this concept (possibly because the surface of Venus is a molten hellscape featuring boiling lead, sulfuric acid rain, and crushing pressure).  Remember though, we don’t need to ever go down to the Venutian surface: we can hang around in floating bouncy castles drifting through the balmy spring at the top of the atmosphere. Imagine taking your family zeppelin out for a night on the floating town! All of the people who express such an unwholesome interest in cold resource-poor Mars should pause to reexamine its relative area on Mr. Munroe’s excellent map!

Mars, Earth, Venus

Left to right: Mars, Earth, Venus

Today, Ferrebeekeeper ventures far far beyond my comfort zone into that most esoteric and pure realm of thought, mathematics.  But don’t worry, we are concentrating on topology and geometry only for long enough to introduce a beautiful, intriguing shape, the torus, and then it is straight back to the real world for us…  Well, hopefully that will prove to be the case–the torus is anything but straight.  It is, in fact, very circular indeed, and, as we all know, it has at least one big hole in it….

Wikipedia defines a torus as “a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle.” That’s hard for me to wrap by head around but the meaning becomes much more comprehensible in the following illustration.

So a torus is a circle wrapped around in a circular path.  You can find a variety of other ways of mathematically representing the torus here, but the simple definition suits our purpose.

One ring toroid them all....

I admire torus shapes because I think they are very beautiful.  Just as the golden ratio and the Fibonacci sequence are aesthetically appealing, there is a pleasure to merely beholding or touching a torus: ask anyone who has contemplated a ring, a golden diadem, or a cinnamon donut.  Talk to an indolent adolescent sprawled on an inner-tube bobbing on the surf, and you will immediately grasp the hold that toroids have on humankind.

And beyond humankind....

In addition to its obvious aesthetic merits, however, there is a mysterious aspect to the torus, a hint at hidden dimensions, negative space, and infinity.  Kindly contemplate the old eighties video game Asteroid (you can play the game here if you are too young to remember: amusingly, your ship is an “A” which reminds me of Petrus Christus’ enigmatic painting).  If you pilot your ship to the far left of the screen you emerge on the right side of the screen: the flat screen represents a cylinder. However, to quote Bryan Clare from Strange Horizons, “the bottom of the screen is connected to the top as well. This has the same effect as if the screen were rolled into a cylinder, and then bent again to glue the two circular ends together, forming the familiar donut shape.” So, when you play asteroids you are trapped in a miniature toroid universe which appears 2-dimensional. Try to blast your way out of that!

The following famous math problem further illustrates the nature of the torus.  Three utility companies need to connect their respective lines (gas, water, and electric) to three different houses without ever crossing the lines.

Connect each utility to each house. Don't cross the lines.

The problem is impossible on a two-dimensional Euclidean plain and even on a sphere, however topologists realized that if you poke a hole through the plane or the sphere (thereby making it a torus) the lines can be connected.

To finish the article here is a movie of a torus being punctured and turned inside out. The result is a torus of the same dimensions but with reversed latitude and longitude.  It’s hard not to love such a funny shape.  But it is hard for me to wrap my mind around the larger implications.  I think I’m going to stop trying and head off for some donuts.

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