Is there any heavy enough gas that could be used to make an artificial atmosphere around Ceres without it escaping into space?
Asked
Active
Viewed 764 times
3
-
3What research have you done? For example what is the surface temperature and escape velocity of Ceres, what elements or compounds are gaseous at that temperature, what atmosphere does Ceres already have? – Apr 27 '15 at 11:30
1 Answers
11
Jeans escape is one of the principal mechanisms via which planets and moons loses their lighter atmospheric gases. Jeans escape would be a viable escape mechanism even for xenon on Ceres.
Molecules of gas have a random velocity described by the Maxwell distribution. The most probable velocity is a function of temperature and atomic weight: $v_p = \sqrt{2kT/m}$. Escape velocity is independent of mass. The velocity distribution of a component of a celestial object's atmosphere needs to be well below escape velocity in order for a celestial object to hold on to that component of the atmosphere.
I'll assume a modest atmosphere on Ceres of some high molecular mass gas. The Earth's exobase is about 600 km. I'll assume a much smaller value of 20 km for Ceres. The temperature in the Earth's atmosphere is complex. It drops linearly in the troposphere, rises in the stratosphere, falls again in the mesosphere, and rises in the thermosphere. It's the temperature at the top of the thermosphere that drives thermal escape. In the Earth's atmosphere, this can be well over 1000 kelvin. Ceres is further from the Sun; I'll assume a smaller value of 400 kelvin.
Escape velocity from an altitude of 20 km on Ceres is about 500 m/s. The most probable velocity of xenon at 400 kelvin is about 225 m/s. This is far too large. The Maxwell distribution has a long tail. The loss rate is proportional to $v_\text{p} (\lambda+1) e^{-\lambda}$, where $\lambda = {v_\text{esc}}^2/{v_\text{p}}^2$. In the case of xenon at 400 kelvin and an escape velocity of 500 m/s, $\lambda$ is about 5. (Compare to helium escaping from the Earth's atmosphere, where $\lambda$ is almost 14.) Ceres wouldn't be able to hold on to a xenon atmosphere. It would escape thermally.
What about a complex molecule whose molecular mass is greater than that of xenon? There are two problems here. One is that Ceres is rather cold. Most large complex molecules aren't gases at 168 to 235 kelvin, Ceres' surface temperature. Uranium hexafluoride (molecular weight = 352) would be a nice candidate if Ceres was hot. Sulfur hexafluoride is close with a triple point of 223.5 kelvin at 2.3 bar, but its molecular mass of 146 is only slightly larger than that of xenon. Another problem is that the high energy radiation from the Sun would dissociate those complex molecules, and then it's game over because the products have smaller molecular masses and hence higher thermal velocities.
Nathan Tuggy
- 4,566
- 5
- 34
- 44
David Hammen
- 74,662
- 5
- 185
- 283
-
-
This is nice, but you're not considering temperature change with increased pressure and thermal absorption of various gases. – TildalWave Apr 27 '15 at 11:53
-
@TildalWave - One common attribute of celestial objects with an atmosphere is that they have a thermosphere. It's the temperature at the top of the thermosphere that drives thermal escape. I assumed 400 kelvin. A value of 200 kelvin seems non-physical to me, but even with that low of a temperature, $\lambda$ is still around 10 for xenon, which is too low. Ceres couldn't hold on to a xenon atmosphere, at least not for long. – David Hammen Apr 27 '15 at 11:57
-
-
What about higher molecular compounds (like polymerized perfluorocarbons) at further away celestial bodies (such as, say Rhea) so that they not to dissociate? – Anixx Apr 27 '15 at 12:29
-
Can the atmosphere be sustainable at lower pressure, say, 0.01 bar so that more heavy compounds were at gaseous state? – Anixx Apr 27 '15 at 12:40
-
@Anixx - 400 kelvin was a number I plucked out of the clear blue sky. Maybe it will be 500 kelvin, maybe 300. Every solid celestial object with more than a trace of an atmosphere has an exobase (thermopause) temperature higher than that of the surface, so it's certainly not 200 kelvin - and that's still too hot for even a very massive molecule in Ceres' weak gravity field. – David Hammen Apr 27 '15 at 14:05
-
@Anixx - Regarding polymerized perfluorocarbons, those aren't gases at standard temperature and pressure. The partial pressure at 200 kelvin would be ridiculously low. How low? You should do a bit of research on your own before you ask questions here. Hexafluoroethane has a nice low triple point, but its molecular mass is 138, about the same as that of xenon. So no help here. I suspect you're asking about perfluorocarbons because of your now deleted terraforming tag. The ability to hold onto a very massive gas won't help. Oxygen and lighter components will escape very quickly. – David Hammen Apr 27 '15 at 14:11
-
Does the termosphere temperature really affects how the atmosphere can escape, I mean significantly affects? – Anixx Apr 27 '15 at 14:14
-
@Annix - The temperature and escape velocity at the exobase (basically, top of the atmosphere) are what drive thermal escape. The temperature at the surface or top of the troposphere is irrelevant. – David Hammen Apr 27 '15 at 14:16
-
My own calculations mixing empirical curve fit and physical theory shows that it might hold onto a gas with a molar mass of 877 for 100,000,000 years. However, it can't hold onto anything we normally think of as a gas in an atmosphere. Too little mass, too weak gravity. Of the non-planets, only Titan, Triton, and Ganymede stand much of a chance of holding onto gases we think of as an atmosphere. Only Titan does it very well. – Jim2B Apr 30 '15 at 04:10
-
Putting it another way, every body that can retain an atmosphere has retained an atmosphere. FWIW, none of those bodies can retain water. Even Mars is too light to retain water, it'd have to be about 3x more massive to do that. Venus could retain water against Jeans Escape but loses it to other gas loss mechanisms. – Jim2B Apr 30 '15 at 04:17