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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

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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

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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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Chapter 4: Atmospheric Circulation

The next variable we’ll consider in determining the general climate on a model planet, is it’s atmospheric circulation system.

The surface wind systems with their distribution of atmospherically absorbed solar energy and powers of precipitation and evaporation, are immensely important in creating climate and determining basic direction in which biological adaptations must be made.

At the beginning of this section, I should point out that my use of the terms, ‘tropic’ and ‘subtropic’ are not meant to suggest jungle or climatic conditions similar to those found on Earth, but as geographic locations and ‘conditions relative’ to the given average planetary surface temperature.

The tropic region is that area extending about 20º latitude on either side of the point perpendicular to the planet’s parent star, for most of the models, this is above or somewhat near the equator.

The average temperature of tropic (usually, but not always equatorial) regions on the planet models used herein, extend between 41ºF and 151ºF, depending on the selected model.

The sub tropic region, is an area about 25º latitude above and below the point perpendicular to the planet’s sun. Let’s consider the basic planetary climatic zones, seen in the illustration below.

The tropical, subtropical, temperate and frost zones on our model planets may be nearly stationary and relatively tranquil, as in Figure A; or they may move up and down across the latitudes with specific seasons, seen in Figure B; or they may move across longitudes with sweeping change, as in Figure C.

Air movement
Air close to the ground in the tropic zone absorbs ‘relatively’ large amounts of heat. As this occurs, the capacity of the air to hold moisture increases and the warm mass of air begins to rise in the atmosphere. The rising air is replaced by cooler air as it moves onto progressively cooler regions.  As the warm air cools, it looses it’s ability to carry moisture, where upon the excess moisture is lost through precipitation.

The cooling air mass continues to move away from the tropic zone toward those areas which receive a lesser amount of seasonal sunlight/ As the air moves, it further cools and begins to sink.

In order to gain a background understanding of atmospheric circulation we’ll now discuss only those planetary models with relatively low angles of axial inclination.

Around 35º latitude, the relatively cool and drier air finally reaches the ground and creates a general band of high pressure; from this point, the now cooler air begins to move back toward the tropic zone.

Cool air does not carry much moisture, so as the cool air mass moves from about 35º latitude to 20º latitude, it will be crossing relatively arid terrain. Since these latitudes still receive about 80% of the sunlight available in the tropics, this zone will be relatively hot, as well as dry. This portion of the atmospheric circulation system can be seen in the associated illustration, Tropic and Sub tropic Zone Circulation.

On the whole, the circulation system of the tropic and sub tropic zones will be quite large and fairly steady, except on worlds with high axial inclination,

Biologically, conditions in the tropic zone depend on temperatures and the availability of water.

On planets with low axial inclination and low to mid range APST (about 0ºC-30ºC), I suspect we would find something between temperate and steamy tropical forests as temperatures were elevated. Between an APST of 45ºC and extending up toward 60ºC, I believe the tropical forest would break down to be replaced by simpler plant communities with smaller individuals. Under these conditions, hot temperatures become a limiting factor in much the same way as cold temperatures limit growth in Earth’s tundra.

Around 50º to 60º latitude, on either side of the central tropic zone, there is a low pressure area. This region is cooler than the tropic low since it receives only about one half the solar energy. Being cooler, this mid latitude area is less humid and receives less precipitation.

The asterisks at 1.0 in the above graph, Relative Precipitation and Latitude axis, indicates the average precipitation level for the model world. Once the average precipitation and evaporation rate has been calculated a good model can be made for precipitation.

The following precipitation table was computed using data from the table in Chapter 3: Climatic Factors, Table: Data for Computing precipitation and Evaporation Rates used in either the associated equation or the BASIC computer program.

Table:  Average Inches of Precipitation and Evaporation for Planets with the given Mass and APST

Planetary Mass   Ê = 1
   APST ↓ 0.25 0.5 1.0 1.5 2.0 3.0
APST ºC 0ºC 55.1 50.4 41.7 35.2 29.5 18.2
15ºC 56.5 49.6 41.2 34.6 28.6 15.9
30ºC 55.8 49.6 40.6 33.6 27.4 13.0
45ºC 55.2 48.7 40.8 31.9 25.0 7.8
60ºC 55.0 48.4 38.9 30.4 19.2 5.2

In order to see if the preceding table had relevancy, I also ran calculations for Earth, where the averages are fairly well known, see following table:

Table: Average Inches of PPT & Evaporation on an Earth Mass Planet with 24 Hr Rate of Rotation

APST ºC 0 15 30 45 60
Inches Precipitation 41.7 42.07 40.6 38.9

Earth, with al 20ºC APST, has an actual  average annual precipitation rate of 40 inches.  The theoretical (calculated) Earth mass planet with 20ºC APST and 24 hour rate of rotation  has 41.6 inches of precipitation, a 4% difference between the actual and theoretical. Graph the above table (using the Chapter 3- Table: Cosine of planetary latitudes)

Although the theoretical precipitation rate works out well for an Earth type planet, meaningful equation results seem to degenerate as we approach the much smaller 0.25 Ê mass or the larger 3.0 Ê mass planets.

On the 0.25 Earth mass planet: At 0ºC to 15ºC there is a fairly small habitable zone which may indeed receive the theoretical amount of precipitation; however, most of what water exists on the planet will be locked up as ice in higher latitudes. Also, because there is a small water to land ratio, there is a very large area which will be arid-cool arid and cold arid.

In the 30ºC to 60ºC range, we’d find the higher latitude ice and frost caps either gone or greatly diminished. This would not lead to larger bodies of liquid water. The 0.25 Earth mass planet is a planet losing its moisture. The surface gravity is such that at higher temperatures, water molecules in the atmosphere simply drift out into space, resulting in a planet that is slowly drying. Therefore, in the higher APST range, I would suspect the precipitation and evaporation figures to break down. Several billion year old planets of this small size and high temperature would have relatively dry atmospheres.

On the large 3.0 Earth mass planets there maybe only small land masses, perhaps only island chains as opposed to ‘continents’. Warm moist ocean air might not move out onto large cool land masses.

At 0ºC to 15ºC, there would exist in the north and south latitudes, very large ice caps. Under cooler conditions the oceans would have reduced depth and the island land masses may have expanded to form small continents. This scenario would tend to increase the precipitation level for those areas, above the data given in the Precipitation and Evaporation table.

In the 30ºC to 60ºC APST range, we would find the ice caps diminishing to frost caps and finally entirely absent. As the APST increases, the atmosphere would become more and more saturated with moisture. Instead of true precipitation, we may find states of continual condensation occurring on terrestrial objects, especially at night and in latitudes experiencing change of season. Humidity would be extreme.

Wind deflection
Because all of the planet models rotate on their axis, we can expect wind systems to be deflected at various latitudes on either side of the tropic zone. The basic global air circulation for models, with a low to mid range axial inclination may be illustrated as follows.

As we study the Basic Global Circulation model above and recall the concepts derived from Tropic and Sub tropic Zone Circulation, illustration, page 21 and Relative Precipitation and Latitude graph, page 21, we are able to predict some interesting bits of information about continental climates.

Looking at the Subtropical Highs, we see the winds have a tendency to move from east to west as they return to the low pressure area in the tropic zone. This moving air mass is relatively cool and dry, and as previously mentioned, the area of the planet’s surface crossed will tend to be warm and arid, relative to the APST and the average planetary precipitation rate. The biotic community, which extends across these bands of high pressure depend on the APST, so that on worlds with an

APST  0ºC: The planet may carry cold/dry adaptive, coniferous forest type vegetation

APST  30ºC: Zone may be a hot desert.

APST 60ºC: Plant life is sparse and terrestrial animal life nocturnally active.

Local Climates
At any latitude, where high mountain ranges are situated perpendicular to the prevailing winds, we could expect higher moisture on the windward side and more arid conditions on the lee side.

On planetary models with some degree of axial inclination, that hemisphere undergoing Spring would have its land masses heating up faster than the oceans. This results in a low pressure system developing over the land and a high pressure system developing over the adjacent ocean. Conversely, in the Fall, the land would cool faster than the ocean and the high and low pressure systems would be reversed.

Water has a greater capacity to hold heat than does soil. Therefore the temperature variation between land and ocean would remain more stable in  the equatorial region that at higher latitudes on worlds with much free surface water.

Inland areas of continents have a far greater annual variation in temperature than coastal areas of the same latitude.

The planet’s surface temperature range
Planets with small axial inclinations have small variations in seasonal temperatures. As the axial inclination increases, the total range of temperatures for each latitude expands.

Model planet A, at left, has  0º axial inclination. An observer at 0º latitude would note his Sun rises to a point directly overhead every day and that the average temperatures through out the year is, let’s say, 81ºF.

Model B has a 15º axial inclination. An observer at 15º N will note that the sun is directly overhead at noon during the summer and that his summer average  temperature is perhaps 81ºF. Half a year later, the Sun has apparently moved to a point 15º below the equator and is now 30º lower in the sky to our observer. Recording his average Winter temperature of 70ºF, the observer notes that there is a 11ºF difference between his Summer and Winter temperatures averages.

Model C has a 45º axial inclination. This time, our observer is located at 45º N latitude. He notices the sun directly over head at noon and a temperature of 81ºF during the summer. Half a year later, the Sun has moved to a point 45º below the equator and is now 90º lower in the sky to the observer. At noon during the winter, the Sun will rise to a point where it just peeks over the southern horizon and the average temperature will be about -25ºF,

For the sake of comparison and to develop a better understanding of axial inclination and the subsequent temperature range, see the following table:

Table: Approximate Change in Temperature Range  (from the concept explanation above)

     AXIAL    INCLINATION SUMMER      ºF WINTER   ºF TEMPERATURE RANGE ºF
        0º     81      81        0
       15º     81      70        11
       45º     81     -25       106
For a planet of 1.0 Earth mass and 20ºC APST (Earth like); the axial inclination has been varied in the table to show simplified temperature effects. Our imaginary observer is located at a latitude above the equator which is equal to the planets axial inclination. For any given location on a planet, the greater the axial inclination, the greater the temperature range for that location and therefore, the greater the variation in its seasonal climate.
The chart shows, the greater the axial inclination, the more pronounced are the ‘seasons’ of the year.
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Thunderstorms
All the planets whose mass and APST fall within the parameters of this study will have thunderstorms, with possible exception of the 0.25 Earth mass planet. The ingredients necessary for thunderstorm development are unstable warm air and humidity. These conditions exist in at least some latitudes on all the other, larger habitable planets. About the only area that would not be at least occasionally affected by thunderstorm activity would be the ice caps and other extensive desert (arid) regions

Continued in Chapter 5: Atmospheric Retention

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Chapter 3: Climatic Factors

Attempting to determine the basic climatic conditions for our model planets, we will take into account several major variables. We will attempt to treat some of these variables in order to develop an insight into general planetary climatology. You should keep in mind that the approach taken in the survey is a combination of intuition and empiricism and that even current attempts to calculate mean annual temperatures for Earth (mid to late 1960s) have not been highly successful.

Axial Inclination
Axial inclination refers to the number of degrees which a planet’s equator is tilted from its orbital plane.

Since all of the planets in our Solar System display axial inclination, we may theorize that whatever the process leading to its development here, perhaps exists universally. However, since the process isn’t understood, we’ll consider various degrees of axial inclination to develop an understanding of their general effect on a planet’s surface temperature.

Axial inclination, near 0º
On a planet with 0º or near 0º axial inclination, the temperature, precipitation rate and length of day would not vary appreciably in any one spot throughout the year, assuming a nearly circular orbit. circular.Because the planet has no tilt, there  would be no seasonal change as the year progresses. At any point on the planet’s surface, the  prevailing conditions in January would be the same as  in July. Low latitudes, near the equator, would experience the planets perpetual summer temperatures. High latitudes, nearer the poles would exist in a relative condition of winter with low illumination. On either side of the equatorial summer zone, there would exist temperatures we may classify as relatively spring like. The next zone would be fall like, with temperatures declining as one approached the high latitude winter zone.

Proceeding from the equator toward either pole, you would almost imperceptibly move across the planet’s surface temperature gradients, from relatively hot, to relatively cold.

Many plant species on Earth require a certain number of days with frost, a particular number of hours sunlight or some other abiotic factor to trigger seasonal growth. On worlds with 0º or very low axial inclination, plant life would have made other adaptations to the essentially non varying climate at their latitude. We might expect more sensitive biological triggers and a greater number of species which were perennials and fewer annuals.

Axial inclination approaching 90º
Worlds with axial inclinations approaching 90º would experience some really exciting seasonal climatic variation.

As the planet orbited its parent star, it would alternately have one of its poles bathed in summer sunlight for a quarter year, have a quarter in semi dark winter. Between the long hot polar summer cold winter cycles, the lower latitudes would gradually shift into a regular day and night cycle. The day and night cycle on this model would be complex, with the polar regions growing tropically warm in their seasonal summer and declining to Arctic cold in their seasonal winter.

Note from the preceding diagram that , the planets south polar region is experiencing summer. A few months later having orbited to position B, the polar regions are now located at a point approximately 90º from the sun, therefore are experiencing conditions similar to those at Earth’s poles. Note also that in position A, the “spring and fall” moderate temperature zones on the illuminated side of the hemisphere do not experience night. In these locations, the sun would simply circle in the sky. But it would not set As the planet orbits to position B, the spring  and fall temperature zones acquire a day and night cycle.

To a person standing on the illuminated hemisphere in planetary position A, the sun would appear to circle in the sky, but as the weeks passed, the apparent circle would spiral closer to the horizon. At some point midway between points A and B, the sun would dip below the horizon for a period of sunset, then it rise again. Approaching position B, the sun would set and nights would become longer. At position B, the sun would rise on one side of the horizon and set on the other, visually similar to what we experience.

As the planet orbited toward position C, the sun would  be seen to rise lower and lower in the sky, the days would shorten and temperatures. At position C, an observer at the south pole would be in several months of cold darkness. Southern latitudes would be in s state of extended twilight. Northern latitudes would be basking under extended periods of continuous daylight. At the same time, the north polar region would be baking in a summer season under overhead tropical sunlight.

Note that between location A and C, the poles experiencing summer and winter have reversed.

If this planet had an APST of 68ºF (20ºC) then a large percentage of the planet’s surface would experience a temperature range from between 81ºF to -25ºF. I would more or less expect tundra type terrain and vegetation on either side of the equator and vegetation specialized for hot and cold temperatures in higher latitudes.

Should such a planet exist in the ecosphere of a F class star, it would have a long year and therefore longer seasons for growth, before dormancy. Migration might play a major influence amongst larger life forms. If the planet orbited a relatively small cool class K star the year would be short and the growing season reduced.

Intermediate axial inclinations
Climatic factors arising on planets with intermediate axial inclination would vary according to the level of inclination. Planets with axial inclinations of 10º-15º will have milder seasonal temperature variations than planets with larger inclinations.

Those of us living in the mid latitudes on Earth (my 1980-2005 home is roughly on 45º33’ north latitude) can attest to the seasonal climatological effects of Earths 23½º axial inclination.

A mid latitude location on a planet with an APST of 20ºC and a 40º-60º axial inclination would be subjected to a steamy tropical summer and a frigid Arctic winter. On small to mid size planets with moderate inclinations, plant life would have developed highly protective tissues against the relative cold and heat. Desiccation and starvation  would be major biological problems.

Warm vs. Cold-bloodedness
Axial inclination and APST are two very important variables in broadly determining whether intelligent life on our model planets are warm or cold-blooded.

Basically, the difference between being ‘cold blooded’ or ‘warm blooded’ is that the former life forms are dependant on external temperatures while the latter have developed mechanisms to maintain internal temperatures under a wide range of external temperatures.

Persistent wide variability, periodic extreme oscillations and ‘cold’ or ‘hot’ are conditions conductive to the development of warm ‘bloodedness’. On the contrary, mild and seasonal temperature changes in a warm climate (not hot) are favorable to cold ‘bloodedness’.

It takes more biological equipment to be warm-blooded than cold-blooded; however, the extra activity gained in a hostile environment, apparently make the investment worthwhile.

I’ve worked out the following graphic to demonstrate the gross conditions where I believe we might find the development either cold or warm-blooded life forms.

In the upper portion of the graph, hot temperatures tend to be a limiting factor for cold-blooded dominant life forms. Low and to the left, it is general cold that limits cold-blooded expansion and-or probabilities. Looking up and to the right, we see that warm ‘bloodedness’ is favored as the  planets axial inclination rises, since this increases the summer high and drops the winter low temperature average for each latitude.

Although warm-blooded dominant life forms could exist on all the planetary models represented in the graph, cold blooded dominant life would probably be found on planets whose general climatic scheme was delineated by the green hashed area.

Planetary energy balance
In order to determine evaporation rates, we need to start with the total available solar radiation, make the necessary subtraction for albedo, etc. and thereby find the planets working energy balance.

We’ll start at the top of the planet’s atmosphere with the solar constant, a ‘constant’ because it varies little over a long period of time.

Coming down through the atmosphere, the first quantity of energy we subtract from the solar constant is the albedo, this amount is reflected back into space by atmospheric reflection (from the cloud cover). The remaining energy  is almost entirely used to heat the planet’s surface and to circulate the atmosphere.

Since atmospheric surface pressure is related to atmospheric density, the ratio between percent energy absorbed by our atmosphere and the surface pressure were used to determine the percent energy absorbed by the atmospheres of our model planets.

In the following table, the percent energy absorbed from the incoming radiation by the atmosphere is shown related to the corresponding planets mass.

Mass of planet ,  Ê = 1 0.25 .50 1.0 1.5 2.0 3.0
Percent energy absorbed 7 12 17 20 22 25

Having  reduced the solar constant by subtracting out the albedo and the energy absorbed by the atmosphere, what we have left is the radiant energy actually reaching the planet’s surface. Of this energy, some is lost as long wave radiation and some is reflected. When water or ground moisture is available, nearly all the remaining energy is used in evaporation.

Computing precipitation and evaporation
It’s been calculated that the average evaporation and precipitation rate for Earth is 100 cm (40 inches) per year. However, this is merely an average, because there is a sizeable difference in this rate over land and sea. The oceans have a precipitation rate close to 111 cm. (44 inches) and an evaporation rate of 120 cm (48 in), with the difference being returned to the oceans by river flow.

On land, the average precipitation rate is 71 cm (28 inches) per year with about 24 cm (10 inches) lost by river discharge.

The average evaporation rate for land is misleading because it takes into account a large portion of the land surface which contributes little to the figure, for example, tundra, icecaps, deserts and mountains. When these areas are taken into account, we find that the balance of the land receives about 100 cm (40 in) per year, the global average.

On a global scale, total evaporation equals total precipitation, or “what goes up must come down”. The following equation may be used to calculate precipitation or evaporation rates for our model planets:

Average annual Planetary Precipitation (cm) = [(1-(A+a)) *(0.29d)* (0.4E((/R3*8760)/Z)]/H

Conversions: The precipitation rate in cm/2.5 = the precipitation rate in inches.

Factors used in the Precipitation computation See the required data in Table: Data for computing precipitation and evaporation rates, below.

A   = Percent energy absorbed by the planet’s atmosphere.
a   = Percent albedo loss, See below, Table: Data for computing precipitation and evaporation rates.
d   = Planetary rate of rotation in minutes.
E   = See Determining Solar Constants (read in cal/cm² min), Chapter 2.
R   = See Orbital Radius, See Chapter 2.
H   = Latent Heat of vaporization.
Z   = See Planetary Rate of Rotation (in hours).

The following Table: Data for Computing Precipitation and Evaporation Rates, provides the data required to calculate average precipitation and evaporation for the model planets:

Table : Data for computing precipitation and evaporation rates

M Mass  w = 1 0.25 0.50 1.0 1.5 2.0 3.0    
A1 % Energy absorbed by the Planets Atmosphere 0.07 0.12 0.17 0.20 0.22 0.25 0.31 0.34
A2 % Albedo loss 0ºC 0.20 0.22 0.30 0.36 0.42 0.54    
15ºC 0.22 0.26 0.33 0.39 0.45 0.57    
30ºC 0.26 0.30 0.36 0.42 0.48 0.61    
45ºC 0.30 0.33 0.38 0.46 .052 0.61 = x  
60ºC 0.33 0.36 0.42 0.49 0.59 0.61   = x
D Rate of Rotation (minutes) 1380 1200 1020 900 870 780    
Z Rate of Rotation (hours) 23 20 17 15 14.5 13    
E Solar Constant(cal/cm² min) 0ºC 1.34 1.4 1.58 1.7 1.88 2.36    
15ºC 1.58 1.62 1.82 2.0 2.22 2.4    
30ºC 1.8 1.9 2.08 2.3 2.6 2.8    
45ºC 2.06 2.16 2.38 2.72 3.0 3.3    
60ºC 2.34 2.48 2.7 3.08 3.48 3.92    
H Latent Heat of Vaporization of Water (cal/gm) 0ºC 595    
15ºC 588    
30ºC 580    
45ºC 571    
60ºC 563    

Left column labels M, A, A2, etc. are computer variable names used in the following computer program.

x = Seen at right in the table show the percent energy absorbed at 100% cloud cover, the last two 61% albedo loss only.

Using data from, Table: Data for Computing Precipitation and Evaporation Rates, you may compute the average precipitation and evaporation rates with the following B.A.S.I.C. language program.

Line Number Northstar B.A.S.I.C.
10 REM   CALCULATE INCHES PRECIPITATION FOR PLANETS
20 !CHRS$(11)
30 INPUT   “Mass of planet ?”, M
40 INPUT   “APST ?”, W
50 INPUT   “% Energy absorbed by atmosphere ?”, A1
60 INPUT   “% albedo loss ?”, A2
70 INPUT   “Rate of Rotation  (in minutes) ?”, D
80 INPUT   “Planets Solar Constant ?”, E
90 INPUT   “Rate of rotation (in hours) ?”, Z
100 INPUT   “Latent Heat of Vaporization (water) ?”, H
110 REM   L=SPECTORAL CLASS-G0-STAR LUMINOSITY
120 L=1.04
130 REM   CALCULATE ORBITAL RADIUS RELATIVE TO EARTH
140 E1=E/1.97
150 R1+L/E1
160 R2=SQRT(R1)
170 R3=R2*R2*R2
180 REM   R4=RELATIVE SIDEREAL PERIOD
190 R4=SQRT(R3)
200 REM   PRECIPITATION EQUATION IN CENTIMETERS PPT.
210 P1=[1-(A1+A2)]*(0.29*D)*[0.4*E(R4*8760/Z)]/H
220 REM   CONVERT CENTIMETERS PPT TO INCHES PPT
230 P2=P1/2.5
240 !   ”MASS PLANET”, M
250 !   “APST”, W
260 !   “INCHES PPT”, P2
270 INPUT   “Do calculations again ? Y or N”, Q$
280 IF   Q$=”Y” THEN 20, ELSE 290
290 END

If you multiply the planet’s average precipitation or evaporation rate by the cosine of the planet’s latitude you’ll be able to roughly determine the precipitation or evaporation for the chosen latitude.

Table: Cosine of planetary latitudes

Latitude 10º 20º 30º 40º 50º 60º 70º 80º 90º
Cosine 1.0 0.984 0.939 0.866 0.766 0.642 0.500 0.342 0.173 0

The preceding method of determining precipitation rates over the planet’s surface will be modified in the next chapter.

Continued in Chapter 4: Atmospheric Circulation

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Chapter 2: Average Planetary Surface Temperature (APST)

The Average Planetary Surface Temperature (APST) range used in this study was taken in part from the wide limits found amongst life forms on Earth. The range is 0ºC to 60ºC for the vast majority of the Plant and Animal Kingdom. Below the freezing point of water, 0º C, as ice,  water is no longer a dispersion medium for chemical activity, and above 60°C, protein coagulates.

It should be realized that on Earth, a few organisms that have adapted to extreme temperatures that are much higher or lower than the average. These organisms already had a several billion year evolutionary history of thriving in more normal temperature environments, before slowly adapting to these more extreme, hostile conditions.

Temperature Discussion
Temperature means “intensity of heat” and the average amount of heat in a body is the average kinetic energy of the molecules of which that body is composed.

In the plant kingdom, temperature and precipitation are the  major climatic factors determining a species range. Temperature influence the plant activities of water absorption, transpiration, germination, growth, photosynthesis and reproduction.

The effects of high temperature on plants are: desiccation and basically, starvation, since the rate of respiration becomes so high that food consumption exceeds production by photosynthesis.

As temperatures rise, the rate of chemical reactions increase, so that with each, approximately 10ºC increase in temperature, there is a 100% rise in the rate of chemical reaction. This occurs because the increase in temperature causes greater molecular activity and more molecules reach the energy plateau necessary for their specific reaction.

Enzyme catalyzed reactions increase in rate until about 50ºC, above this the enzymes are rapidly inactivated and destroyed by heat denaturalization. Protein extracted from living tissue coagulates around 60ºC, but some thermophilic bacteria have adapted to temperatures as high as 75ºC.

Most of our food crops require a temperature between 10ºC and 30ºC during their growing season. Where as the overall majority of plants cease functioning below 0ºC, many are capable of short-term survival at exposures down to -50ºC to -62ºC. At low temperatures (approaching 0ºC) plants cease to  be metabolically active, because internal temperatures are similar to external temperatures; the result being a greatly reduced enzyme activity and the freezing of water.

As can be seen, temperature plays a strong role in the biology’s of Earth. The same basic chemical building blocks, ie, carbon, nitrogen, water, sulfur, lead, iron, etc, exist on planets beyond our solar system. Alien life forms will be circulating the elements from the natural environment through their bodies in a way not necessarily identical to us, but in similar ways for their own nutritive needs.

Because plants cease to function below 0ºC, this will be the lower Average Planetary Surface Temperature (APST) used in this study, because protein coagulates at or around 60ºC, this will be the high APST used in this study.

Table: Intuitive Comparisons of Planetary Surface Temperatures

0°C 32°F Average surface temp on Mars -67°F with an overall range of -207°F to 80°F. The annual mean temperature at the North Pole is -40°F in winter and 32°F in summer.
15°C 59°F 59°F is Earth’s average temperature.  Los Angeles averages 66°F, with a seasonal low of about 45°F to highs around 90°F.
30°C 86°F HUMID: Manila,   Philippines – mean annual relative humidity 73.8%, (82% RH during rainy season, about the maximum moisture that the atmosphere can hold, with an average temperature of 82°F;  88°F to  93°F daytime high temperatures are common.
Bangkok, Thailand – mean annual RH 80%, with an average temperature of 82°F; 88°F to 92°F daytime highs common. These places experience extreme humidity during their rainy seasons combined with warmth giving the feel of a lukewarm sauna.  [Wet planet with 30°C ASPT-think ‘lukewarm sauna’]
30°C 86°F DRY: The average annual temperature for the Sahara desert is 86°F (30°C) with an   average humidity of 25%. Hot dry air and soil.
Dallol, Ethiopia, is the warmest   place on earth with an average yearly ambient surface air temperature   of 34°C = 93°F.  [Dry planet with 30°C ASPT-think, ‘typical hot, arid desert’]
45°C 113°F In July the Sahara desert reaches temperatures of 113°F to 122°F degrees; with the sand reaching 170°F, and rocks 100-110°F. [Dry planet: Think, ‘extreme desert conditions’. Wet planet: Think, ‘extremely dangerous heat and humidity’].
60°C 140°F Earth record   temperatures: Lut Desert of   Iran, 159°F (2005), El Azizia, Libya, 136°F (1922); Death Valley, California, 34°F (1913).

Formula for converting from °C to °F:
(°C x 9/5) + 32 = °F

Percentage Cloud Cover
Having chosen the APST limits for our model planets, it is necessary to determine what environmental conditions would create such temperatures. The first problem I encountered was the need to have a correlation between APST, planetary mass and cloud cover. I intuitively derived the multi axis graph entitled, Cloud Cover Determination, seen below.

Cloud Cover Determination Diagram

Read the Cloud Cover Determination Diagram, proceed as follows: 1) Choose a planetary mass from the bottom axis and an APST from the left axis, 2) Read up from the selected mass to intersect with the selected APST. 3) At the mass-APST intersection read to the upper right to the associated Percent Cloud Cover scale. Example: A planetary mass of 0.5 (Ê = 1) and APST of 15ºC would be found with approximately a 30% cloud cover.

The Cloud Cover Determination chart is important, because ‘cloud cover’ is a factor in the determination of the amount of sunlight that reaches  the planet’s surface and how much is reflected by clouds, back into space.

 In order to make the Cloud Cover Determination Diagram, I compared the APST, cloud cover and mass of Venus and Mars with Earth. It became apparent that average planetary cloud cover is correlated with two major parameters: planetary mass and APST. In the case of Venus, a planet with nearly the mass of Earth, but with a much higher APST, the cloud cover grew to 100% transforming it from optically thin to optically dense. The dense cloud cover further increased the APST through the greenhouse effect, which in turn vaporized yet more material and created a still denser atmosphere.

By considering the crystallization of albite as an example of the process leading to the formation of water, and saying that an equal percentage of the mineral composing each planet’s crustal material, then the amount of water released from the crust of the largest planet would be about twelve times greater than the water released from the crust of the smallest planet. Note that the planetary mass range in this study extends from 0.25 to 3.0 Earth masses.

Since the surface area of the largest planet is only three times as great as the smallest, yet carries twelve times more water. It is clear that the surface of the largest planet is nearly covered with water, while the smallest planet is covered primarily by dry land.

As the size of the planet increases from 0.25 to 3.0 Earth masses, the percentage of the  planet’s surface covered by water increases. At any given average planetary surface temperature, between 0ºC and 60ºC, there would be more total evaporation occurring from the surface of a large planet than from the surface of a small planet. See diagram below.

Comparing Several Features of Large and Small Habitable Planets
For the purpose of this study, and to gain a relative insight into planet’s ecology under varying conditions, I have with some thought, assigned each of the following planetary models with a reasonable percentage surface exposed to land and water.

Land Mass vs. Water Ratio table

Planetary   Mass, Ê = 1 0.25 0.50 1.0 1.5 2.0 3.0
Percent Land 95 60 30 22 15 5
Percent   Water 5 40 70 78 85 95

The  ratios given in the previous table would be variable, since on cold planets, water would be frozen out to form thick expansive polar icecaps; while on relatively warmer planets, there would be little or no ice, hence less surface area in dry land.  [Note: Mars has a mass of 0.1 Earth, only 40% the size of the smallest planet used in this study, and would therefore expected to have very little surface water. Being further from the Sun, most of the water that has not evaporated from the planet’s atmosphere would be found frozen in polar sheets; leaving a very large dry land to (frozen) water surface ratio – as we’ve found.]

On a large planet, the atmosphere is quite dense near the surface, but loses density rapidly with elevation. On small planets, the atmosphere is less dense near the surface and trails of more gradually with increased elevation.

These factors affect the percentage cloud cover in such a way that when comparing a larger and smaller planet of similar average planetary surface temperature; the larger planet would have a larger, thicker cloud cover, while the smaller planet would have a smaller, thinner cloud cover.

On any of our planetary models, the warmer the APST, the greater the percentage cloud cover. Naturally, the warmer it is, the greater the evaporation, the more moisture the air can carry and the greater the cloud cover.

Planetary Parameters Table

Planetary Mass, Ê = 1 0.25 0.5 1.0 1.5 2.0 3.0
Planetary Mass, Nx10^27 grams 1.49 2.98 5.97 8.96 11.93 17.9
Surface Gravity, Ê = 1 0.52 0.69 1.0 1.23 1.36 1.69
Surface Area, Ê = 1 0.46 0.68 1.0 1.2 1.42 1.70
Surface Area, Nx10^8 mi. 0.93 1.41 2.02 2.41 2.86 3.43
Circumference, Ê = 1 0.67 0.83 1.0 1.1 1.2 1.3
Radius in miles 2730 3360 4020 4400 4780 5240
Planetary Density, Ê = 1 0.79 0.85 1.0 1.13 1.17 1.28
Escape Velocity, Ê = 1 0.60 0.76 1.0 1.16 1.28 1.5
Escape Velocity, km/sec 6.7 8.6 11.2 13.0 14.4 16.8
Mass of Atmosphere, Ê = 1 0.19 0.43 1.0 1.43 1.87 2.55
Mass of Atmosphere, Nx10^21 grams 1.0 2.4 5.3 7.6 9.9 13.5
Surface Pressure (lbs/²) 6.2 9.5 14.7 17.2 19.0 21.7
Rate of Rotation (hours) 23.2 20.2 17.0 15.3 14.4 12.8
Incoming energy absorbed by the Atmosphere., Ê = 1 0.79 0.85 1.0 1.13 1.17 1.28
General Planetary description. Small Dry Small Damp Medium Wet Medium Wet Large Liquid Large Aquatic

.

Incoming radiation
The next step in determining the factors which affect average planetary surface temperature was to create a graphic in which there was an alignment between APST and radiant  energy heating the planet’s surface at the equator; this criteria was further correlated with the planetary cloud cover. (From the Determining Incoming Radiation Diagram above).

After computing (with a slide rule) the surface values for Earth and Mars and positioning them in the chart’s grid at their known APST, percent cloud cover and mass, the graph then provided a scale from which to determine the equatorial surface radiation energy levels for our planetary models.

 Having derived the amount of radiant energy striking a planet’s surface at the equator, thereby deducing its APST, it was necessary to track the sunlight back up through the atmosphere, add-on the albedo losses and end up with the solar constant (amount of ‘sunlight’) at the top of the atmosphere.
Definitions:
•  Solar constant: The amount of sunlight per square centimeter at the top of the planet’s atmosphere above the equator; the solar constant for Earth is 1.97 gm cal/cm² min.
•  Albedo: The amount of sunlight reflected back into space from the clouds, snow, sand, etc. The    albedo is expressed as a fraction of the total sunlight falling on the top of the planet’s atmosphere; on Earth, the albedo has a value of 0.36.

These relationships may be expressed as follows:

Radiant energy heating the planets surface at the equator = Solar constant – (albedo x solar constant)
1.28 gm cal/ cm² minute Ê =  2gm cal/cm² minute – (0.36 x  2 gm cal/ cm² minute)

In order to determine a table for the range of albedos used in our planetary models, I graphed the Martian cloud cover and albedo against those of Venus. See Determining Incoming Radiation diagram above.  Note that Earth has about a 47% cloud cover, which on the diagram, yields a 0.34 albedo. Since atmospheric scientists  have determined Earth’s albedo is 0.36, I felt my albedo Determination graph was well within the acceptable range of error that could be associated with a study of this nature.

NOTE: You do not need to do the following calculations to work with the SRAPO templates. The data: Solar Constant, % Energy absorbed by the Planets Atmosphere, % Albedo loss, Rate of (planetary) rotation and Latent Heat of Vaporization of Water are presented in Chapter 3: Climatic Factors, Table: Data for computing precipitation and evaporation rates.

Determining Solar Constants
The next step resulted in the graph Determining Solar Constant. This is the tool to use when trying to determine the solar constant of a planetary model. See the following page. With it,  you can choose a planetary mass and APST then derive the resulting percentage cloud cover and the solar constant. If for example, you choose a 0.25 mass planet with a 30ºC APST, find the intersect within the body of the graph. Now, read horizontally across to the left Y axis scale for a 32% cloud cover and down to the lower X axis scale for a 1.80 gm cal/ cm² min solar constant.

Orbital Radius
At this point, we have the ability to begin with a set of basic planetary conditions , planetary mass and APST, and derive a specific solar constant.

The next question was, “How far is the planet from its parent star?” To answer this, you must first choose a Main Sequence star by its spectral classification,  thereby selecting its luminosity relative to the Sun. See Stellar Parameters, page 37.

With the following equation, you can calculate a habitable planets orbital radius about the given spectral class of star.

Radius of the planet’s orbit = The stars Luminosity (where Š =1) / the planets Solar Constant (where Ê = 1)
R2 =  L/S

At this point, we’ll stop and review the pieces of information we have deduced about our planetary models.

In the chart above: Cloud Cover is in the left axis. The amount of ‘sunlight’ hitting the top of the planet’s atmosphere is along the bottom axis. Each diagonal line inside the chart represents a planet of given mass (0.25 to 3.0 Earth masses) each is shown with a sliding scale of average planetary surface temperature – which correspond to the planet’s cloud cover and how much sunlight arrives from its parent star (Sun).  Example: A planet of 0.25 Earth masses (bottom diagonal brown line) with a 60ºC APST would have a Stellar Constant of about 2.35 cal/cm² min and about a 45% Cloud Cover.

Concepts Illustration: In the drawing above there is a parent star. Sunlight travels some distance (the orbital radius) to the planet and hits the upper atmosphere, this amount of energy is the planets Solar Constant. Some of the light is reflected back into space from the Cloud Cover, and some reflected from the snow, ice or sand on the surface, the average amount lost by reflection is the planet’s Albedo.

The drawing also shows an undefined land to water ratio and some percentage Cloud Cover. By choosing a planet’s mass and the APST, and plugging those values into the diagrams  found earlier in this chapter, you get the Solar Constant. This is important in determining how far the planet is away from its parent star, but more about that in a while.

Planetary Rate of Rotation
Based on observation of our own solar system, it appears that a planet’s rate of rotation is a function of its mass. The correlation between rate of rotation and mass is not perfect; however, the trend seems to indicate that it is not due to chance alone.

A reasonable theory that could explain the planet’s rotation is: During the process of planetary formation, by accretion, each particle of captured mass affects the rotational energy of the protoplanet. The net effect being an increase in the rate of rotation with an increase in mass.

Since all the planets in our solar system, except Uranus, rotate in the same direction as their orbital motion, its evident there is a tendency for incoming particles to impart a direct spin to the planet. Graphically, this may be seen as follows.

The mathematical formula expressing this relationship in hours per revolution (or more commonly ‘hours per day’)  is:

Hours / revolution = /(((2п/2MpK1)/K2)/3.6 x 10³ sec/ hr)

/ = square root
Mp = mass of the planet
R = the planet’s radius
K1 = constant, 1.46 x 10-19 cm² / sec² g
K2= constant, 0.4 (Maclauin’s spheroids)

The rate of rotation (length of day) imparted to a planet during its formation may be affected by tidal retardation. A relatively  large satellite orbiting the planet can slow the planet’s  rotation. This can be clearly seen in the Earth-Moon system. If Earth did not have the Moon in orbit, our ‘day’ would be seventeen hours, instead of twenty-four hours long.

Planets with an APST between 0ºC and 60ºC which are orbiting the relatively luminous stars of spectral class F through G, are at such a distance from their parent star that the rate of rotation is not affected. However, spectral class K stars are relatively cool stars and planets orbiting them must be in a very close orbit in order to fall with in the proper average planetary surface temperature range. Beginning with spectral class K2, the orbit for habitable temperatures is so close to the star that tidal retardation would arrest the planet’s rotation.

The habitable temperature zone around a star is called the ecosphere. We have set the ecosphere boundaries to provide the model planets an average planetary surface temperature (APST) range between 0ºC and 60ºC. The concept of ecosphere boundaries can be seen in the following diagrams.

Looking at the drawing above, we see that there are limits to the orbital diameter for a habitable planet. If the planet orbits inside the Inner boundary, the APST is above 60C and protein coagulates.; if it orbits beyond the Outer boundary, there is no liquid water.

If you will for a moment, turn back to the graph, “Determining Solar Constants’. Note that  for each planet there is given 0ºC to 60ºC temperature range. If you read from 0ºC on any planet to the Solar Constant scale on the bottom of the graph and again from 60ºC to the scale at the bottom, you will notice that these Solar Constants set the planet’s ecosphere boundaries, in terms of illumination arriving from the parent star.

By using the equation (discussed above):

L/ S = R²

Read the equation: The parent star’s Luminosity (where Š =1) [divided by] / the planet’s Solar Constant (where Ê = 1) [equals] = Radius of the planet’s orbit squared.

We can now locate a planet’s ecosphere boundaries in astronomical units.

1AU (astronomical unit) = 93 million miles

A planet whose rotation was being severely retarded might lose all of its surface water through photo-decomposition before the planet’s rotation was finally arrested. Once rotation was stopped, the planet might continue to orbit with one side always facing the parent star or it could enter a situation where one day equals a year.

Arrested planetary rotation
On planet which always present the same face to their Sun, the exposed side would be very hot and dry. If free water still existed on the planet it would have precipitated out of the atmosphere on the dark side and would exist as an ice pack. Wind circulation might follow the pattern: Cold, dry air flowing from the dark side would become hotter and hotter after it crossed the terminator (from darkness into light) to the exposed side of the planet. The vapor pressure deficit would cause rapid evaporation of any water brought to the surface by geysers, etc. As the winds move toward the center of the illuminated surface, they heat and rise higher and higher. This would in effect create a gigantic, permanent low pressure system on the illuminated side and a permanent high pressure system on the dark side.

One day equals a year 
On a planet with arrested rotation, where one day equals a year, the same type of atmospheric circulation would exist. Cool air would  cross the terminator near ground level, it would heat, rise and eventually flow back to the dark side. There is however, a major difference, the hot part of the planet and icepack would be in slow, but constant motion, around the planet as the year progressed. In this case, there would be an area associated with the moving terminator where water would exist in liquid form; however, it might do so for only a few weeks in any area.

The larger life forms we are attempting to resolve in this study, would probably not evolve on a planet whose rotation was arrested. It would be theoretically possible for such life to develop on a  arrested planet about a very cool star providing the parent star was part of a binary star system; SRAPO, however, does not directly address binary star systems.

We will then draw a general conclusion: Life as we know it will not exist on planets orbiting Main Sequence stars of spectral class K2 or lower, providing the star is isolated and not part of a binary or other complicated orbital star system.

Continued in Chapter 3: Climatic Factors

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What is SRAPO?

SRAPO¹: A Pursuit in Exobiology
Developed during the years 1965-2011, by Larry F. Pierce
[Above: The Carina  constellation]

Have you ever looked up at the myriad of stars sprinkled across the sky on a clear and beautiful warm summer night…and wondered? Did you wonder if perhaps a creature living on a planet around one of those far away lights was looking at his night sky too? …and perhaps just at the moment you were looking at his home star, he was looking across the gulf of space at our sun…and you were both wondering about one another. Did you wonder what the alien might look like? Did it ever cross your mind to wonder what he’d see when he stopped staring into the night sky, and again looked around at his own familiar surroundings? What if you could look through his eyes?

Imagine its late in the afternoon, almost dusk and you’re whisked away, then set down safely, but elsewhere on planet Earth. Without knowing your location, maybe you were set in any of these environments (see photographs below and imagine the sensations): Sahara desert; Death Valley; the Kalahari desert; the Eurasian Steppes;  US prairie; prairie-woodland;  woodlands of the eastern USA; the Pantanal Swamp; tropical Kauai, Hawaiian;  forests of central Oregon; the Tundra of northern Canada; the dry valleys of Antarctica, island chains, the shore of a continent… You’re standing there in one of those environments…its twilight, the colors have largely faded into grays. You look about, while feeling the temperature and humidity; you can  identify the general type of environment you have been set in. You can tell whether the vegetation is tall or short, thick or spindly, dense or thinly spread about, there may be sounds and smells carried in the air. Kicking at the ground you can just see whether the soil is sandy, composed of pebbles, whether its rocky, or covered by some type of  ‘organic’ matter. The things you sense and see about you are the way they are for a reason.


If you were not on Earth, but instead on a habitable planet about one of those distant stars, the things about you would still be the way they are, for a reason. Large habitable planets are generally quite wet, small ones are much drier; very hot or dry environments are likely to have water or temperature as the limiting factors for intelligent life; high relative gravity favors short and squat forms; high relative ultra violet ‘sunlight’ favors protective pigmentation; increasing planetary axial inclination favors life form mobility and hibernation…

SRAPO is a construct, a filtering lens that removes the unreasonable and focuses on the probable.

What is SRAPO?
Exploring the Construct
Book Introduction
Chapter 1: Water
Chapter 2: Average Planetary Surface Temperature
Chapter 3: Climatic factors
Chapter 4: Atmospheric Circulation
Chapter 5: Atmospheric Retention
Chapter 6: Stellar Parameters
Chapter 7: The Morphology of Intelligent Life
Chapter 8: Into A New World
Chapter 9: Data Correlation
Chapter 10: Templates
———————————-
Note 1: SRAPO is an acronym for Stellar Radii and Planetary Orbits)

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