# How does the Pluto-Charon orbital 'dance' affect Pluto's elliptical orbit around the Sun?

Like many Scientists (and people in general), I have been watching the New Horizons mission results with great interest.

One aspect in particular caught my attention - the Pluto-Charon orbital 'dance', as it is labelled on the NASA page The View from New Horizons: A Full Day on Pluto-Charon, where

Pluto and Charon orbit around their barycenter

As shown below (from the same page):

It is well known that Pluto has a highly elliptical orbit at an angle with respect to other planets in the Solar System, a diagram from NASA included just to serve as a reminder this differences:

Additionally, according to the University of Colorado page Pluto,Charon & the Kuiper Belt, the Pluto-Charon orbit is at an oblique angle to Pluto's already-elliptical orbit around the Sun, as shown below (from the same site):

So, given that the Pluto-Charon orbital 'dance' occurs with an oblique spin axis, orbiting the Sun in a significantly elliptical orbit, my question is, does this oblique-angled orbital 'dance' have any affect on Pluto's elliptical orbit around the sun?

• What kind of effect on Pluto's orbit are you asking about. Certainly, there's a wobble if you were to plot Pluto's movement, it would wobble or spiral is probably more accurate, around its orbit - kind of like this: i.stack.imgur.com/sQTE7.gif - Source: astronomy.stackexchange.com/questions/10979/…. Were you thinking about something more than that? That's probably the only measurable effect. – userLTK Jul 25 '15 at 3:07
• That kind of thing, yes- but would Pluto's elliptical orbit cause a difference?. Also, would this potentially cause any long term alterations to Pluto's orbit around the sun? – user77400 Jul 25 '15 at 3:10
• I think the answer is no and yes. The Pluto-Charon orbit in and of itself, no. That's stable and the angle doesn't matter, but with any 3 body system, in this case, Sun/Pluto/Charon, there's, I'm tempted to say inevitably some kind of orbital influence with any 3 body system. With 3 body influence in mind, the angle would likely make a difference but Pluto is so far from the sun that those effects are very small - perhaps billions of years before there's a significant change. I could try to answer in more detail but any answer I could give would be clumsy. – userLTK Jul 25 '15 at 3:24
• This sounds like the beginning of a good answer in itself - I understand that the research on this may be scant, if present at all. – user77400 Jul 25 '15 at 3:27
• This question might interest you. physics.stackexchange.com/q/8517. Ultimately the question is a version of the 3 body problem which can be modeled by computer, but it tends to get a little bit long. – userLTK Jul 25 '15 at 4:34

Pluto and Charon orbit around their common center of mass. And their common center of mass orbits around the sun, following an elliptical trajectory. Analogously, the Earth and the Moon orbit around their common center of mass, and their common center of mass orbits around the sun. All of this is well described by Newtonian gravitation.

The only remarkable thing in the Pluto-Charon system is that their masses are comparable, such that the motion of Pluto around the common center of mass is quite visible. Edit: Since the common center of mass follows an elliptical trajectory around the sun, and the planet Pluto orbits around the common center of mass, the trajectory of the planet around the sun is not elliptical, but it is given by the combination of the two motion, i.e., revolution of the common center of mass around the sun, and revolution of the center of mass of Pluto around the common center of mass. The shape of this trajectory is qualitatively similar to the trajectory of the Moon in the reference frame of the sun, which is shown in the picture below.

Both the planet and the moon follow a "wobbled" trajectory, given by the combination of the elliptical motion of the common center of mass, and by the orbital motion of the planet and the moon around the common center of mass. Please note that if the mass of the planet $M$ is much larger than the mass of its moon $m$, the common center of mass is inside the planet (as is the case with the Earth-Moon system), and the "wobbling" of the planet trajectory is very small compared with the "wobbling" of its moon. If the two masses are comparable, as is the case in the Pluto-Charon system, the common center of mass is outside the planet and the "wobbling" of the two trajectories are comparable.

Note that the common center of mass of the Pluto-Charon system is indeed outside Pluto, as you can see from the first picture in the question, which was taken in the reference frame of the common center of mass. Note also that Pluto and Charon have a rotational motion (spin) around their own rotational axis.

Further Edit: I just found a short review of the relative motion of planets and moons can be found in the Wikipedia article Barycenter. The figures in particular are very clear and self-explanatory.

• If you downvoted this you really should give a reason for it. It's not off-topic and it's not wrong. If it didn't answer the question as well as you believe it should have, then your comment might prompt a more complete answer. – Bill N Jul 25 '15 at 2:46
• Not my downvote either, but I believe the notable thing about the common center of mass in the pluto-charon system is that it is not within either body. – Warren Dew Jul 25 '15 at 3:38
• @WarrenDew And so? The center of mass is a mathematical point and has no effect whether inside or outside a mass. example : a bomb in a rocket in space; before explosion the center of mass is within the body of the bomb. After explosion it will be in air, but still its newtonian trajectory will still be describing part of the motion of the fragments of the bomb – anna v Jul 25 '15 at 5:35
• Not my downvote either, but this answer is incorrect. – David Hammen Jul 25 '15 at 5:54
• @DavidHammen why is it incorrect? Please write what you consider the correct answer. – anna v Jul 25 '15 at 13:24