Slightly less than a year ago, New Horizons was on final approach to its target. After a 9-year journey, the small spacecraft still had several months to go before it would make its headline-grabbing flyby of the Pluto system. In preparation for the big event, New Horizons turned its long-range camera forward, scanning for Pluto and Charon to make sure everything was on track for the flyby. Over the next week, at a rate of one frame per day, a simple yet beautiful video was made:
From 200 million kilometers away, that camera saw two fuzzy white dots slowly dancing around each other. The smaller one, Charon, traces out an elliptical path through space, one that that surrounds it’s larger companion, Pluto. However, the larger, more central body also traces out its own little elliptical orbit, around an empty point in space. There’s a hole in the middle of the dance.
Why does Pluto orbit empty space? After all, the moon goes around the Earth (along with all of the satellites that humans have put up there over the years), and the Earth goes around the sun; in all of these cases the central body seems to be very… well, central. But in the case of Pluto and Charon, both trace a path around an empty point in space, apparently orbiting nothing. Why?
As odd as they are, sitting out there on the edge of the solar system, Pluto and Charon follow the same gravitational rules as everything else. The effect that results in an empty space at the center of the Pluto system also applies all other orbiting bodies. However, by virtue of the relative masses of Pluto and Charon and the distance between them, a subtle aspect of the orbital dance is illuminated clearly — one that happens in every system, but is not usually so visible.
When a moon orbits a planet (or dwarf planet), the two objects are pulled towards each other by the force of gravity — which, like that other Force, surrounds us and binds the galaxy together. It can be tempting to think of gravity as that force that pulls us all down to the ground. However, it’s important to bear in mind that gravity is more than a force that one object exerts on another. It’s a force between two objects, pulling them towards each other — a cosmic example of the equal and opposite action/reaction pair described in Newton’s Third Law of Motion. The Earth pulls you down onto the ground, but you also pull the Earth up onto the bottom of your feet.
The consequence of this action and reaction is that an orbit is not just one object going around the other, but rather both objects going around the center of mass of the system — a point called the barycenter. In technical terms, the barycenter sits at one of the foci of the elliptical orbits of each object. But the net result is that, like Jack and Rose on the Titanic, the two dancers spin around and around the balance point between them. Their momentum tries to throw them apart, but gravity holds them together.
Finding the Barycenter
For most orbital pairs, one object is much larger and more massive than the other. As a result, the barycenter is located within the sphere of the larger object — not exactly at the center, but somewhere deep beneath the surface. The central planet may wobble slightly as its center goes around the barycenter, but it doesn’t orbit an empty point in space.
For example, the Earth is about 81 times more massive than the Moon. To determine the location of the barycenter relative to the center of the Earth, we divide the distance from the Earth to the moon (about 378,000km on average) by 1 plus the ratio of masses. The result is approximately 4,600km — about the same as the distance from Boston to the coast of Ireland. The Earth’s radius is about 6,371km, so this barycenter sits nicely within our planet.
In the case of Pluto and Charon, however, the ratio of the larger mass to the smaller one is more like 8.2 — almost ten times lower. The distance between the two is about 19,600km, and as a result the barycenter is just over 2,100km from the center of Pluto. This point, however, is nearly 1,000km above the surface, and as a result we see the odd motion of Pluto in the video above.
A Simple Beauty
When New Horizons made its close approach to Pluto last summer, it sent us jaw-dropping images of alien landscapes. We’ve learned (and are still learning) so much, and it’s incredible that we have the capability to throw our little robots far into space and begin to understand what’s going on out there.
But among all of the incredible results from this mission, the video of those two fuzzy dots dancing around each other — a simple illustration of orbital dynamics — is still one of my favorites. Billions of kilometers away in the cold darkness at the edge of the solar system, a tiny former planet and its slightly tinier companion spin slow circles around their mutual center of gravity — and that’s a beautiful thing.