These images of Jupiter, Saturn, Uranus, and Neptune 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.
Tag Archives: Jupiter
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.
On Binary Planets, and Binary Polyhedra
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.]
Oceans, Further from the Sun
Since earth’s oceans will be boiled away by the sun’s increasing luminosity, as I mentioned in my last post, we’ll eventually need to find other oceans elsewhere — or learn to do without water, which seems even less likely.
The news today is running a story about a subsurface ocean under Enceladus, a moon of Saturn. Here, in an obviously-photoshopped picture from one of those news stories, it’s shown in an impossible location, next to the U.K., for the purposes of size comparison. In addition to this moon, subsurface water is expected to exist on Titan, another moon of Saturn, as well as three of the four Galilean moons of Jupiter: Europa, Callisto, and Ganymede.
The Jovian system doesn’t get closer than 4.2 AUs from earth, and Saturn’s moons are further out still — but at least our descendants do have other places to go, once our oceans become too hot to stay liquid. They’re expected to be boiled away, by the sun’s increasing luminosity, in ~1.5 billion years.
The Galilean Moons of Jupiter on a Rotating Dodecahedron
Software credit: see http://www.software3d.com/stella.php