Pluto's Expanding Atmosphere Confounds Researchers, Pluto Atomosphere Options

[Drkskywxlt]

would the region of greatest gas escape tend to concentrate around the anti-Charon point?

Hmmm...not sure the answer to that. Charon is about 12 Pluto radii away. All of the literature that I've seen regarding models/simulations of hydrodynamic escape of Pluto's atmosphere have ignored contributions from Charon's gravity. Remember the r^2 law...even if gas is escaping at several Pluto radii above the surface, the gravitational influence from Pluto is still going to be dramatically larger than that of Charon.

With such a huge scale height to the atmosphere, centripetal acceleration (due to Pluto's motion around the system's barycentre) might be just enough to give gas molecules the heave-ho on the anti-Charon side.

Again I haven't seen any discussion of this in the literature. Pluto's rotation rate is quite slow so I don't think this would add appreciable energy. The energy that really drives this process is heating by solar EUV and UV. That's a much bigger energy source than centripetal acceleration.

[Paolo]

I get L1 for Pluto lying around 5050km from the centre of Charon, 14520km from the centre of Pluto.

Thank you for the quick computation. I am wondering whether a Roche lobe-like mass transfer between the atmosphere of Pluto and Charon is possible
http://en.wikipedia.org/wiki/Roche_lobe

[brellis]

I'm confused. Does the L1 point of the Pluto system actually orbit Pluto along with Charon?

[nprev]

Yes, it does; just like the Earth-Moon Lagrange points.

[Rob Pinnegar]

Again I haven't seen any discussion of this in the literature. Pluto's rotation rate is quite slow so I don't think this would add appreciable energy. The energy that really drives this process is heating by solar EUV and UV. That's a much bigger energy source than centripetal acceleration.

That's probably true. I just did a back-of-the-envelope calculation to that effect (literally... it actually *was* on the back of an envelope).

Pluto's orbital speed around the system barycentre turns out to be only about 23 metres per second (a bit slower than normal highway driving speed). The centripetal acceleration from that amounts to around 2-3 cm/s^2. This is quite a bit less than Pluto's surface gravity, which is about 66 cm/s^2.

Of course, at really high altitudes the gravity would be a bit lower. Also, I've based my centripetal-acceleration calculation on the distance from the system barycentre to Pluto's centre... so that effect would be a tiny bit larger as well at high altitudes. But either way, we're talking a difference of a few percent.

I don't know enough about this topic to say whether a difference of a few percent would translate into a measurable difference in gas escape.

[Greg Hullender]

I get L1 for Pluto lying around 5050km from the centre of Charon

I get 5210 km from Charon. Wonder where the discrepancy comes from?

--Greg

[Paolo]

Wonder where the discrepancy comes from?

that's not really important. the point to me is that Pluto's swollen atmosphere fills a sizeable portion of its Roche lobe, making Mass transfer to Charon possible

[Alan Stern]

that's not really important. the point to me is that Pluto's swollen atmosphere fills a sizable portion of its Roche lobe, making Mass transfer to Charon possible

Paolo,

You might be interested to know that papers about mass transfer to Charon over Pluto's Roche lobe go back to the early 1980s, and this point was emphasized numerous times to review committees during the 90s era when a Pluto mission was being sold within the planetary mission advisory structure.

-Alan

[Paolo]

thanks Alan. I know I will spend a large part of the weekend searching for papers on that on the ADS service

[AndyG]

I get 5210 km from Charon. Wonder where the discrepancy comes from?

The options seem to be:

1/ Listed masses for Charon and Pluto
2/ Excel
3/ My maths

I err towards 3/ in this instance - but whats a hundred miles between results? ;-)

Hmmm.

Andy

[Greg Hullender]

So Andy and I worked through this offline, and we now get the same result through different means, so I'm pretty confident this is correct.

The first step is to get the best numbers possible for the masses of Pluto and Charon and for the distance between them. It turns out there's some recent work using the orbits of Nix and Hydra to do exactly that: http://iopscience.iop.org/1538-3881/132/1/...1_132_1_290.pdf

Pluto: 1.28726E+22 kg
Charon: 1.69741E+21 kg
center-to-center Distance: 1.9571E+07 m

My results are:

Charon-center to L1: 5.9716E+06 m
Charon-center to L2: 7.4611E+06 m

Andy's numbers differ from mine by just a few hundred meters now. In this case, his math and Excel were correct from the start; I was the one with the math error.

In case anyone's interested, here's how to compute it: let m be the mass of the smaller body divided by the mass of the larger one and let h be the distance from the center of the smaller body to the L1 point as a fraction of the distance from the smaller body to to larger one. Then

(1+m)*h^5 - (3+2*m)*h^4 + (3+m)*h^3 - m*h^2 + 2*m*h - m = 0

There are a variety of ways to find h given m. (I used Newton's method, but you can brute force it too.)

For L2, the only change is that the quartic and linear terms change sign, like so:

(1+m)*h^5 + (3+2*m)*h^4 + (3+m)*h^3 - m*h^2 - 2*m*h - m = 0

I hunted and hunted to find something that laid it out like this, but everything seemed focused on the harder problem of finding L4 and L5 and proving their stability.

--Greg

[AndyG]

Never too keen on terms to the fifth power, and always keen to ditch "G" my route was:

Masses:
Pluto = Ma
Charon = Mb
Both = Mt

Distances:
Pluto - Charon = R
Pluto - Barycentre = Ra = R*Mb/Mt
Charon - Barycentre = Rb = R*Ma/Mt
Barycentre to L1 point = X

X needs solving in the L1 equation:

Mb/(Rb-X)^2 + Mt*X/R^3 - Ma/(Ra+X)^2 = 0

The three terms here are the force of Charon plus the centripetal force at L1, minus the force of Pluto. The easiest way to solve this (for me) was to parametrically define X and iterate towards "= 0" in Excel.

Andy

[Greg Hullender]

Grin. Terms in the denominator are just as bad as 5th-order terms, depending on what you're trying to do. I was also surprised that eventually G dropped out. In fact, everything dropped out except the masses of the two bodies and the distance between them. Pretty cool.

I'm surprised there isn't more interest in UMSF about the mathematics of space travel. It was nice to find someone else who wants to compute these things for himself.

--Greg

[tasp]

My thanks to the folks who can do the math. I am interested in the number crunching, I just don't have the ability. Heck, I effed accounting, and all that is addition and subtraction . . .

[algorimancer]

It was studying the mathematics of space travel that led me to studying mathematics in college, then careers in teaching and programming and research. Haven't done much with orbital mechanics since high school (barring a bit writing software for nasa), but it was what set me on my way. Still doing plenty of math, though -- lately, mostly in statistics. Serendipity