Power output needed to "blow off the atmosphere"

[Kane Starkiller]

OK we know of an incident in which 3 Star Destroyers have blown off the atmosphere of a planet namely Dankayo.
The method I thought of using is the Stefan-Boltzman law in search for the lower power limit turbolasers would have to impart into the atmosphere to exceed the rate it's shedding the heat in the form of blackbody radiation.
I don't think there is any information about the exact size of Dankayo so I'll use Mars and Earth as benchmarks.

Now Mars's atmosphere consists of 95% carbon dioxide and it's escape velocity is 5027m/s. I'll now assume that carbon and oxygen atoms start out separated to simplify the calculation and be conservative at the same time since the individual particles will be less massive. Mass of an oxygen atom is 2.67*10^-26kg while mass of a carbon atom is 2*10^-26kg. Average mass of CO2 will therefore be 2.44*10^-26kg. In order to blow off the atmosphere you need to give it escape velocity which means the energy of each particle should be at least 3*10^-19J. The connection between the energy of a particle and temperature is given by the formula E=3/2*k*T. Therefore the temperature of atmosphere should be 14,500K. At that temperature Mars's atmosphere should radiate 3.58*10^23W. If the attacking vessels wish to blow off the atmosphere they need to impart at least that much power merely to keep the atmosphere from cooling down. Among 3 Star Destroyers that is about 10^23W for each ship or 24,000 gigatons per second.

Using Earth as benchmark with it's mostly Nitrogen atmosphere, 11.2km/s escape velocity and 12,756km diameter we arrive at 7*10^26W or 2.3*10^26W for each Star Destroyer.


Now thermodynamics is not my area of expertise so I am certainly open to corrections and outright ridicule if need be.

[Howedar]

You demonstrate a fundamental lack of understanding of gas dynamics. The relevant characteristic of a gas is that a volume of gas can have considerable particular kinetic energy without having significant overall velocity. Thus it is not necessarily reasonable to look at heating as a direct mode of imparting escape velocity. There are many more factors that must be analyzed.

I stopped reading after that, but you are suggesting a necessary power to perform an event which requires a necessary amount of energy. Just looking at your end units, I'm not likely to put much credence in your calculations.

Not to mention that the atmosphere doesn't need to reach escape velocity in order for it to have been "blown off". Putting all of that gas into, for example, a high circular orbit could be considered to accomplish that feat.

And, of course, if you did want to find out the amount of energy needed to put all that gas into an escape hyperbola, that's pretty easy. KE=.5*m*v^2, and the velocity for an escape hyperbola is simply sqrt(-GM/a), with a being the semimajor axis of your hyperbola (characteristically negative).

[Vympel]

Not to mention that the atmosphere doesn't need to reach escape velocity in order for it to have been "blown off". Putting all of that gas into, for example, a high circular orbit could be considered to accomplish that feat.

Well, he is referring to Dankayo, and the context of the passage makes it pretty clear the atmosphere was gone- i.e. "as the last [of the atmosphere] drifted away" IIRC.

[Kane Starkiller]

I don't think you realize what I'm trying to calculate. Yes obviously calculating the total energy is relatively easy. All we need is the mass of atmosphere and velocity BUT what I'm trying to find is the time interval needed to impart that energy. Bombarding the atmosphere with say 1Mt/s for 1000 years won't cut it since the atmosphere will have time to shed the excess energy. And the more energetic the atmosphere gets the more quickly it will shed the excess energy requiring greater power output of the turbolasers.

You demonstrate a fundamental lack of understanding of gas dynamics. The relevant characteristic of a gas is that a volume of gas can have considerable particular kinetic energy without having significant overall velocity.

Yes because of external pressure and weight of the atmosphere. But when the atmosphere becomes energized enough to overcome the gravitational force it will shoot out into space.

Thus it is not necessarily reasonable to look at heating as a direct mode of imparting escape velocity. There are many more factors that must be analyzed.

Well obviously the turbolaser will strike the surface vaporizing a chunk of it and the resulting expansion of superheated plasma will take the atmosphere with it. But then the particles of surface material will need to have sufficient temperature to blow themselves and the atmosphere into space which can only increase the energy and power requirement.

Not to mention that the atmosphere doesn't need to reach escape velocity in order for it to have been "blown off". Putting all of that gas into, for example, a high circular orbit could be considered to accomplish that feat.
And, of course, if you did want to find out the amount of energy needed to put all that gas into an escape hyperbola, that's pretty easy. KE=.5*m*v^2, and the velocity for an escape hyperbola is simply sqrt(-GM/a), with a being the semimajor axis of your hyperbola (characteristically negative).

The relative velocity between atmopshere and ground is zero so atmosphere should have to be blown to geostationary orbit which is 42,000km which requires energy of 8.2MJ/kg. Individual carbon atom would thus need to have a velocity of 4km/s. This decreases the energy but not by more than an order of magnitude.

[Howedar]

Yep, you're right, I glossed over the first paragraph. Apologies.

[Ender]

Why are you using Mars instead of Earth? Trying to generate a lower limit, as it has a far lower escape velocity (earth's is 11.6 km/s)

[Kane Starkiller]

Why are you using Mars instead of Earth? Trying to generate a lower limit, as it has a far lower escape velocity (earth's is 11.6 km/s)

I had a discussion with Mike DiCenso recently who whined that we should use Mars instead of Earth. So I thought I'd use it myself. But I did provide calculations for Earth which I naturally think is a more appropriate benchmark.

[Ender]

Why are you using Mars instead of Earth? Trying to generate a lower limit, as it has a far lower escape velocity (earth's is 11.6 km/s)

I had a discussion with Mike DiCenso recently who whined that we should use Mars instead of Earth. So I thought I'd use it myself. But I did provide calculations for Earth which I naturally think is a more appropriate benchmark.

Why the fuck did he think we should use an uninhabitable planet to model an inhabitable one?

[Darth Wong]

Why are you using Mars instead of Earth? Trying to generate a lower limit, as it has a far lower escape velocity (earth's is 11.6 km/s)

I had a discussion with Mike DiCenso recently who whined that we should use Mars instead of Earth. So I thought I'd use it myself. But I did provide calculations for Earth which I naturally think is a more appropriate benchmark.

Why the fuck did he think we should use an uninhabitable planet to model an inhabitable one?

DiCenso is the last of the old-school Trektards. He's like Anton Polinger and all of those other names that are mostly long-forgotten. He's one of those people that got comfortable playing in a little Trekkie sandbox in the early 1990s, where a bunch of kiddies with the scientific aptitude of spam all sat around showing their technobabble weenies to each other, and he never really adjusted to the new reality when some people with real backgrounds waded into the fray. Apart from losing one's mind a la RSA, there were only two options at that point:

1) Accept that the cherished beliefs of most early 1990s Trek vs Wars people were just plain wrong, and either move on or retrench to a more reasonable position. Most of the smarter Trekkies did this.

2) Avoid direct conflict with the heavy hitters, and try to create new sandboxes elsewhere on the Internet in order to reproduce that nostalgic old-time early 1990s feeling.

[Kane Starkiller]

I should say, however, that the numbers I calculated above are based on roughly uniform heating of atmosphere which may not be the case. Theoretically a ship could continually blast a single point on the ground and cause the atmosphere to drift away at that point thus slowly depleting it.
However it is obvious that primary objective of a BDZ is uniformly melting/vaporizing the surface and blowing off the atmosphere is a side effect which, I believe, brings the model close to uniform atmosphere heating.

[Lost Soal]

Why are you using Mars instead of Earth? Trying to generate a lower limit, as it has a far lower escape velocity (earth's is 11.6 km/s)

I had a discussion with Mike DiCenso recently who whined that we should use Mars instead of Earth. So I thought I'd use it myself. But I did provide calculations for Earth which I naturally think is a more appropriate benchmark.

Why the fuck did he think we should use an uninhabitable planet to model an inhabitable one?

Isn't Mars uninhabitable mainly due to location rather than its size?

[Ender]

I had a discussion with Mike DiCenso recently who whined that we should use Mars instead of Earth. So I thought I'd use it myself. But I did provide calculations for Earth which I naturally think is a more appropriate benchmark.

Why the fuck did he think we should use an uninhabitable planet to model an inhabitable one?

Isn't Mars uninhabitable mainly due to location rather than its size?

Its a combination as I understand it - its location puts it in a position where its low magnetic field and low gravity let it be battered so badly it is unihabitable. A more massive planet witha more active core would have weathered the eons better. But you should probably ask someone in SL&M.