Heavenly Choreography

“Lonely” Pluto’s been in the news lately due to the fly-by of the U.S. New Horizons probe. Startling images and geological questions have arisen, and two new moons have been photographed. But what piqued my interest was the pronounced wobble in Pluto’s motion, not a new discovery, which has to do with both the proximity and similarity in mass of it’s largest moon Charon. This led to a general investigation into how and why bodies are influenced by each other in space, according to conventional physics.

long-range radio image
pluto and charon
pluto-charon orbits
pluto, charon, and U.S.

Pluto and Charon’s Wobble Dance

Forty-eight years separated the discoveries of Pluto (1930) and it’s first known moon, Charon (1978). Visual resolution was one contributing factor in this delay, these objects beings between 4.5 and 7.5 billion kilometers away, about a measly 2400km and 1200km in diameter respectively, and having an average inherent brightness of magnitude 16, making them about 1 billion times dimmer in the night sky than Venus. Distant, tiny, and dark.

But there was another factor. Pluto and it’s largest moon are locked into a wonderful and strange dance, stable yet dynamic, always opposite each other as though connected by an invisible cosmic bicycle spoke, sometimes moving faster and sometimes slower, circling about a single point. From our earthly vantage point with mid-20th-century technology, this looked like one distant wobbling object exhibiting an almost immeasurably small fluctuation in brightness. Nowadays it is exactly these features which permit astronomers to catalog distant stars and scan them for decent sized exoplanets, which are computed rather than seen.

Motions of Two Bodies

Pluto and it’s nearly half-as-large moon, Charon, wobble around each other a bit like a double star system. Any two celestial bodies with stable gravitational effect upon one another both orbit around a central point called the barycenter. Usually, at least in our solar system, this barycenter is located inside the larger celestial object (as is the case with the earth and moon), but not always. It depends upon the relative sizes, masses, and distances between the two bodies.

For example, the moon has about 27% the radius and a little more than 1% the mass of earth, while positioned at an average distance of about 60 earth-radii away. These strictly numeric facts allow one to calculate that the earth-lunar barycenter is about 1700 kilometers under your feet, affording us the very comforting impression that the moon revolves about the earth. It’s very slightly off-center, contributing to ocean tides, but appearing quite stable from a distance. (Somewhat similar to first animation on left.)

2 bodies
pluto-charon wobble
pluto-charon wobble dance
2-body same orbit

Turning to Pluto, it’s main moon Charon has about 51% of it’s radius, and 12% of it’s mass, and orbits at a relatively intimate 16 pluto-radii distance. This places their common barycenter about 900 kilometers outside of Pluto. Hence a significant wobble. Charon gives an obvious impression of tugging on Pluto. (Closer to the 2nd animation above; note that the 3rd animation is an actual long-range digital image of this pair of objects.) There is also a theoretical case where both bodies exert force upon each other equally, having very similar masses, and move about a barycenter placed exactly midway between each other. But in all cases, the two objects revolve around a specific common point. It is imprecise to say that the smaller object orbits the larger.

From the Barycenter’s Point of View

The situation gets more complex and more gorgeous with multiple-body examples, such as the solar system. Counting just planets, known moons, so-called ‘dwarf planets’ and it’s featured star, there are currently 190 major objects within the solar system. This leaves aside for the moment millions of asteroids, meteorites, comets, and very distant objects yet to be cataloged far beyond Pluto. The sun’s gravitational influence is thought to extend as a sphere of solar wind (the heliosphere) about 20 billion kilometers in all directions. Yet, in terms of mass, the two largest objects, Sun and Jupiter, account for much much more than 99% of the entire system. The 2-body barycenter for the sun and Jupiter lies about 80,000 kilometers outside the solar surface, still only about 1/10,000th of the way to Jupiter. Picture to yourself Jabba-the-Hut playing see-saw with a ladybug: in order to balance, Jabba would need to sit 80,000 times closer to the central pivot than the ladybug!

But what about the entire solar system? Let’s imagine reversing the perspective so that instead of seeing planets and stars moving in relation to a fixed common point, we have the celestial objects fixed and watch where the barycenter wanders with respect to them. (This is entirely in keeping with Einstein’s thought experiments regarding moving trains and sound or light waves, or for example the cognitive shift occasioned by earth-centric vs. heliocentric worldviews.)

movement of solar system's barycenter with respect to sun over 50-year period. source:wikipedia

movement of solar system’s barycenter with respect to sun over 50-year period. source: wikipedia

Then, the solar system’s barycenter moves around in a complex wobble dance, sometimes inside the sun, and sometimes not. There are so many variables that I doubt this traced path ever repeats. (A worthy research question!) During the years 1951 and also 1990, the barycenter passed very close to the sun’s center. In 1983, it strayed maximally outside of the sun. In the delightful Wikipedia illustration, the changing colors of the curve tracing the barycenter path represent different decades in earth history. Question for non-materialists: will future astronomer/astrologers discover subtle sensitive psychological effects connected with this? One last thing: this entire discussion has basically been simplified into two dimensions, but in reality it all moves in 3-D space.


If you want to look more deeply into the rules of ‘heavenly choreography‘, a good beginning point would be the Wikipedia entries for terms like barycenter, binary stars, and gravity waves. There also exist some neat interactive sites where you can plug in your celestial bodies and distances and watch the resulting dances. Also, there’s a wealth of interesting information out there about Pluto and it’s 5 moons. The topic of tides is fascinating and also connected with all of the above.

Handy INDEX — scan through all available ||SWR|| articles.


  1. A fascinating article, thanks.

    With a diameter ratio of 2:1 and a barycentre external to both objects, surely the Pluto-Charon system is a double dwarf-planet?

    The wobbling Sun, as the solar system barycentre cycles above the surface and dives back down again every fifteen years or so, would be very instructive to an alien scientist observing it from outside.


    1. Maybe so, I suppose we could ask a bona-fide astronomer, but they have even declassified Pluto as a planet, so who knows what the criteria are. I bet you are correct about the sun wobble.


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