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.]

Seven Moving Lights in the Sky, the Seven Days of the Week, and Other Significant Sets of Seven

days of week and lights in the sky

Have you ever wondered why the number seven appears in all the places it does? We have seven days in the week. Churches teach about the seven deadly sins, and “seven heavens” is a common phrase. There are seven wonders of the ancient world, and seven of the modern world. The number seven has appeared in many other socially significant ways, in societies all over the world, for millennia.

It is no coincidence, I think, that the ancients were able to see seven lights in the sky which are either visible in daylight, or move against the background of “fixed” stars at night. They ascribed great significance to what went on in the sky, since they viewed “the heavens” as the realm of the gods in which they believed. The evidence for this lives on today, in the names of the seven days of the week, and numerous other sets of seven, all over the world.

It is possible to see the planet Uranus without a telescope, but it is very dim, and you have to know exactly where to look. No one noticed it until after the invention of the telescope. If Uranus were brighter, and had been seen in numerous ancient societies, I have no doubt that we would have eight days in the week, etc., rather than seven.

Oceans, Further from the Sun


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.