Martian Atmosphere: The Numbers

[peadar1987]

Another Mars thread!

Every time discussion of terraforming Mars comes up, I end up posting pretty much the same thing, often multiple times in the same thread. I'm sticking this up here so it's easily findable and linkable.

First off, a few bits of info about Mars:

-It has 28% of the surface area of earth

-It has 37.6% of the surface gravity of earth

Earth's atmosphere has a mass of about 5.15*10¹⁸kg.

Atmospheric pressure is determined by the weight of the air column above you, so to have the same pressure on Mars as on earth takes a column 2.66 times the mass, due to the lower gravity. Assuming the height of the atmosphere is small in comparison to the radius of the planet, the mass of the atmosphere will then scale with the surface area.

If Mars is to have an atmosphere as thick as earth's, it needs a column of gas 2.66 times as heavy as earth's, spread over 28% of the surface area, so 74.5% the mass of earth's atmosphere (3.83*10¹⁵kg).

If you are going to walk on the surface of Mars without a pressure suit, the pressure must be above the Armstrong Limit, which is about 6.25% the atmospheric pressure of earth, and is the point below which water will begin to boil at human body temperature. That needs an atmosphere with a mass of 4.66% that of earth's atmosphere (2.4*10¹⁴kg).

So, whatever you want from a Martian atmosphere, you're going to need a LOT of mass. Where can we get it from?

One place that has been suggested is the polar ice caps. It is estimated that together they contain 4.1 million km³ of frozen CO₂, which has a density of about 1.5kg/m³. That gives you a mass of 1.5*4,100,000*1000*1000, or 6.15*10¹²kg. That's only about 2.5% of what we need even to get to the Armstrong limit. Looks like we're going to have to look off-world for that mass.

So let's assume we want to bring the pressure of Mars up to the Armstrong limit within 200 years. That requires redirecting 2.34*10¹⁴kg of material. To give that mass an acceleration of 10m/s over that time period would require a constant power input of 3.7MW. 100m/s would require 371MW.

People often talk about moving Venus' atmosphere to Mars using a mass driver. A Venus to Mars transfer costs about 4km/s. Add maybe 8km/s to Venus orbit, ignoring atmospheric losses, and you get 12km/s, which gives us a power over 200 years of 5.34TW. Venus has an insolation of about 2kW/m², so you'd need about 2.7*10¹⁰ m² of 10% efficient solar panels to power your mass drivers (plus massive storage, as you would only be able to fire during transfer windows). That's 26,700 km², or a square 163km. We're talking cloud cities and beamed power from orbital stations on a monstrous scale here. Not practical.

The best bet is probably to move frozen material from the outer solar system using the Interplanetary Transport Network. If you don't mind your mass taking a long time to get to the inner solar system, a 100m/s nudge should be enough to move a Neptune or Uranus trojan from L4 or L5 into a position where it can be redirected into the inner solar system using gravity assists. That just leaves the far-from-trivial problem of delivering 400MW to outer solar system bodies over a period of 200 years, then precisely guiding the mass you throw into the inner solar system so it gets all of the right gravity assists and hits Mars. We're going to probably need large-scale nuclear fusion before this becomes even remotely a possibility.

So we've established that giving Mars an atmosphere, even one just barely thick enough that our eyeballs don't boil away, is going to be incredibly difficult. Let's assume that we can give Mars an atmosphere though. How quickly is it going to escape into space? 

This is the best source I have been able to find for Jeans' Escape, or the thermal escape of gas into space. It gives most parameters needed to calculate the flux, but not enough information about the exobase, or the altitude at which molecules at escape velocity are likely to be able to leave the atmosphere without hitting another particle.

This is where I quickly start to get out of my depth. My gut feeling says that Mars could hold on to a thick atmosphere for millions of years, but I don't think we know enough about the exosphere of Mars, in particular a Mars with a hypothetical 0.06 bar atmosphere, to accurately determine all the parameters required to calculate the flux of atmospheric gases to space.

Anyway, I'll leave this up here in case anybody is feeling particularly mathematical today!

[Findthepin1]

Mars' solid CO2 storage is much larger than that. By the more extreme estimates it can get you between 0.1 atm (extreme low) and 1 atm (extreme maximum). By my own estimate it's more like 0.1-0.2 atm. The issue now is that the atmosphere is all CO2. If we convert that to oxygen using plants, then it's oxygen. Done. 0.1 atm of oxygen is fine, there are people who live at 0.5 atm where the partial pressure of oxygen is 0.1 atm. 

[peadar1987]

27 minutes ago, Findthepin1 said:

Mars' solid CO2 storage is much larger than that. By the more extreme estimates it can get you between 0.1 atm (extreme low) and 1 atm (extreme maximum). By my own estimate it's more like 0.1-0.2 atm. The issue now is that the atmosphere is all CO2. If we convert that to oxygen using plants, then it's oxygen. Done. 0.1 atm of oxygen is fine, there are people who live at 0.5 atm where the partial pressure of oxygen is 0.1 atm. 

Yup, but how much of it is readily accessible, and how much is geologically bound?

In any case, you're not going to be able to convert 100% of it into oxygen anyway. 1/3 of the mass is carbon, so your plants will just fix that, leaving you with just over 2/3 of the mass of CO₂ as oxygen. You're also going to need huge amounts of water, as photosynthesis uses an equal number of moles of water and CO_2.

The relevant equation is: CO₂+H₂O -> Carbohydrate + O₂. So you're still going to have to bring in all that mass from off-world.

Edited March 10, 2016 by peadar1987

[SargeRho]

Mars has a lot of frozen water, though. So, once it's warm enough, there'll be plenty of water to go around.

That's no argument against crashin' some comets though

[AngelLestat]

what matters most is the amount of co2 you need, which as you said, is not enough (this was knew in recent years when they discover that mars had several times lower frozen co2 of what they originally thought).
So you need to drop comets to rise the dust similar to Kim Stanley Mars trilogy with many other strategies.

The time that this atmosphere can stand (I read about 10000 years instead millions), but it does not matter, because in just 500 years the level of energy that a civilization can achieve is a lot (without even counting by exponential technology growth).

But from our point of view (if technology stays forever with our current level), terraform any planet is beyond our reach, it would be much cheaper to fill the mars surface of domes than terraform the planet.

[KerikBalm]

1 hour ago, SargeRho said:

Mars has a lot of frozen water, though. So, once it's warm enough, there'll be plenty of water to go around.

That's no argument against crashin' some comets though

While there are substantial amounts of water, the Deuterium to hydrogen ratio also shows it has lots *a lot* of water you won't get the oceans it once had just by raising the temperature and pressure, then you have to worry about water soaking down into underground aquifers, binding to other chemicals and forming hydrates, etc. Its not so easy.

A lot of the water was lost, but the moleclar oxygen remains while the hydrogen is gone. So now there's all this excess oxygen that has literally rusted the planet... the wors are those perchlorates.

Without a magnetic field, when the water was split by UV light, that Hydrogen escaped. If I recall correctly, the latest studies have show n the atmospheric loss occurred faster than expected, because the solar wind was causing loss in unexpected ways. It should still lasts for thousands of years though, if you get it back.

Plants will also need nitrogen

2 hours ago, Findthepin1 said:

Mars' solid CO2 storage is much larger than that. By the more extreme estimates it can get you between 0.1 atm (extreme low) and 1 atm (extreme maximum). By my own estimate it's more like 0.1-0.2 atm. The issue now is that the atmosphere is all CO2. If we convert that to oxygen using plants, then it's oxygen. Done. 0.1 atm of oxygen is fine, there are people who live at 0.5 atm where the partial pressure of oxygen is 0.1 atm. 

Citations? what do you base your estimate on, you just like that number?

 

5 hours ago, peadar1987 said:

If Mars is to have an atmosphere as thick as earth's, it needs a column of gas 2.66 times as heavy as earth's

You mean 2.66 times as massive, but I think you understood that on the basis of other things you said in your post

[fredinno]

11 hours ago, peadar1987 said:

Another Mars thread!

Every time discussion of terraforming Mars comes up, I end up posting pretty much the same thing, often multiple times in the same thread. I'm sticking this up here so it's easily findable and linkable.

First off, a few bits of info about Mars:

-It has 28% of the surface area of earth

-It has 37.6% of the surface gravity of earth

Earth's atmosphere has a mass of about 5.15*10¹⁸kg.

Atmospheric pressure is determined by the weight of the air column above you, so to have the same pressure on Mars as on earth takes a column 2.66 times the mass, due to the lower gravity. Assuming the height of the atmosphere is small in comparison to the radius of the planet, the mass of the atmosphere will then scale with the surface area.

If Mars is to have an atmosphere as thick as earth's, it needs a column of gas 2.66 times as heavy as earth's, spread over 28% of the surface area, so 74.5% the mass of earth's atmosphere (3.83*10¹⁵kg).

If you are going to walk on the surface of Mars without a pressure suit, the pressure must be above the Armstrong Limit, which is about 6.25% the atmospheric pressure of earth, and is the point below which water will begin to boil at human body temperature. That needs an atmosphere with a mass of 4.66% that of earth's atmosphere (2.4*10¹⁴kg).

So, whatever you want from a Martian atmosphere, you're going to need a LOT of mass. Where can we get it from?

One place that has been suggested is the polar ice caps. It is estimated that together they contain 4.1 million km³ of frozen CO₂, which has a density of about 1.5kg/m³. That gives you a mass of 1.5*4,100,000*1000*1000, or 6.15*10¹²kg. That's only about 2.5% of what we need even to get to the Armstrong limit. Looks like we're going to have to look off-world for that mass.

So let's assume we want to bring the pressure of Mars up to the Armstrong limit within 200 years. That requires redirecting 2.34*10¹⁴kg of material. To give that mass an acceleration of 10m/s over that time period would require a constant power input of 3.7MW. 100m/s would require 371MW.

People often talk about moving Venus' atmosphere to Mars using a mass driver. A Venus to Mars transfer costs about 4km/s. Add maybe 8km/s to Venus orbit, ignoring atmospheric losses, and you get 12km/s, which gives us a power over 200 years of 5.34TW. Venus has an insolation of about 2kW/m², so you'd need about 2.7*10¹⁰ m² of 10% efficient solar panels to power your mass drivers (plus massive storage, as you would only be able to fire during transfer windows). That's 26,700 km², or a square 163km. We're talking cloud cities and beamed power from orbital stations on a monstrous scale here. Not practical.

The best bet is probably to move frozen material from the outer solar system using the Interplanetary Transport Network. If you don't mind your mass taking a long time to get to the inner solar system, a 100m/s nudge should be enough to move a Neptune or Uranus trojan from L4 or L5 into a position where it can be redirected into the inner solar system using gravity assists. That just leaves the far-from-trivial problem of delivering 400MW to outer solar system bodies over a period of 200 years, then precisely guiding the mass you throw into the inner solar system so it gets all of the right gravity assists and hits Mars. We're going to probably need large-scale nuclear fusion before this becomes even remotely a possibility.

So we've established that giving Mars an atmosphere, even one just barely thick enough that our eyeballs don't boil away, is going to be incredibly difficult. Let's assume that we can give Mars an atmosphere though. How quickly is it going to escape into space? 

This is the best source I have been able to find for Jeans' Escape, or the thermal escape of gas into space. It gives most parameters needed to calculate the flux, but not enough information about the exobase, or the altitude at which molecules at escape velocity are likely to be able to leave the atmosphere without hitting another particle.

This is where I quickly start to get out of my depth. My gut feeling says that Mars could hold on to a thick atmosphere for millions of years, but I don't think we know enough about the exosphere of Mars, in particular a Mars with a hypothetical 0.06 bar atmosphere, to accurately determine all the parameters required to calculate the flux of atmospheric gases to space.

Anyway, I'll leave this up here in case anybody is feeling particularly mathematical today!

Mars can remain habitable w/o a magnetosphere, assuming it is terraformed, for max. 100 million years. Sounds bad, until you consider Earth will become uninhabitable in 500 million years.

 

7 hours ago, SargeRho said:

Mars has a lot of frozen water, though. So, once it's warm enough, there'll be plenty of water to go around.

That's no argument against crashin' some comets though

Not enough tho.

[KerikBalm]

"habitable" for 100 million years only in the loose sense of the word.

Earth will likely be uninhabitable for humans in 500 million years, but not because of atmospheric pressure. I suspect any martian biosphere would have major extinction events and challenges to habitability long before enough atmosphere has escaped to drop below the armstrong limit.