This polyhedral image was created using Stella 4d, a program you can try for yourself, for free, at http://www.software3d.com/Stella.php.
This polyhedral image was created using Stella 4d, a program you can try for yourself, for free, at http://www.software3d.com/Stella.php.
I’ll start this analysis with a simple land/water breakdown for Earth’s surface:
The two figures in the chart above are familiar figures for many — but how does “land” break down into continents, and how does “water” break down into oceans, as fractions of Earth’s total surface area? That’s what this second chart shows.
With continents, I placed them on the chart to make it easier to see physically-connected continents as sets of adjacent wedges of similar color, separated only by thin lines. The most obvious example of this is Europe and Asia, which are considered separate continents in the first place only for historical reasons, not geographical ones. Combine them, into Eurasia, and it has 36.3% of Earth’s total land area, which is (36.3%)(0.292) = 10.6% of Eath’s total surface area. Even then, Earth’s three largest oceans (the Atlantic, Indian, and Pacific Oceans) are each larger than Eurasia.
There are other naturally-connected continents, albeit with much smaller land connections — narrow enough for humans to have altered this fact, only a “blip” ago on geographical time-scales, by building the Suez and Panama Canals. In the case of the Suez, its construction severed, artificially, the naturally-occurring land connection between Eurasia and Africa, and the term “Afro-Eurasia” has been used for the combination of all three traditionally-defined continents. Afro-Eurasia has 56.7% of Earth’s land, but that’s only (56.7%)(0.292) = 16.6% of Earth’s total surface area. That’s larger than the Indian Ocean, at (19.5%)(0.708) = 13.8% of Earth surface area. However, both the Atlantic Ocean, at (23.5%)(0.708) = 16.6% of Earth’s surface area, and the Pacific Ocean, at (46.6%)(0.708) = 33.0% of Earth’s surface area, are still larger than Afro-Eurasia.
The Pacific Ocean alone, in fact, has a greater surface area than all of Earth’s land — combined.
The other case that can be made for continent-unification involves North and South America, since their natural land connection was severed, only about a century ago, by the construction of the Panama Canal. Combine the two, and simply call the combination “the Americas,” and that’s 28.5% of earth’s land, which is (28.5%)(0.292) = 8.3% of Earth’s surface area. (I didn’t simply call this combination “America” to avoid confusion with the USA.) The Americas, even in combination, are not only smaller than each of Earth’s three largest oceans (the Atlantic, Indian, and Pacific), but also smaller than Afro-Eurasia, or Eurasia — or even Asia alone, by a narrow margin.
By the way, there are lots of things that don’t show up on the second chart above: islands, inland seas, lakes, rivers, etc., and there’s a good reason for that: on the scale of even the larger pie chart above, all these things are so small, compared to the oceans and continents, that they simply aren’t large enough to be visible.
This image of binary polyhedra of unequal size was, obviously, inspired by the double dwarf planet at the center of the Pluto / Charon system. The outer satellites also orbit Pluto and Charon’s common center of mass, or barycenter, which lies above Pluto’s surface. In the similar case of the Earth / Moon system, the barycenter stays within the interior of the larger body, the Earth.
I know of one other quasi-binary system in this solar system which involves a barycenter outside the larger body, but it isn’t one many would expect: it’s the Sun / Jupiter system. Both orbit their barycenter (or that of the whole solar system, more properly, but they are pretty much in the same place), Jupiter doing so at an average orbital radius of 5.2 AU — and the Sun doing so, staying opposite Jupiter, with an orbital radius which is slightly larger than the visible Sun itself. The Sun, therefore, orbits a point outside itself which is the gravitational center of the entire solar system.
Why don’t we notice this “wobble” in the Sun’s motion? Well, orbiting binary objects orbit their barycenters with equal orbital periods, as seen in the image above, where the orbital period of both the large, tightly-orbiting rhombicosidodecahedron, and the small, large-orbit icosahedron, is precisely eight seconds. In the case of the Sun / Jupiter system, the sun completes one complete Jupiter-induced wobble, in a tight ellipse, with their barycenter at one focus, but with an orbital period of one jovian year, which is just under twelve Earth years. If the Jovian-induced solar wobble were faster, it would be much more noticeable.
[Image credit: the picture of the orbiting polyhedra above was made with software called Stella 4d, available at this website.]
[Source: This is the lead story in the most recent issue of The Charon Space Central Daily, published electronically every 6th or 7th Earth day, since Pluto’s day lasts almost as long as our week. I simply translated it into English, after I intercepted the transmission, so that at least some other humans can read it.]
Earth is the most massive of the inner rocky planets, with the mass of 459 plutos, according to the most accurate measurements relayed so far by Wizonn Shore, in recent days, on the robotic spacecraft’s approach to the giant rocky world. Earth’s radius, 5.5 times that of Pluto, gives it a volume of about 160 plutos, so it is almost three times as dense as either of our homeworlds. Its surface area, as the largest rocky body in the solar system, is almost 23 times greater than that of Pluto and Charon combined. However, as this chart shows, much of Earth’s surface is covered with deadly oceans, utterly useless for any form of life as it evolved in the Pluto / Charon system. These enormous accumulations of liquid dihydrogen monoxide are the largest yet discovered anywhere, so incredibly hot (averaging ~300 kelvins) that, at Earth’s high atmospheric pressure, that compound exists as a freely-flowing, highly-reactive liquid covering over 70% of earth’s surface, except for rare areas where it is frozen, mostly near the poles and/or at the top of Earth’s taller mountains. Unfortunately, 300 kelvins is about seven times what natives of Pluto, Charon, or our colonies are used to, in terms of temperatures above absolute zero, so Earth is believed by most scientists to hold no potential for colonization.
It was this high temperature that prevented exploration of the inner solar system’s rocky planets — until recent developments in high-temperature adaptive technology made it possible for us to begin our exploration of the inner solar system, breaking the previously-inviolable heat-barrier at the asteroid belt, and sending our now more heat-resistant spacecraft into the previously “forbidden” region — first, Mars, which has been studied already with two separate mission; and now, finally, Earth. The exploration of Venus and Mercury by robot craft, however, at least for now, awaits further improvements in heat-resistant materials science.
The first surface-reconnaissance rover, similar to those used on Mars, was sent to a place with relatively low large-alien population density, as estimated by artificial light-output from different parts of the land surface, during Earth’s night. However, of course, its landing position had to be somewhere in the 29.2% of Earth’s surface not covered with oceans — for a rover landing in liquid dihydrogen monoxide would instantly be destroyed, as it sank to ever-more-crushing pressures in a hot liquid often called, on decoded Earth voice-transmissions, “water.” On both Pluto and Charon, in all laboratory experiments, this dangerous “water” has quickly rendered inert any electronic components — of anything — to which it is exposed. (Indeed, this, as well as the numerous deaths which resulted, was the reason that such “water” experiments have largely been abandoned, except by Earth-colonization advocates who have, a few admit, no good answers to the questions about Earth already being inhabited, nor how to deal with the toxic oxygen gas making up nearly one-fifth of Earth’s atmosphere.)
Despite the care given to choosing a landing-spot, this was still the first and only image sent before our spacecraft’s first rover was unexpectedly deactivated, for unknown reasons. These reasons are suspected to be related to the strange, pink alien creature dominating the image, although that is, at this point, speculation.
With data transmissions from the first landing probe ceased, Pluto/Charon’s automated spacecraft Wizonn Shore, launched from Charon eight years ago, continues to take pictures, from Earth-orbit, as fast as it can, while waiting on instructions from Charon Space Central regarding when to risk launching a second landing rover. Transmission of the images taken from orbit is a secondary priority to actually taking the pictures, as is happening now, so our news services do not yet have images of Earth of any higher resolutions than those already sent as Wizonn Shore approached Earth over the last few weeks.
While there has been some speculation in the press that the alien pictured in the one image sent from Earth might be the dominant species on Earth, that is not supported by visual transmissions decoded in the radio part of the electromagnetic spectrum, most of which depict the activity of a relatively hairless biped which compensates for its nudity, for reasons unknown, by covering itself with “clothes,” the buying and selling of which is, judging from the transmissions we have decoded so far, a major activity for Earth’s bipedal inhabitants.
It is these mysterious bipeds, and their activity as observed by our own devices, which all of Pluto, Charon, and our colonies on the outer moons are waiting to see images of, as taken by Wizonn Shore. Will it match what they beam out in all directions, using radio waves, with what seems to be careless abandon — or will the “as seen on TV” version of Earth prove to be an elaborate deception, on the part of Earth’s inhabitants?
Of course, the computers processing these images do not care about our collective frustration, and so we continue to wait. Might “clothes” be adopted only at a certain age by Earth’s dominant bipeds? Might that single, naked, pink-skinned alien, photographed by our short-lived landing-rover, simply be an immature form of the same species? At this time, those questions, and more, remain open.
In which direction is the polyhedron above rotating? If you say “to the left,” you’re describing the direction faces are going when they pass right in front of you, on the side of the polyhedron which faces you. However, “to the left” won’t really do . . . for, if you consider the faces hidden on the side facing away from you, they’re going to the right. What’s more, both of these statements reverse themselves if you either turn your computer over, or stand upside-down and look at the screen. Also, if you do both these things, the situation re-reverses itself, which means it reverts to its original appearance.
Rotating objects are more often, however, described at rotating clockwise or counterclockwise. Even that, though, requires a frame of reference to be made clear. If one describes this polyhedron as rotating clockwise, what is actually meant is “rotating clockwise as viewed from above.” If you view this spinning polyhedron from below, however, it is spinning counterclockwise.
Since I live on a large, spinning ball of rock — of all solid objects in the solar system, Earth has the greatest mass and volume, both — I tend to classify rotating objects as having Earthlike or counter-Earthlike rotation, as well. Most objects in the Solar system rotate, and revolve, in the same direction as Earth, and this is consistent with current theoretical models of the formation of the Solar system from a large, rotating, gravitationally-contracting disk of dust and gas. The original proto-Solar system rotated in a certain direction, and the conservation of angular momentum has caused it to keep that same direction of spin for billions of years. Today, it shows up in the direction that planets orbit the sun, the direction that most moons orbit planets, and the direction that almost everything in the Solar system rotates on its own axis. Because one direction dominates, astronomers call it the “prograde” direction, with the small number of objects with rotation (or revolution, in the case of orbital motion) in the opposite direction designated as moving in the “retrograde” direction.
So which is which? Which non-astronomical directional terms, as used above when describing the spinning polyhedron there, should be used to describe the prograde rotation of Earth, its prograde orbital revolution around the sun, and the numerous other examples of prograde circular or elliptical motion of solar system objects? And, for the few “oddballs,” such as Neptune’s moon Triton, which non-astronomical terms should be used to describe retrogade motion? To find out, let’s take a look at Earth’s revolution around the Sun, and the Moon’s around the Earth, for those are prograde is well. This diagram is not to scale, and the view is from above the Solar, Terran, and Lunar North poles.
[Image found reblogged on Tumblr, creator unknown.]
Prograde (Earthlike) motion, then, means “counterclockwise, as viewed from above the North pole.” To describe retrograde (counter-Earthlike) motion, simply substitute “clockwise” for “counterclockwise,” or “South pole” for “North pole,” but not both. Here’s the spinning Earth, as viewed from the side:
If you’ll go back and check the polyhedron at the top of this page, you’ll see that its spin is opposite that of this view of the Earth, and it was described as moving clockwise, viewed from above. That polyhedron, and the image of Earth above, would have the same direction of rotation, though, if either of them, but not both, were simply viewed upside-down, relative to the orientation shown.
Stella 4d, the software I use to make rotating polyhedral .gifs (such as the one that opened this post), then, has them spin, by default, in the same direction as the Earth — if the earth’s Southern hemisphere is on top! As I live in the Northern hemisphere, I wondered if that was deliberate, for the person who wrote Stella 4d, available at www.software3d.com/Stella.php, lives in Australia. Not being shy, I simply asked him if this were the case, and he answered that it was a 50/50 shot, and simply a coincidence that it came out the way it did, for he had not checked. He also told me how to make polyhedral .gifs which rotate as the Earth does, at least with the Northern hemisphere viewed at the top: set the setting of Stella 4d to make .gifs with a negative number of rotations per .gif-loop. Sure enough, it works. Here’s an example of such a “prograde” polyhedron:
When I was a little kid, my sister and I dug a big hole, in our front yard, and simply called it “the digging-hole.” It looked a lot like the hole shown above, except for the fact that, during daylight hours, our digging-hole usually included two small, dirt-covered, determined children, armed with plastic shovels. We tried, for years, to dig that hole as deep as possible. My personal goal, of course, was the Earth’s molten core, not India, and certainly not China.
Why do Americans so often talk about digging a hole straight down to China, anyway? Even if the Earth were solid all the way through its interior, digging straight down, from almost anywhere in the contiguous 48 states of the USA, would not put you in China, nor even India (which is, at least, closer to being correct than is China), but at the bottom of the Southern Indian Ocean. Salty water would suddenly rush into your newly-dug tunnel, killing you instantly, as soon as you got close to enough to the other side for the extreme water-pressure there to finish your digging project for you. The only exceptions to this watery doom would be coming out of the tunnel on one of the islands in that ocean, which would require great precision to hit deliberately.
Also, the fact that China and the USA are both Northern-hemisphere nations easily rules China out as the hypothetical “solid-earth” destination for Americans who dig straight down, and all the way through. If you could go through the center of the earth from North of the equator, you’d have to end up South of the equator. Isn’t that obvious? Don’t people look at globes?