Moons and Planets: Binary Planets
Published on Aug 17, 2006 at 2:22 pm.
1 Comment.
Filed under planets.
Following up on yesterday’s post, I thought that I’d say a bit more about moons and planets. As you gather from how I ended yesterday, I am not thrilled with the new definition of planet that has been proposed. For one thing, it doesn’t really clear things up. Under the new definition we now have 12 planets and a dozen or so “maybe” planets. This is far worse than 8 or 9 planets and 1 or 2 maybe planets.
The other thing that I wanted to mention is that the new definition of planet says that a body is a planet if it is big enough to pull itself essentially into a sphere (hydrostatic equilibrium is the actual concept used) and orbits a star, and not another planet. Then, it makes an exception for binary planets.
Moons don’t really orbit planets. Rather planets and moons both move. They orbit around the barycenter (the center of mass between the two bodies). The barycenter lies along a line between the centers of mass of the two bodies. For the Earth-Moon system, the Earth is enough larger than the Moon that the barycenter is much closer to the center of the Earth than it is to the center of the Moon. In fact, it lies less than one Earth radius from Earth’s center, putting it below the Earth’s surface. So, it sure looks like the Moon orbits Earth if you look at it. But if you look carefully, you see that the Earth wobbles. This works for the other planets, too, and even with stars. As the Earth orbits the Sun, it really orbits the barycenter between the Sun and Earth. Again, the Sun is much more massive than Earth, so the barycenter lies beneath the surface of the Sun. The Sun just wobbles a little (a very little!) as Earth goes around. So, the smaller body looks like it orbits the larger one. But, the bigger that the smaller body is, the farther out that the barycenter moves from the center of the larger body. Also, the barycenter distance is proportional to the ratio of the masses of the bodies. It isn’t an absolute number, so if you move the smaller body farther out, then the barycenter also moves farther out. If our Moon were bigger, then the barycenter would be farther from the Earth’s center than an Earth radius. But, if the Moon were the same size as it is today, but far enough away, then the barycenter would again be farther from Earth’s center than one planetary radius.Â
Under the proposed definition of planet, a body is also defined to be a planet if it is big enough to pull itself into a sphere and it also orbits with a barycenter above the surface of a larger body. At first glance, this seems reasonable. For, that would mean that body bodies are orbiting a point outside of each of them. If the two objects are nearly equal in mass, then the barycenter would be almost midway between them. Clearly, looking at them, they’d appear to be orbiting each other.
Charon, Pluto’s moon, as it’s been called since its discovery by James Christy in 1978, is a bit over half Pluto’s diameter, and 15% of the mass of Pluto. 
This means that the barycenter between Pluto and Charon is about 13% of the way from the center of Pluto to the center of Charon. That makes the barycenter about 25,000 kilometers from the center of Pluto. But, Pluto is only 2300 kilometers across! So, the barycenter lies well outside of Pluto. Thus, Pluto and Charon are binary planets. I have no problem with this, per se. For years, I’ve taught my students that whatever Pluto is (a planet, a Kuiper Belt Object, an asteroid, or something else) that Pluto and Charon are a binary whatever system.
But, the definition does leave some questions. What if Charon were closer? If Charon’s orbit were only 9000 kilometers from Pluto, then the barycenter between the two would be at Pluto’s surface. Would that meant that Charon isn’t a planet if it is closer than that magic distance, but it is a planet if it is farther out? Is that fair? An even bigger question comes from the eccentricity of orbits. Moons don’t normally orbit in perfectly circular orbits. But, the barycenter is a proportion of the distance between the two bodies. That means that the barycenter distance changes as the actual distance between the to bodies changes. Suppose Charon were close to Pluto, and its orbit were elliptical enough that it varyied between 8800km and 9000km. Would that mean that it is a planet half of the time and a moon the other half of the time?
This may seem like a moot issue, since Pluto and Charon are not that close together. But, we haven’t found all of the things out there in the Kuiper Belt yet. There may yet be a pair of bodies in which this happens. Also, the planet definition is supposed to be general enough to apply to extrasolar planets. What if we find something like this out there around another star?
We don’t need to go far away, though, to have this problem. We only need to go far into the future. Our own Moon has a mass of about 1.2% that of the Earth. So, the barycenter is just under 1.2% of the way between the center of the Earth and the Moon. That means that the barycenter is about 4600 kilometers from the center of the Earth. But, Earth’s radius is about 6380 kilometers, so the barycenter is nearly 1800 kilometers below the surface of the Earth. Fine, the Moon is a moon. But, we know from bouncing laser beams off of reflectors left on the Moon by the Apolll astronauts that the Moon is receding from Earth at about 3.8 centimeters per year. So, the barycenter is moving outward. In another few billion years, the barycenter between the two bodies will be outside of Earth. So, will the Earth and Moon then become the Earth-Luna binary planet?
Hmm. Again, I don’t think that this new definition really solved our problems. They’ve been working on this for a long time now. You’d think that they’d have thought of these problems and addressed them.
And, this still doesn’t address all the criticisms of this new definition. Next time, I’ll say a bit more about the distinction between moons and planets.
-Astroprof
(Images courtesty of NASA and NASA/JPL)
Derrick F on April 24, 2008 at 3:31 pm: 1
The only concept I’m not sure I see here is how the sun is really orbiting the barycenter it shares with earth. There are however many planets (I’m going to pretend it’s nine) in this solar system. Why the barycenter it shares with earth? It seems more like it would be all at the same time, which is feasible to me in some ways, but not all of them.