COMET “AERODYNAMICS”
With the recent visit from Comet NEOWISE I thought it would be fun to dive into the fascinating world of fluid dynamics relating to comets. Beware: some of these concepts are REALLY weird but I certainly enjoyed researching the topic. Here we go…(a thread)
With the recent visit from Comet NEOWISE I thought it would be fun to dive into the fascinating world of fluid dynamics relating to comets. Beware: some of these concepts are REALLY weird but I certainly enjoyed researching the topic. Here we go…(a thread)
DISCLAIMERS: I researched this post & while I study high-speed aero (including gas dynamics and some statistical mechanics), I don’t specialize in rarefied interplanetary flows.
Also, we’re dealing with some ridiculous numbers approximated to many orders of magnitude in spots.
Also, we’re dealing with some ridiculous numbers approximated to many orders of magnitude in spots.
First, what is a comet?
These are “cosmic snowballs” (HT to @NASA for that one), composed mostly of rock, dust, ice, frozen CO2, and a mix of other things. They orbit the sun in highly eccentric (long) elliptical orbits and range from < 1 km to 10s of km in diameter.
These are “cosmic snowballs” (HT to @NASA for that one), composed mostly of rock, dust, ice, frozen CO2, and a mix of other things. They orbit the sun in highly eccentric (long) elliptical orbits and range from < 1 km to 10s of km in diameter.
We only really see comets when they approach the sun, as they get hot enough to begin releasing gas & dust in a long tail. Comets don’t melt—they actually sublimate, meaning that solid ice turns directly into gas, skipping the liquid phase. (Image is CO2 sublimation [Britannica])
A quick aside: water-ice in your freezer sublimates. Take a cube of ice and put it on your freezer shelf--it will slowly sublimate water vapor. The cube will shrink & eventually will be gone (takes weeks or longer depending on your freezer). Riveting, edge of your seat excitement
When we can see a comet like NEOWISE there are a few distinct features to note.
1) Nucleus: solid, icy core of the comet
2) Coma: a cloud (basically an atmosphere) around the comet formed by the gas products
3) Tail: the trail of gas & dust particles left behind the comet’s wake
1) Nucleus: solid, icy core of the comet
2) Coma: a cloud (basically an atmosphere) around the comet formed by the gas products
3) Tail: the trail of gas & dust particles left behind the comet’s wake
A factoid about the coma that blew me away is that this feature can grow to be larger than the diameter of the Sun (> 1M km). Similarly mind-blowing: the tail can extend to distances longer than 1 AU (the distance between the Earth and the Sun or 150M km)
The tail has two components: the dust tail & ion tail. The dust tail follows a path somewhat aligned w the comet’s orbit. Small dust particles (~10s of um) are pushed away from the Sun by radiation pressure & larger chunks follow the orbital path more closely, giving curvature
The ion tail is made of gas particles strongly impacted by the solar wind & points away from the sun. While the dust tail looks white since the particles are in the Mie scattering regime & reflect sunlight, the ion tail is BLUE as a result of CO+ absorption, fluorescing @ 420nm
There have been some particularly remarkable shots over the past month highlighting the two tails of Comet NEOWISE, like this one (white is dust tail, blue is ion tail):
So now that we’ve covered comets we can get into the “fluid dynamics” that were promised. The first thing to understand is that the interplanetary medium (the soup that our solar system sits in, comets “fly” through, and that most of us just refer to as “space”) is a bit weird…
This “soup” is actually plasma: composed of ionized particles (missing electrons) & a bunch of free electrons. It’s mostly ionized hydrogen & highly conductive among other things. + it's extremely hot (~100,000 K) & exceedingly *rarefied* meaning that there are not many particles
This rarefied point is critical, because it changes the manner of fluid dynamics analysis. At sea level in air there are ~30 billion BILLION molecules in 1 cubic cm (about the size of a single 6-sided die) but in the interstellar medium there are <100 molecules in that space!
This means molecules interact with one another in an entirely different way. A concept used to define this difference is called “mean free path” which is the average distance a molecule travels before colliding with another molecule, in a sort of molecular game of PLINKO.
At sea level this value is ~70 nm (1000x smaller than the width of a human hair), and since air molecules move on average ~400 m/s in standard atmosphere (900 mph) that means a molecule experiences BILLIONS of collisions each second.
Contrast w the interplanetary medium & the mean free path is on the order MILLIONS of km (or miles) w collisions potentially not happening for days! These molecules have no trouble social distancing (by molecular standards) & the implications for fluid mechanics are significant
In a typ fluids problem on Earth we make the simplifying assumption of “continuum” where we treat a fluid as a uniform body rather than worrying about discrete particles. This is a good approx. when the ratio of your mean free path to the flow scale is small (called Knudsen no.)
In the interstellar medium, unless fluid length scales ~size of the solar system, we can't assume continuum—requiring new equations & what's known as statistical mechanics. This is called “free molecular flow” & we need to account for indv. particles that travel in straight lines
The fluid dynamics NEAR comets are different as the coma is @ higher density so w/i <1000km of the surface continuum can be assumed & gas expands @ ~1km/s. This includes jets on the surface that eject gas. Everywhere else (including the tail) can be treated as free molecular flow
This might be too technical (or obvious?), but you can relate Knudsen #, Reynolds #, and Mach #, as Re ~ M/Kn. So low-Re laminar flow is more likely if you’re going slow (relative to sound speed) or if your length scales are small (relative to mean free path), and vice-versa.
Another interesting feature is the comet’s bow shock (similar to hypersonic vehicles). The comet is approaching the Sun at high velocities (10s of km/s). The vel. of particles in the tail is also O(10 km/s) but these numbers are << velocity of the solar wind which is ~400 km/s.
The definition of speed of sound isn’t quite the same in the interplanetary med. as what you may be used to for atmos. flows, given that it's a highly rarefied plasma. But it does exist & 400 km/s is supersonic, so you get a bow shock with stand-off distances larger than the coma
You don’t see this bow shock when you see a comet (nothing to visualize) & there is also a separate “inner shock” within the coma, where you likely have continuum flow and the sound speed and fluid mechanics are quite different (honestly more similar to what we are familiar with)
Last cool thing: you can actually see the tail of a comet “whipped” back and forth by fluctuations in the oncoming solar wind, as shown in this NASA animation shared in a great post by @fyfluiddynamics fyfluiddynamics.com/2013/12/fluid-…
Phew! Ok that was a lot, so congrats if you hung in this long! Feel free to jump in with questions/corrections.
Here are a few references where I got some content:
Comet structure and fluid mechanics: arc.aiaa.org/doi/pdf/10.251…
Coninuum/free molecular flow: sciencedirect.com/science/articl…
Here are a few references where I got some content:
Comet structure and fluid mechanics: arc.aiaa.org/doi/pdf/10.251…
Coninuum/free molecular flow: sciencedirect.com/science/articl…
Source: ESA esa.int/ESA_Multimedia…
Source: ESA blogs.esa.int/rosetta/files/…
Source: Berch et al. researchgate.net/publication/22…
Source: ESA blogs.esa.int/rosetta/2015/1…
Source: onlinereg.ru/school-nf-2015…
Source: pikist.com/free-photo-vch…
Source: spark.iop.org/collections/me…
Source: D Brewer researchgate.net/publication/23…
Image Credit & Copyright: Petr Horalek apod.nasa.gov/apod/ap200716.…
Source: Gerald Rhemann astronomynow.com/2020/07/17/don…
So I have been informed this is not the best figure. As explained by @nick_attree comets are composed of smaller pebbles and “the inside looks like the outside”. This is coming from someone who *actually studies comets* so I’m going to trust him!
Animation source: NASA svs.gsfc.nasa.gov/12900
Image Credit & Copyright: Zixuan Lin (Beijing Normal U.) apod.nasa.gov/apod/ap200722.…
