The Galilean Moons of Jupiter on a Rotating Rhombic Dodecahedron

These images of Ganymede, Io, Callisto, and Europa were all acquired by NASA. I placed them on this polyhedron, and created this rotating .gif, using Stella 4d, which you can try for free at this website.

An Astronomical Dodecahedron

NASA’s Artemis I spacecraft snapped this picture of the Earth moving out from behind the far side of the Moon. I put it on this rotating dodecahedron using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

A Rhombic Enneacontahedron, Decorated With Craters From the Far Side of the Moon

The crater-pictures used on the faces of this rhombic enneacontahedron come from here, and I projected them onto the rhombic faces of this polyhedron using Stella 4d: Polyhedron Navigator. If you’d like to try Stella for yourself, you can get a free trial download at this website. I blogged a similar image once before (here), but that was before I received the helpful suggestion to slow down the rotation speed of the polyhedra I post on this blog — so I decided to revisit this idea in a new post.

Happy Moon Day!

To celebrate Moon Day — the anniversary of the first Moon landing — this year, I made a rhombic triacontahedron with colored images of the Moon on each face. I got the image of the Moon from its Wikipedia page, and made this polyhedral image using Stella 4d, a program you can try for free right here.

The Sun, Earth, and Moon Adorning the Faces of a Great Rhombicosidodecahedron

Trunc Icosidodeca

This polyhedral image was created using Stella 4d, a program you can try for yourself, for free, at http://www.software3d.com/Stella.php.

The Moon Unit Proposal

moon unit

I propose that 384,400 km (238,855 miles), the average distance from the Earth to the Moon, be called a “moon unit.” Example: “The mileage of my car is over one moon unit.”

Thoughts on Colonizing Space

OSIRIS_Mars_true_color

[Image found here.]

It is no secret than I am not a fan of our current president, Donald Trump. I’ve been watching him carefully, and have found exactly one point of agreement with the man: humans should colonize the planet Mars. The two of us differ, however, on the details. What follows is my set of reasons — not Trump’s — for supporting colonization of Mars.

First, we should not start with Mars. We should start, instead, by establishing a colony on Luna, our own planet’s moon. There are several reasons for this. First, as seen in this iconic 1969 photograph brought to us by NASA, we’ve been to the Moon before; it simply makes sense to start space-colonization efforts there.

apollo-flag2

At its furthest distance, the Moon is ~405,000 km away from Earth’s center, according to NASA. By contrast, at its closest approach to Earth in recent history, Mars was 55,758,006 km away from Earth. With the Moon less than 1% as far away as Mars at closest approach, Luna is the first logical place for an extraterrestrial colony. It need not be a large colony, but should at least be the size of a small town on Earth — say, 100 people or so. There are almost certainly problems we haven’t even discovered — yet — about establishing a sustainable reduced-gravity environment for human habitation; we already know about some of them, such as muscular atrophy and weakening of bones. Creating a lunar colony would demand of us that we solve these problems, before the much more challenging task of establishing a martian colony. (To find out more about such health hazards, this is a good place to start.) Once we have a few dozen people living on the Moon, we could then begin working in earnest on a martian colony, with better chances for success because of what we learned while colonizing the Moon. 

An excellent reason to spend the billions of dollars it would take to colonize Mars (after the Moon) is that it is one of the best investment opportunities of the 21st Century. Space exploration has a fantastic record of sparking the development of new technologies that can help people anywhere. For example, the personal computers we take for granted today would not be nearly as advanced as they are without the enormous amount of computer research which was part of the “space race” of the 1960s. The same thing can be said for your cell phone, and numerous other inventions and discoveries. Even without a major space-colonization effort underway, we already enjoy numerous health benefits as a result of the limited exploration of space we have already undertaken. Space exploration has an excellent track record for paying off, big, in the long run.

Another reason for us to colonize Mars (after the Moon, of course) is geopolitical. The most amazing thing about the 20th Century’s Cold War is that anyone survived it. Had the United States and the Soviet Union simply decided to “nuke it out,” no one would be alive to read this, nor would I be alive to write it. We (on both sides) survived only because the USA and the USSR found alternatives to direct warfare: proxy wars (such as the one in Vietnam), chess tournaments, the Olympics, and the space race. In today’s world, we need safe ways to work out our international disagreements, just as we did then. International competition to colonize space — a new, international “space race” — would be the perfect solution to many of today’s geopolitical problems, particular if it morphs, over the years, into the sort of international cooperation which gave us the International Space Station.

Finally, there is the best reason to establish space colonies, and that is to increase the longevity of our species, as well as other forms of life on Earth. Right now, all our “eggs” are in one “basket,” at the bottom of Earth’s gravity well, which is the deepest one in the solar system, of all bodies with a visible solid surface to stand on. A 10-kilometer-wide asteroid ended the age of the dinosaurs 65 million years ago, and there will be more asteroid impacts in the future — we just don’t know when. We do know, however, that past and present human activity is causing significant environmental damage here, so we may not even need the “help” of an asteroid to wipe ourselves out. The point is, the Earth has problems. The Moon also has problems, as does the planet Mars — the two places are far from being paradises — but if people, along with our crops and animals, are located on Earth, the Moon, and Mars, we have “insurance” against a global disaster, in the form of interplanetary diversification. This would allow us to potentially repopulate the Earth, after the smoke clears, if Earth did suffer something like a major asteroid impact.

Since Moon landings ended in the 1970s, we’ve made many significant discoveries with space probes and telescopes. It’s time to start following them with manned missions, once again, that go far beyond low-Earth orbit. There’s a whole universe out there; the Moon and Mars could be our first “baby steps” to becoming a true spacefaring species.

[Later edit: Please see the first comment, below, for more material of interest added by one of my readers.]

A Scenario I Would Like to See: Friendly Competition, Between Teachers’ Unions and School Administrators, to Help School Libraries Everywhere

school libraries

During the Cold War, the usual way nations compete (direct warfare) was taken off the table by the invention of the hydrogen bomb. With the alternative being mutually-assured destruction, the two sides, led by the USA and the USSR, had to find other ways to compete. Some of those ways were harmful, such as proxy wars, as happened in Vietnam. Others, however, were helpful, such as the space race. The United States put men on the Moon in order to beat the Soviet Union there, as this iconic 1969 photograph makes evident (source: NASA).

planting the flag

We are all still reaping the benefits of the technological and scientific advances made during this period, and for this purpose. The most obvious example of such a benefit is the computer you are using to read this blog-post, for computer technology had to be advanced dramatically, on both sides, in order to escape the tremendously-challenging gravity-well of the Earth.

Wouldn’t it be wonderful if other conflicts in society took beneficial forms, as happened in this historical example?

This could happen in many ways, but the one that gave me the idea for this post is the conflict between teachers’ unions and school districts’ administrators, now taking place in school districts all over the place. I think it would be awesome if this previously-harmful competition changed, to take a helpful form: book drives, to help school libraries.

Please do not misunderstand, though: I’m not talking about taxpayer money, nor union dues. My idea need not, and should not, affect the budget of any school district, nor union budget. All that need happen is for individual people — teachers and administrators  — to go home, look at their own bookshelves, and help students directly, by donating some of their already-paid-for books to school libraries.

While I make no claim to represent any organization, I am a teacher, and a member of the NEA (the National Education Association) in the United States, as well as my state and local NEA affiliates. In an effort to start this new, helpful way to compete, I will give books to the school library where I teach, next week, which is the second week of the new school year. That’s a lot easier than, well, putting men on the Moon. 

This is something we can all do. All of us in the education profession, after all, already agree that we want students reading . . . and this is something we can easily do, to work together towards that goal. School libraries need hardcover books which are student-friendly, meaning that they appeal to a young audience, on a wide variety of subjects. Both fiction and non-fiction books are helpful.

Lastly, in the hope that this idea catches on, I will simply point out one fact: helping turn this idea into a reality is as easy as sharing a link to this blog-post. 

Is the Moon a Magnet for Ignorance?

is the moon

Google’s search-suggestions for “is the moon,” shown above, clearly indicate support for the “magnet for ignorance” conjecture.

My favorite one from this list: “is the moon real”? I’ve looked into this, and there are apparently quite a few people utterly convinced that the Moon is a hologram, created by NASA, for reasons I have not been able to discern.

On Binary Planets, and Binary Polyhedra

Faceted Augmented Icosa

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.]