Chapter 5: Atmospheric Retention

At the beginning of this study, we  set the upper and lower limits for our planetary models at 0.25 and 3.0 Earth masses. The lower limit denoted a small planet which was in  the process of losing its water. The upper mass was the largest planet capable of losing its reducing atmosphere and still retain a potentially habitable average planetary surface temperature. Let now look at how these parameters were derived.

Exosphere Temperature
The outer most region of a planet’s atmosphere is called it’s ‘exosphere’. It is from the exosphere that molecules of atmospheric gasses, i.e.,, hydrogen, helium, water molecules, nitrogen and oxygen escape into space.

There are three basic factors at work in the exosphere which result in the loss of atmospheric gasses, these are:

  1. The planet’s gravity. Gravity is related to mass in such a way that the smaller a planet’s mass, the weaker its gravity. The weaker the gravity, the easier it is for a gas molecule to reach the planets escape velocity and become lost from the atmosphere. Compare the Planetary Mass, Gravity and Escape Velocities listed in the  previous, Table: Planetary Parameters Table, .
  2. The molecular weight of the gas is important: water  (H20) has a molecular weight of 18 and can escape from the atmosphere much more easily than oxygen (O2), which has a molecular weight of 32.
  3. The exosphere temperature: A cool exosphere temperature provides less of the energy required for gasses to escape.

Below is the method I used to determine a formula for calculating exosphere temperatures.

 Table: Comparative Cloud Cover & Exosphere Temperatures

Planet Exosphere Temperature ºK APSTºK Cloud Cover% Exosphere Temp/APST
Venus ~ 2500 ~ 426 100 5.8
Earth ~ 1650 ~ 293 ~ 47 5.6
Mars ~ 1200 ~ 223 ~ 10 5.4

From the table above, I divided each planet’s exosphere temperature by it’s APST providing the results listed in right most column, ‘Exosphere Temp/APST’. The average of these numbers, 5.6, was used as a rough constant, that when multiplied by the APST (ºK) of any of our planetary models, should give a close to actual exosphere temperature (ºK).

In order to calculate exosphere temperatures, first convert degrees Centigrade or degrees Fahrenheit into degrees Kelvin, then multiply your result by the constant, 5.6.

CONVERSIONS:

From Centigrade to Kelvin: APST ºC + 273 = APST ºK

From Fahrenheit to Kelvin: [(APST ºF – 32) * 5/9] + 273 = APST ºK

 Exosphere Temperature (K) = APST (K) * 5.6

By inserting each of our theoretical APST into the preceding equation we find the range of possible exosphere temperatures, seen below in the Table: Average Exosphere Temperature Range.

Table: Average Exosphere Temperature range

APST (ºC) 0 15 30 45 60
Exosphere Temperature (ºK) 1528 1613 1696 1780 1864

.

Determining Atmospheric Gas Retention
In order to determine what gasses would be retained in the atmosphere for about 5-1/2 billion years, it was necessary to compute the Mean Square Root Molecular Velocity of an unknown gas. See Equation #1 below. Then using Equation #2, the molecular weight of the gas was found.

Equation #1 Equation #2
c = Ve/R M = 3rt/c²
c =  Mean square root molecular velocity
M =  Molecular weight of the gas
Ve =  Velocity of escape
r =  Constant: (8.314*10^7 erg/C mol)
R =  Retention factor
t =  Exosphere temperature C

.
The Atmospheric Component Retention Table, seen below, shows what gasses are being retained or lost from the planet’s atmosphere. The separate, vertical red lines labeled, “Low Exo Temp” and “High Exo Temp” are the outside boundaries for the average exosphere temperatures previously determined, therefore encompass the 0ºC to 60ºC APST range used in this study.

The horizontal blue line labeled H2O (with a molecular weight of 18) is the upper limit for retaining water vapor in the atmosphere.

Where the  sloped, brown planetary lines remain below the molecular weight of 18, conditions favor the retention of water vapor, above 18 and the water will eventually lose its water. A 0.5 Earth mass planet (1/2 Earth mass) can be seen slowly losing its water at higher APSTs. The 0.25 Earth mass planet (1/4 Earth mass) is losing its water , therefore becoming more and more arid, across the habitable temperature range.

At lower APST, a 5.5 billion year old, 0.25 Earth mass planet may still have considerable water tied up in ice in mid to high latitudes. Life on these worlds may be very active along the seasonally melting permafrost regions. At higher temperatures there will be less water on the planet’s surface, because of the lack of substantial or any, ice caps.

Volcanism, geysers, etc., may be important in maintaining habitable zones. In any case, there will still be considerable water tied up chemically across the face of the planet. Please note that Mars with only 40% our hypothetical 0.25 Earth mass planet (1/10 Earth mass) is thought to have polar accumulations of frozen water and frozen CO2  (carbon dioxide). [Written in the 1980s – lfp]

We should view the small 0.25 Earth mass planet as a planet that is slowly drying up. It did not have much water to begin with (relatively speaking) and after 5-1/2 billion years it has considerably less. We should also realize that our calculations have been aimed at a 5-1/2 billion  year residency of potentially loseable gasses. If the planet were, lets say, 3-1/2 billion years old, there would be more water available. A large asteroid or comet strike every billion years or so would bring about more volcanic activity and release meaningful quantities of H2O (water) from the planet’s crust, being favorable for the creation of life, yet a hazard to existent life.

All of the planets in this study can be seen to have retained oxygen in their atmosphere. (molecular weight 32). Note, however, that the large, 3.0 Earth mass, planet has barely lost its primal atmosphere envelope of hydrogen.

Continued in Chapter 6: Stellar Parameters

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1 Comment

Filed under SRAPO (Stellar Radii and Planetary Orbits), __Chapter 5: Atmospheric Retention

One response to “Chapter 5: Atmospheric Retention

  1. Ted Haynie

    This one sounds like so many conversations we had back in the 60-70’s. But we didn’t have the formulas then…
    Nice going Bro..

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