# Barycenter of Pluto and Charon

## QUOTE OF THE DAY

With ordinary talents and extraordinary perseverance, all things are attainable.

— Sir Thomas Buxton

## Introduction

Figure 1: Artist's Conception of the Pluto System.

I am excited about the New Horizon's flyby of the Pluto system (Figure 1) occurring on July 14, and I will be glued to my computer as the data is returning. Fortunately, there is already some data coming back on Pluto and its moons. One interesting aspect of the Pluto system is the fact that the mass ratio of Charon to Pluto is large enough that the barycenter of their orbit is outside the bodies of both Charon and Pluto.

Figure 2 shows an animated GIF of Charon and Pluto in orbit. The blue cross shows where the barycenter is (source: APL/New Horizons GeoViz).

Figure 2: Animated GIF showing the movement of Charon and Pluto about their barycenter.

My goal here is to compute the location of the barycenter and compare my results with the published data.

## Background

The Wikipedia does an excellent job describing the barycenter here and here. NASA also has an excellent web page.

For a terrestrial example of the barycenter concept, I have included a video showing a  hammer thrower (Figure 3). Notice how the human and the ball rotate about a point in-between them, just like Pluto and Charon.

I used to throw the discus in high school – I remember well the feeling of rotating about a point outside of my body.

## Analysis

Figure 4 shows my calculations for the barycenter of the Pluto and Charon.

Figure 4: Pluto-Charon Calculations.

My results for the barycenter distances agree with those in the Wikipedia's article on Charon.

## Conclusion

Just a quick calculation to verify that I am seeing Pluto and Charon rotating about a point that is clearly between the two of them.

To whet your appetite for the New Horizon's mission, Figure 5 (source) provides a quick look at how New Horizon's will encounter the Pluto system.

Figure 5. Animation of the New Horizon's Encounter with Pluto.

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### 9 Responses to Barycenter of Pluto and Charon

1. Very interesting! Question--- if the barycenter is outside the planet, if you were standing on Pluto with the barycenter directly overhead, would the center of gravity pull you off the planet? I always wondered about this but cannot find an answer anywhere.

• mathscinotes says:

I have not worked through the numbers. Take a look at this astronomy stack exchange discussion.

mathscinotes

• MHigg says:

I think you need to look at the combined gravitational pull of your mass and Pluto’s against that of Charon and your mass. Since the pull between you and Pluto is greater, you would remain on the surface, or more accurately, you would maintain your orbit around the baricenter (which is on the surface of Pluto).

2. GClark says:

Now that You have landed on Pluto, You have added your mass to Pluto’s, so now the (relatively minute) increased mass on Pluto has brought the system barycenter ever so slightly closer to Pluto (and to Charon and the rest — since the entire system mass has increased “ever so slightly”). Therefore relatively speaking, Pluto (and You with it) has been drawn “ever so slightly” closer to the barycenter; so while You — [given that the mean equatorial orbital velocity at Pluto’s surface is about 857.33·m/s (1917.8·mph) and mean escape velocity at Pluto’s equatorial surface is about 1212.45·m/s (2712.18·mph); also that yours and Pluto’s common “1-body” barycenter is identical to the center of Pluto’s mass, of which You have now become a part; and by which You and Pluto are incidentally pulled into hydrostatic equilibrium (practically)] — (“so while You”) remain in physical contact with Pluto’s surface: yes! apart from that, You are also drawn closer to the constantly moving Pluto system multi-body barycenter (by a minute distance), also the orbital periods of the various bodies comprising the system have all decreased “ever so minutely” (immeasurably).

It might also be interesting to speculate approximately how much higher a person who can high jump 2.45·m on Earth might be able to jump on Pluto with the system barycenter at zenith (that is, from Pluto’s tidally-locked side facing Charon and the system barycenter), versus at nadir (from Pluto’s opposite side), while at either location, in a dome pressurized with earth air at 1·bar at 25°C, and an equatorial surface gravity of 0.06325·g₀ (or 0.62027·m/s²) (supposing that Pluto’s surface didn’t melt or evaporate under said conditions).

• GClark says:

PS: Compare Earth’s tidal bulges relative to the Earth system barycenter ~ 1700·km (1000·mi) beneath Earth’ lunar-facing surface; and its’ low tides at right angles to the lunar direction.

3. Subhash Chandra Sawhney says:

If Pluto revolves around barycenters, it has as many barycenters as many satellites it has. I am at a loss to know how Pluto can revolve around so many barycenters? In case of earth there is no such problem since it has only one satellite. Can you help me with an answer?

• David Back says:

Pluto and Charon are the most massive objects. the other 4 moons of Pluto don't have anywhere near the mass required to SIGNIFICANTLY shift the barycenter. But it DOES shift a bit as the orientation of the other moons change

• Sven Cazier says:

Pluto and its satellites have a common barycenter, different from the barycenter of Pluto and Charon. Given the mass of the other satellites however it would be pretty close to the barycenter of Pluto and Charon. And unless all of Pluto's satellites were to orbit in a straight line that barycenter also changes position based on where they are in their orbit.

The same is true for the solar system. The Sun and Earth have a barycenter, but Earth does not orbit that barycenter it orbits the barycenter of the solar system. The barycenter of the solar system shifts position based on where the planets are in the solar system (mostly Jupiter because of its large mass), even objects entering and leaving the solar system have minute effects on the barycenter. And to be correct, it's not Earth itself that's doing the orbiting around the solar system's barycenter. Earth orbits the Earth-Moon barycenter, and that barycenter orbits the barycenter of the solar system.

4. Eli says:

What would the acceleration rate be if you fell to pluto from just below the barycenter? Or the same for falling to Charon.