Atmosphere Parameters

The behavior of an atmosphere is very important for terraforming. There are a few formulas that can calculate if a planet is suitable to support an atmosphere and under what conditions.

You can determine average gas speed with the formula [1]:

Gs = 3*0.017077*(T(C)+273.15)/m

This formula is adapted by myself, to fit better. Gs is gas speed (in km/s), T(C) is temperature in Celsius degrees and m is the molecular mass of the gas (1 for hydrogen, 16 for atomic oxygen, 32 for molecular oxygen). By using it, you will get for oxygen at 31 C, the speed of 0.4869 km/s. Gs is the average speed of a gas molecule, but some will move faster and some far slower.

The second thing we need to consider is escape velocity, to see if the gas will escape or not the planet. The formula, adapted for our simulation and our measure units, is:

Ev = ((1601*mass)/diam)^0.5

Here, Ev is the escape velocity in km/s, mass is the planet's mass (Earth's mass = 1) and diam is the diameter, in thousands km.

By combining both formulas, we get the next value:

xxx = ((3*0.017077*(T(C)+273.15)/m))/(((1601*mass)/diam)^0.5)*100

The symbol xxx is again my invention, there is no such thing. This formula allows you to quickly see if a planet will be able to sustain an atmosphere or not. Here, T(C) is the temperature (in Celsius), m is gas molecular mass, mass is planet's mass (Earth = 1) and diam is planet's diameter in thousands km. The numbers you will get for Earth, at 15 C, are as follows:

Hydrogen: 131
Helium: 33
Nitrogen (molecular): 4.7
Oxygen (molecular): 4
Carbon dioxide: 3
Methane: 8

The bigger the number, the lower the chance for specified gas to remain in the atmosphere. If we compute the same data for Earth's moon, we get:

Hydrogen: 653
Oxygen (molecular): 20
Carbon dioxide: 15.

Basically, I would say that a gas is safe if the calculated value is less then 10. Also, if value is below 100, the gas can still remain in the atmosphere for a human lifetime.

Gerald Kuiper designed a planetary constant which he named k. This constant shows the probability for a celestial body to host an atmosphere (the probability that majority of molecules will not be in escape velocity). For him, if k had a higher value then 5, the planet or moon could host atmosphere. This way, he proved a long time ago that Titan has an atmosphere. His formulas are more complex, but more accurate.

Atmosphere Size[]

Small bodies have a weaker gravity. Their atmospheres will be really huge, extending perhaps hundreds of km. The following is what you need to write a Microsoft excel table, where you can simulate atmosphere parameters around any planet or moon:

Formulas are written in bold;
Non-formula text is written in plain;
Explanations are in italic.

A1: ATMOSPHERE SIMULATION
A2: Mass (Earth = 1):
C2: write planet's mass.
A3: Ks (Earth = 1):
C3: write the Solar Constant.
A4: Atmos. Mass:
C4: write the mass of the atmosphere (play with values and see what happens). For Earth = 1.
A5: Temp (local C):
C5: write planet's average temperature (as you want it to be once terraformed).
A6: Diam (/1000 km):
C6: write planet's diameter in thousands of km (Earth = 12.756).
E1: INFERRED PARAMETERS
E2: Temp (cosmic C):
G2: =(379.3*(C3^(1/4)))*0.759689-273.15 this is planet's equilibrium temperature.
E3: Surface gravity:
G3: =C2/((C6/12.756)^2) planet's gravity, Earth = 1.
E4: Mass/surface:
G4: =C4/((C6/12.756)^2) the amount of gas mass per square unit, for Earth = 1; this is the value for atmospheric density you will need to write for Climate simulations.
E5: Surface pressure:
G5: =C4/G6 this is the pressure one would feel on the surface of the planet.
E6: Atm vol (Earth=1):
G6: =(E13/10)*(C6^3)*0.000203587 total volume of gas.
A8: Parameter:
C8: Cosmic: on this column you will get the atmospheric properties if no greenhouse gasses exist or if no anti-greenhouse technology is used.
D8: Local: on this column you will get atmospheric properties if all the atmosphere is subject to greenhouse or anti-greenhouse effect.
E8: Mix: on this column you will get atmospheric properties if some layers of the atmosphere are subject to greenhouse or anti-greenhouse effects and some layers are not (this is the most likely scenario).
A9: Stability (O2): stability of oxygen molecules (and nitrogen, as they have nearly the same mass).
C9: =((3*0.017077*($G$2+273.15)/32))/(((1601*$C$2)/$C$6)^0.5)*100
D9: =((3*0.017077*($C$5+273.15)/32))/(((1601*$C$2)/$C$6)^0.5)*100
E9: =(C9+D9)/2
A10: Stability (H20): stability of water molecules.
C10: =((3*0.017077*($G$2+273.15)/18))/(((1601*$C$2)/$C$6)^0.5)*100
D10: =((3*0.017077*($C$5+273.15)/18))/(((1601*$C$2)/$C$6)^0.5)*100
E10: =(C10+D10)/2
A11: Stability (H2): stability of hydrogen molecules.
C11: =((3*0.017077*($G$2+273.15)/2))/(((1601*$C$2)/$C$6)^0.5)*100
D11: =((3*0.017077*($C$5+273.15)/2))/(((1601*$C$2)/$C$6)^0.5)*100
E11: =(C11+D11)/2
A12: Total height: total height of a stable atmosphere, for bodies with less stable atmospheres, gasses will just be lost at this height.
C12: =(0.29846*($G2+273.15))/($C4*$G3)
D12: =(0.29846*($C5+273.15))/($C4*$G3)
E12: =(C12+D12)/2
A13: Flyable height: max height for an airplane; if this is higher than planet's radius, atmosphere is unstable.
C13: =C12/3.634
D13: =D12/3.634
E13: =E12/3.634
A14: Breathable height: max elevation where, assuming ground pressure of 1 bar, it will be like on mount Everest.
C14: =C13/2.784203
D14: =D13/2.784203
E14: =E13/2.784203

About stability for gasses: A gas is stable for millions of years if the value is below 10 and stable for millennia if the value is below 100. if values are above 100, the gas will be lost quick. This does not account for stellar wind erosion.

If you play a bit with these values, you will get interesting results. For example, if Earth's temperature were -200 C, you would get an atmosphere of only 2 km thick, but with a density of 3.9. For a small object like the Moon, you would in fact need only 88% of Earth's atmosphere to get on the ground a pressure of 1 atm. The gas layer will reach about 72 km high above surface. For Pluto, things are even stranger. To get a pressure of 1 atm. on the ground, you will need a gas layer higher then the planet's radius itself. This proves why Atmosphere around small bodies is difficult to create and maintain.

Greenhouse Effects[]

By adding greenhouse gasses to a planet, two things will happen. Firstly, the lower part of the atmosphere will heat-up and its gasses will move faster. Secondly, the upper part will remain cold, perhaps even colder since it will not receive the same amount of heat radiated from lower layers. So, the lower layer will expand a bit, while the upper one might in fact contract. See Greenhouse Calculator and Greenhouse Gases for details.

Minimum Safe Mass[]

The table below shows for given temperatures and given planet densities, what is the minimum diameter (in km) for a safe atmosphere.

Temperature	Density 1.5	Density 3	Density 4.5	Density 6
-200 C	2 600	1 900	1 400	1 300
-180 C	3 400	2 300	1 900	1 700
-150 C	4 300	3 100	2 500	2 200
-100 C	6 100	4 300	3 500	3 100
-50 C	7 800	5 600	4 500	3 900
15 C	10 500	7 200	5 900	5 100
150 C	15 000	11 000	8 600	7 400
300 C	21 000	15 000	12 000	10 000
500 C	27 000	20 000	16 000	14 000
1000 C	45 000	32 000	26 000	23 000

The table include safe values, since molecules have a low chance of reaching escape velocity. Atmospheres will still be affected by solar winds. Still, the atmosphere will be safe relative to a human lifetime even at smaller diameters.

Atmospheric Thermal Inertia[]

Main article: Climate Inertia.

The formulas listed there allow one to see effects of climate change on other planets and how an atmosphere can mediate thermal balance on a planet.

Downloads[]

You can download Excel simulations from these links:

Climate simulation: [2] (it also has atmosphere simulation)
Planet simulation: [3]
Solar System simulation: [4]
Star simulation: [5].

These files are stored on Mega, the successor of Megaupload.