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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