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Extending the Artificial Habitability Zone to Pluto?Payton E. Pearson III

B.S. Electrical Engineering, 1LT USAFOffutt Air Force Base

payton.pearson.1@us.af.mil

Abstract—This paper—the second in a series of papers expanding upon this topic—seeks to show how the habitability of various celestial bodies throughout the universe can be engineered, nearly regardless of distance from the host star. An atmosphere is hypothetically engineered and shown to be theoretically viable on the dwarf planet, Pluto. This hypothetical atmosphere is engineered to be 280 Kelvin at the surface of Pluto, with half the atmospheric pressure of Earth’s surface (~506 mbar). Nothing else is significantly changed; though an explanation of possible modification of orbital dynamics is posited, placing Pluto in a 390,000 kilometre orbit around a previously designed hypothetical planet, PH. This paper will refer back to the original artificial habitability paper for certain ideas. As with the last paper, the hope in creating this series is to galvanize the interest of prospective scientists, and stimulate discussion on the matter of astrogeophysical engineering.

Keywords— Pluto, magnetosphere, habitability zone, equilibrium temperature, hypsometric equation, Universal Law of Gravitation, solar flux, atmosphere, atmospheric mass, sputtering, orbital dynamics.

I. INTRODUCTION

So, what is it that makes a celestial body naturally habitable? Of course, temperature is a key factor in that the surface temperatures of a celestial body must be adequate to support complex life in some form. Also, atmospheric pressure at the surface is vital, because most organisms require some form of inward pressure in order to sustain physiological equilibrium. In addition to this, metabolism requires some form of sustenance from an atmosphere to allow for more complex life to eventually develop. Once more, the lowest trophic levels of life on Earth oftentimes utilize some form of photosynthesis for metabolic purposes as well, though some extremophiles have been known to utilize chemical processes of Earth instead.

Nevertheless, taking into consideration these basic components to developing complex life on a celestial body, the dwarf planet Pluto, which orbits the Sun at a variable distance between 4 and 7 billion kilometres depending on whether it is at apogee or perigee, the notion of rendering such a distant, cold, dark celestial body habitable sounds absurd. This paper will show that it may not be as absurd as some think.

II. BASIC PARAMETERS OF PLUTO

The dwarf planet Pluto is an icy world that orbits the Sun at a maximum distance of 7.311 billion kilometres and a minimum distance of 4.437 billion kilometres. This large variation in distance of Pluto leads to equitably large variations in surface temperature. The surface temperature of Pluto can be derived

using the equilibrium temperature equation, assuming that Pluto is currently in temperature equilibrium [1].

T eq=4√ L° (1−α )

16πσ RAU2 (1)

Where Lo is solar luminosity (3.839x1026 watts), α is the albedo of the celestial body in question, σ is the Stefan-Boltzmann constant (5.670373x10-8 w/m2K4), and RAU is the distance in meters from the Sun of the celestial body. Using Pluto’s minimum distance from the Sun and its albedo of 0.55, Pluto’s surface temperature reaches a maximum of:

T eq=4√ L° (1−α )

16 π RAU2 =4√ (3.839 x 1026W ) (1−0.55 )

16 πσ ( [ 4.437 x 1012m ]2 )¿41.8883 Kelvin

The same calculation used with Pluto’s maximum distance from the Sun reveals a minimum surface temperature of Pluto of 32.6324 Kelvin. This implies a temperature variation of 41.8883 – 32.6324 = 9.2559 Kelvin, or approximately 16.66 degrees Fahrenheit. This means that while there would be significant swings in the average surface temperature of Pluto, these swings would not be so drastic as to render Pluto completely uninhabitable. So far, in Earth’s astronomers’ relatively limited understanding of the universe, exoplanets have been discovered that have temperature swings of several thousands of degrees Fahrenheit, going from -150 degrees to 850 degrees Fahrenheit over the course of 30 months [2]. Earth experiences relatively constant temperatures, as its closest approach to the Sun puts it just shy of 92 million miles away, and its farthest distance puts Earth at about 95 million miles away from the Sun. This stability is a major contributing factor to the development of the complex ecosystems present on Earth today.

But a 16.66 degree variation is not unacceptable, especially considering that humanity will have the ability to engineer the biosphere of Pluto from scratch. Seeing as how this is the case, temperature variations will nevertheless be a crucial component to understand in order to attain environmental stability.

Another important component to the engineering of Pluto’s atmosphere is the extremely low gravity when compared to Earth. Pluto has a gravitational acceleration at its surface of 0.658 m/s2. This is a mere 6.71% of the gravitational acceleration at the surface of Earth. With such a low gravitational acceleration, a

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proposed atmosphere for Pluto of any significant mass would be exceptionally distended compared to that of the Earth. These calculations will be elaborated upon later in this paper. But beyond this, there comes the issue of atmospheric sputtering due to solar wind, a mechanism that caused the atmosphere of Mars to dissipate from approximately the same surface pressure of Earth to what it is today over the course of 10 million years [3].

The design parameters that Pluto will be engineered to have are as follows:

Atmospheric Pressure of PH = 0.506 barDesired Average Surface Temperature = 280 Kelvin

No other bulk parameters of Pluto will be changed for the purposes of this design.

Fig. 1 This is an artist’s interpretation of how the surface of Pluto might look currently. This would change drastically with the introduction of a liveable atmosphere.

III. PRODUCING THE ATMOSPHERE FOR PLUTO

The most difficult hurdle to overcome when producing an atmosphere for the dwarf planet is the extremely low gravity at the surface. This would cause any atmosphere that would be produced to be exceptionally distended and possibly unstable, perhaps becoming several dozens of times the height of that of Earth’s atmosphere as defined by the Karman Line. This is evidenced through the fact that Pluto’s atmospheric scale height is much greater than Earth. It is calculated as follows [4]:

hscale=kTmg

(2)

Where k is the Boltzmann constant (1.38x10-23 J/K), T is average surface temperature in Kelvin, m is average mass of the atmosphere in kg of atoms, and g is the gravitational acceleration at the surface. Pluto’s atmosphere would more than likely be composed of very similar elements to that of the Earth. This is because the surface of Pluto is comprised in large part of water ice as well as N2 ice. This greatly simplifies the equations of the atmospheric scale height, as the same atmospheric mass per particle that is used for Earth can be assumed for Pluto [4]. In this case, the atmospheric mass per

particle is 4.76x10-26 kg [4]. An average surface temperature of 36 Kelvin will be used for this hypothetical example.

hscale=kTmg

= (1.38 x10¿¿−23 J /deg )(36 K )(4.76 x10¿¿−26 kg)(0.658 m /s¿¿2)=15.886 km¿¿

¿

Compare this to a scale height for Earth’s atmosphere of roughly 8.7 kilometres. This may not seem like a very drastic difference, but this alone can cause the atmosphere to be roughly 1.826 times as distended, for an atmospheric thickness of 182.6 kilometres based upon the Karman Line of Earth. This approaches 16% of the overall radius of Pluto. Once more, this does not even take into consideration the fact that this design is intended to increase the average surface temperature of Pluto to 280 Kelvin. As such, the scale height of such an atmosphere would be 123.6 kilometres. This would potentially increase the thickness of a Plutonian atmosphere to 1421 kilometres, or roughly 120% the radius of Pluto itself.

As can be seen clearly, this would produce an atmosphere that is utterly gigantic by comparison to the size of Pluto. But is this truly a problem? Before this question can be answered, a more accurate estimate of the thickness of Pluto’s atmosphere must be found. We will use the hypsometric equation under the engineering assumptions of temperature and surface pressure to find the overall thickness of the atmosphere. The hypsometric equation is as follows [4]:

hatm=R ∙T

g∙ ln( P1

P2) (3)

Where R is the specific gas constant of the atmosphere. Assuming it is identical to the Earth, it is 287.058 J/kgK. T is the mean temperature of a specified atmospheric layer. As was done in a previous paper [5], we will use the Earth’s atmospheric temperature profile in order to find the temperatures of the respective layers of Pluto’s hypothetical atmosphere. Also, g is the gravitational acceleration of the celestial body with respect to distance above the surface. P1 and P2 are the pressures at the top and the bottom of the layer of atmosphere in question.

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Fig. 2 Earth’s temperature and composition profile as a function of elevation above sea level. As can be seen clearly, the temperature profile does not follow a simple, linear path, but instead is a conglomeration of discrete functions.

It is important to note that if Pluto were heated up to terrestrial temperatures, it would likely take the form of a giant water ball, also known as a water world. This is because a large proportion of the overall mass of Pluto is in fact comprised of water ice, in particular the surface and upper mantle. Once more, a significant layer of frozen nitrogen lies on the very topmost portion of Pluto’s icy crust. The ramifications of the presence of this nitrogen ice will be elaborated upon later.

Fig. 3 This figure shows the dwarf planet Pluto with an engineered atmosphere around it. The distention of 1660 kilometres will be explained shortly.

The total height of the atmosphere will be the addition of several discrete atmospheric layers. The thickness of the atmosphere will thus take the following form:

htot =h1+h2+h3+…+hn (4)

Assuming that one half the proportional pressure of the Plutonian atmosphere corresponds to the atmospheric pressure of the Earth’s atmosphere with respect to the atmospheric layer in question, the temperatures of each layer of atmosphere using the average area theorem are [6]

h1 , 506¿82.552mbar : 280 K+210 K2

=T 1=245 K

h2 , 82.552¿ 43.933 mbar : 210 K+210 K2

=T 2=210 K

h3 , 43.933 ¿5.0412 mbar : 210 K+216 K2

=T 3=213 K

h4 ,5.0412¿0.3797 mbar : 216 K+262 K2

=T 4=239 K

h5 , 0.3797 ¿0.1533 mbar : 262 K+242 K2

=T 5=252 K

As was done in the previous paper in this series [5], the termination point of Pluto’s atmosphere is based upon the pressure at Earth’s Karman Line, not upon the derived Karman Line of Pluto itself, which would be much higher. Other methods can easily be proposed, but this method proves to be adequate for the endeavour, and simplest. The atmospheric temperature profile is thus as follows:

Layer P1 (mbar) P2 (mbar) Tmean (K)H1 506.000 82.552 245H2 82.552 43.933 210H3 43.933 5.0412 213H4 5.0412 0.3797 239H5 0.3797 0.1533 252

Table 1 This is a more organized view of the mean temperatures with respect to the pressure layers. It is important to note that with a much lower equilibrium temperature, the drop off in temperatures past the troposphere would likely be much more dramatic. It must be emphasized that this is merely an engineering approximation. To lend credibility to this approximation however, Titan does not experience such an exponential drop-off in temperature with respect to height until far beyond the Karman Line [7].

Now that the mean temperatures of each atmospheric layer have been found, we can find the thickness of each layer as follows:

hatm=R ∙T

g∙ ln( P1

P2)→ h1

¿(287.058 J

kg∙ K )∙ (245 k )

0.658 ms2

ln( 50682.552 )

¿194,191.6793 metres

This will be done for each respective atmospheric layer. It is very important to note, however, that the gravitational pull

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experienced upon each atmospheric layer is significantly different. Thus, the gravitational pull will need to be recalculated for every layer. Rather than integrating over the entirety of the distention of the atmosphere, a simple recalculation of the gravitational pull at the top of each atmospheric layer will be accomplished for simplicity purposes.

Calculating the gravitational pull of Pluto with respect to height above the surface is done as follows [8]:

F1,2=GM 1 M 2

r2 (5)

Where F1,2 is the force between two bodies of mass (M1 and M2), G is the gravitational constant (6.67384x10-11 m3/kg s2), and r2 is the distance between the two bodies from each respective centre of mass. In the instance of a single celestial body, r2 is simply the radius of the planet itself plus the height above the surface. In addition, if M2 is of small enough mass, it can be omitted, and an approximation of the force due to gravity of Pluto can be found using the equation:

FG, Pluto+h=GM Pluto

(r+h)Pluto2 (6)

¿(6.67384 x10−11 m3

kg ∙ s2 ) ∙(1.305 x1022kg )

([1.0 x107 m ]+[1.941916793 x103 m ])2

¿0.4547 ms2

As can be seen, this is significantly different from the gravitational pull at the surface of Pluto, 30.89% less to be more precise. This will significantly increase the overall size of Pluto’s atmosphere. The table below shows the overall thickness of Pluto’s atmosphere:

Layer Thickness (m) Gravitational Pull (m/s2)

H1 194,191.679 0.658H2 83,622.610 0.4547H3 324,856.529 0.4075H4 633,997.100 0.2706H5 421,219.800 0.1477Htot 1,657.890 km N/A

Table 2 This table is an organized form of the above equation iterated over each pressure interval using the Universal Law of Gravitation to recalculate the gravitational pull at each height.

This atmosphere is absolutely gigantic, roughly 1.4 times the actual radius of Pluto itself. However, even with this very large atmosphere, there is nothing preventing it from being sustainable, as will be illustrated. In addition, the current estimates for the upper limits of the atmosphere that Pluto already has indicate that it is well over 1200 kilometres above the Plutonian surface [9].

IV. THE EFFECTS OF SPUTTERING ON A PLUTONIAN ATMOSPHERE

The primary issue with developing such a humongous atmosphere around the dwarf planet Pluto has to do with the sputtering effects generated by the Sun as well as other celestial bodies with significant magnetic fields. However, Pluto is roughly 39.2 times as far away from the sun as the Earth, indicating that the magnetic field of the Sun is 60,532 times weaker because magnetic field strength is inversely proportional to the cubed distance from a specific frame of reference [10].

B∝ 1d3 (7)

Using the planet Mars as a rough guide of atmospheric sputtering, we can determine how long it would take to sputter away an engineered atmosphere from Pluto. During the epoch when Mars had a significant atmosphere, it is assumed that Mars’ atmosphere was roughly equivalent to 1 bar of pressure, or very nearly the surface pressure of the Earth [11]. Despite this, once the dynamo of Mars dissipated, it took a mere 10 million years to dissipate the atmosphere from Mars [12]. Using the atmospheric mass equation, the rate of atmospheric sputtering can be derived [4].

matm=4 π a2 P s

g (8)

Where a is the radius of the celestial body, Ps is the surface pressure of the atmosphere, and g is the gravitational pull of the celestial body at the surface. As such, the atmospheric mass of Pluto, and that of a proto-Mars for approximation purposes is

matm ,Pluto=4 π (1.184 x106 m )2 (50,600 Pa )

(0.658 ms2 )

¿1.3547 x1018 kg

matm , Mars=4 π (3.396 x106m )2 (101,300 Pa )

(3.711 ms2 )

¿3.9561 x 1018 kg

With Mars’ atmosphere having dissipated down to a mere 2.3432x1016 kg mass over the course of 10 million years, this means that Mars’ atmospheric loss rate was approximately

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3.9561 x 1018 kg−2.3432 x1016kg=3.9327 x1018 kg10million yrs

¿12,470.41 kg/ second

Based upon this rate alone, it would take roughly 3.447 million years for the engineered Plutonian atmosphere to dissipate. However, as gravitational pull decreases, the effects of sputtering are amplified. Also, as distance from the Sun increases, sputtering effects are decreased due to a decrease in solar magnetic field strength. As such, the gravitational pull at the top of the hypothetical Plutonian atmosphere will be used for the most conservative estimate of dissipation rate. Since the dissipation rate is a three-dimensional effect, the effect of sputtering will be cubed.

R sputter=( gMars

gPluto)

3

(9)

R sputter=( 3.147 ms2

0.1477 ms2 )

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=9,672.7×the effect

3.147 m/s2 is the gravitational pull at the top of Mars’ theorized atmospheric sputtering layer. But taking into consideration Pluto’s distance from the Sun in astronomical units as opposed to Mars’ distance from the Sun, the magnetic effect, as shown in equation (7), is drastically decreased. This reduces the sputtering effect by a factor of

R s ,magnetic=( 39.264 AU1.665861 AU )

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=13,094×less effect

This reduces the overall rate of sputtering by 26.1%. Though, it must be noted that this is quite a conservative estimate of the sputtering effect. The lowest gravitational pull of Pluto was used, as well as the three-dimensional rate of sputtering [11]. Nevertheless, this means that such an atmosphere on Pluto would face depletion over the course of 4.35 million years. This is within an order of magnitude of the dissipation rate that could be expected on an engineered Martian atmosphere, which is acceptable, though a means to avoid this sputtering will be discussed shortly.

Fig 4 This figure shows a graphical (and exaggerated) representation of the Sun’s sputtering effect on a familiar celestial body, Mars. This effect is what led to Mars’ atmosphere to being siphoned off over the course of several million years.

V. FINDING A MEANS TO INCREASE TEMPERATURE

The mean surface temperature of Pluto is approximately 36 Kelvin, yet the desired surface temperature is 280 Kelvin. This is a difference of 244 Kelvin, inarguably a humongous required temperature increase, but it isn’t as difficult as some might expect. Using the mean temperature equation developed by Dr. Robert Zubrin and Dr. Chris McKay, the temperature change at the surface of Pluto with respect to an introduced atmosphere can be approximated [3].

T mean=T eq+20(1+S) P0.5 (10)

Where S is the average solar output as a function of the Sun’s age (we will assume it is always 1), and P is the atmospheric pressure of the planet in bars at the surface. I have further altered this equation to include the difference in atmospheric thickness as a means of absorbing more solar energy, as I did in a previous paper [5].

T mean=T eq+20(1+S) H0.5 P0.5 (11)

Where H is the ratio of Pluto’s atmospheric thickness to the atmospheric thickness of Earth. For instance, if Earth’s atmospheric thickness is 100 kilometres, and Pluto’s atmospheric thickness is 300 kilometres, then the ratio would be 3. As the thickness of an engineered Plutonian atmosphere has been previously determined, the mean surface temperature of Pluto would increase to

T mean=36 K+20 (16.57890.5 ) (2 ) (0.506 mbar0.5 )

¿151.854 Kelvin

This still makes the required temperature increase 280 – 151.854 = 128.145 Kelvin. This difference can be overcome using super greenhouse gases.

VI. HEATING UP PLUTO WITH GREENHOUSE GASES

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The greenhouse effect on planets is still only scarcely understood at this point in human history. Though, some valuable information can be gleaned from the body of knowledge that has been developed thus far. From examples such as Venus, we can see that a runaway greenhouse effect on entire planets is not an uncommon occurrence, for it has happened once in our own solar system. If we look at the giant moon, Titan, we can see how having an atmosphere at all acts as a blanket upon the surface of a celestial body, heating it significantly above the solar equilibrium temperature. Then beyond this, we can see how a rarefied atmosphere such as that found on the moon can cause huge temperature swings. Even further, we have Mars, with such a tenuous atmosphere that a human being would instantly embolize without a pressure suit at its surface. The atmosphere of Pluto will be engineered in such a way as to minimize distention above the surface, thus minimizing possible sputtering effects, while simultaneously providing sufficient surface pressures to adequately sustain life.

As it is, we are distinctly aware of the necessity of having a thick atmosphere that contains healthy amounts of heat-trapping molecules, such as water vapour, CO2, methane, and other gases. To figure out exactly how much greenhouse gas would need to be produced on Pluto, we must refer to the Earth’s atmosphere, and how it has evolved over the past 110 years due to human-induced global warming. The chart below shows the increase in CO2 in the atmosphere of Earth in parts per million over the past 50 years, just to give an idea of this. The up-and-down pattern in the chart is due to the seasons; there is a greater land mass in the northern hemisphere of Earth as opposed to the Southern. As a result, the change in seasons sees a change in the total number of carbon-absorbing plants in bloom. However, the chart still shows a very clear trend upwards in CO2 levels [13].

Fig 5 This chart shows the increase in CO2 levels on Earth from 1960 to present day.

Over the past 110 years, the global increase in temperature has been approximately 1 degree Celsius. During that time, we need to determine how much CO2 humans have added to the atmosphere. The chart below shows the yearly CO2 production by humans during this time interval.

Fig 6 This chart shows the total production of CO2 from 1900 to present day in teragrams [14].

Over the course of the past 110 years, approximately 30,000 teragrams of CO2 has been emitted into the atmosphere. This equates to 3.0 x 1013 kg. Thus

3.0 x 1013 kg0.9℃ =3.3 x 1013kg

1℃

A different method will be used in this engineering design compared to my previous paper [5]. Rather than using atmospheric volume to determine the total amount of CO2 required, atmospheric mass will be used to determine the amount of CO2 required. This is much more accurate than a volumetric measurement because the density of any proposed atmosphere decreases rapidly with altitude. This would mean that the volumetric measurement of atmosphere would yield much larger atmospheric numbers than a mass measurement. This is thus more conservative. However, it was merely done as an engineering exercise and will not be reproduced in this design.

As such, having already calculated the atmospheric mass of a ½ bar Plutonian atmosphere as 1.3547x1018 kg, we can compare this to the overall mass of the Earth’s atmosphere. Earth’s atmosphere is roughly 5.27x1018 kg [4, 15]. This means that the proposed atmosphere of Pluto is only 25.71% as massive as that of the Earth. This then means that only 8.483x1012 kg of CO2 is required for the same ppm increase on Pluto, and thus the same temperature change. It must be noted that such a calculation is still a very inexact science at the current level of understanding of atmospheric evolution. It is not yet known if temperature increases are purely based upon ppm compositions of different elements, or if it has to do with a variety of other factors, such as atmospheric thickness, surface area of the proposed celestial body, etc. We will operate under this assumption, however, for this particular engineering design.

Nevertheless, producing this much CO2 is a Herculean effort. Let’s consider a standard 600 MW coal power plant operating at full capacity 24/7. The amount of CO2 produced per kilowatt hour (kWh) is as follows:

Type of Coal CO2 Produced (lbs/kWh)Bituminous Coal 2.08

Sub Bituminous Coal 2.16Lignite Coal 2.18

Average 2.14

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Table 3 This table shows the amounts of CO2 produced based upon the type of coal used [16].

With an average of 2.14 lbs. of CO2 produced per kWh, a single 600 MW power plant would produce

1,000 kWh1MWH

∙ 2.14 lbs.1kWh

∙ 1kg2.2lbs .

=972.7 kgMWH

972.7 kgMWH

∙ 600 MW1 Power Plant

∙ 24 hr1 day

∙ 365 days1 yr

¿5.113 x109 kgpower plant yr

As a conservative estimate, the maximum atmospheric pressure will be used for determining ppm composition of Pluto’s atmosphere. This is important because the current mass of the Plutonian atmosphere, which has a pressure of only 0.3 Pascals at the surface, is only roughly 8x1012 kg. This would mean it would take 1 5 MW power plant 1 year to heat up the Plutonian atmosphere by 1 degree Celsius. Since we do not know whether this is the case or not, and the atmospheric pressure would increase exponentially with the number of power plants producing gases in addition to the melting of surface ices, the most conservative means of determining greenhouse warming of Pluto is to assume its maximum desired surface pressure at the beginning.

In addition, these power plants are not optimized to produce the maximum amount of CO2, so it is likely that tens to hundreds of times the amount of CO2 could potentially be produced from the same amount of coal if such a thing were desired.

Under these assumptions, it would take 1,659 600 MW power plants to increase the surface temperature of Pluto by one degree Celsius in one year. However, a temperature rise of 128.145 Kelvin is required, which means that it would take 212,606 power plants to produce such a temperature change in one year. Though, this is predicated under the assumption that the same amount of solar energy is received by Pluto as that of the Earth, which is not the case. The amount of solar energy that Pluto receives with respect to Earth is

I∝ 1d2 (12)

I∝ 1d2 =

1(39.264 )2

∙ 100=0.0649% Eart h' senergy

Where I is the solar energy intensity, and d is the distance in astronomical units from the Sun. This means that the Earth receives 1542 times the solar energy of Pluto, which thus means it would require 327,766,265 power plants to achieve the required temperature change in one year. This number is astronomical, but as we will find, it is astronomically reduced by yet more factors.

First of all, CO2 does not need to be the greenhouse gas of choice. If, instead, we choose to use SF6 (sulphur hexafluoride) for

greenhouse warming of Pluto, then the situation changes. SF6 is 20,000 times as efficient at trapping solar energy when compared to CO2 [12]. This means that it would require 20,000 times less SF6 for the same temperature change. Thus, the mass required for the same temperature increase becomes

1.676 x 1018 kg20,000

=8.379 x1013 kg

This reduces the number of power plants required to 16,388. But the efficiency of SF6’s heat trapping is not based upon a per mass basis, but a per molecule basis. This means that

146.054 gmol

44.001 gmol

=3.32×the mass required

¿ (8.379 x1013kg ) (3.32 )=2.782 x 1014 kg

Increasing the number of power plants required to 54,408. However, the temperature increase does not need to be accomplished in a single year. Indeed, such an engineering endeavour would be planning for the long term. Thus, the timescale could reasonably be increased to 100, 1,000, or even 10,000 years. If the timescale is increased to 1,000 years, the number of power plants required decreases to 54.408 or approximately 55. This atmospheric production would constitute only approximately 0.021% of the overall atmospheric mass, and thus would not significantly change the specific gas constant, thus leaving the distention of the atmosphere and all other figures derived from it unchanged.

In addition to using SF6, such greenhouse gas-producing power plants would be optimized to produce said greenhouse gases, likely increasing the amount produced per MWH by a factor of 100. With this taken into consideration, the total number of power plants is reduced to 0.54408, or one 330 MWH power plant.

But what about atmospheric loss due to sputtering? Determining the amount of atmosphere lost per year due to sputtering is as follows:

12,470.41kgsecond

∙ (9,672.7 gravity effect ) ∙( 113,094 magnetosphere effect )

¿9,212 kg /second

A single 600 MW power plant produces 162.1 x (efficiency factor increase=100) = 16,210 kg of atmospheric gases per second. This means that at least 0.5683 power plants would be required simply to overcome the sputtering effects caused by the Sun at this distance. Thus, the grand total number of power plants required to produce a significant atmosphere on the surface of Pluto is slightly more than one for a 1,000-year period (1.112). This makes for a total of 670 megawatts of energy production on Pluto. However,

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taking into consideration the maximum gravitational pull of Pluto and the initial rarefied atmosphere, it would take no more than one 30 MW power plant to begin the terraforming effort at first.

These figures are not so ridiculous as to be entirely unfathomable. Human civilization has only been in existence in an organized fashion for roughly 10,000 years. Technological innovation has only in the past 200 years reached true prominence. In the last 200 years alone, humanity went from barely having invented the steam locomotive to sending probes billions of miles into space. With the exponential growth in technology and innovation, attaining a 670 megawatt energy production capacity on a far-flung world may seem inconsequential 1,000 years from now. Indeed, on Earth, it already is, with global energy production topping countless terawatts per year [17].

VII. OTHER CRUCIAL ATMOSPHERIC EFFECTS

An important factor to take into consideration when engineering an atmosphere on Pluto is the large amount of frozen nitrogen on the surface of the planetoid. Based upon the vapour pressure of N2

that constitutes Pluto’s tenuous atmosphere, it can be assumed that there is anywhere between several million, to several tens of millions of square kilometres of frozen N2 on the surface [18]. N2

turns into a gas at approximately 77.355 Kelvin [19], which means that a temperature increase of only roughly 41.355 Kelvin would be necessary to cause the entire bulk of surface N2 to boil off or sublime.

Fig 7 This figure shows liquid nitrogen as it appears on Earth. While much of the liquid boils off into gaseous nitrogen on our home world, on Pluto, N2 would not reach sublimation temperature for quite some time. However, once it did, a massive atmosphere would likely result.

The question then becomes, how much of this N2 is there, and how much of it would be required to cause a runaway atmospheric genesis? If this occurred, which is highly likely based upon the temperature increase, producing an atmosphere on Pluto would no longer be an issue; the only remaining issue would be increasing the temperature of said atmosphere. This same runaway atmospheric genesis is believed to be fundamentally possible on

Mars as well, only with different molecules constituting the Martian atmosphere [3].

Frozen N2 has a mass of 1.027 g/cm3. The mass of atmosphere that needs to be produced is

1.3547 x1018 kg−8.032 x 1012 kg=1.3547 x 1018kg

∴negligible natural atmosphere

With these numbers, we can determine the volume of solid nitrogen required in order to produce a significant atmosphere.

1.3547 x 1018 kg ∙( 1,000 g1 kg ) ∙( 1 cm3

1.027 g )∙( 1 m3

1003 cm3 )∙( 1km3

1,0003 m3 )=1.3191 x 106 km3

With this, we can then find the required average thickness of a nitrogen ice layer on the surface of Pluto. This is done as follows:

T N 2layer=43

π (r Pluto )3− 43

π (r Pluto−r Nitrogen )3

¿1.3191 x 106 km3

∴T N 2layer=1184 km−1183.925km=0.07488 km3

Of course, this is assuming an equal distribution of frozen N2

over the entirety of the Plutonian surface. Current models predict that the amount of frozen N2 on the surface of Pluto is not equally distributed, but patchy. This is evidenced through the unequal albedo of Pluto’s surface, as shown in the figure below. Even so, this estimation for N2 abundance is highly likely to be extremely conservative, with Pluto’s surface possibly covered in patchy layers of frozen N2 several kilometres thick [18].

Fig 8 This figure shows the clearest images of Pluto’s surface to date, as viewed through the Hubble Space Telescope.

One way or another, an average thickness of 0.07488 km3 is more than reasonable, and even expected when more accurate measurements of Pluto’s surface are received by the New Horizons

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space probe, which will reach Pluto in mid-2015 [20]. This frozen nitrogen layer has very important ramifications on the ease of terraforming Pluto. If this nitrogen layer is indeed present, it would mean that the surface of Pluto would only need to be heated by slightly more than 40 Kelvin before a runaway atmospheric thickening would occur. However, this would also significantly change the albedo of Pluto’s surface, as frozen nitrogen has different reflective characteristics when compared to clean, frozen water. Clean, frozen water has an albedo of approximately 0.8 [21]. With this increase in albedo, the equilibrium temperature of Pluto would decrease from its current 36 to 44 Kelvin down to

T eq=4√ L° (1−α )

16 π RAU2 =4√ (3.839 x 1026W ) (1−0.8 )

16 πσ ([5.874 x 1012m ]2 )¿29.725 Kelvin

The difficulty that arises from this decrease in temperature is maintaining a subsequent increase in temperature of the surface that outpaces the boiling off of frozen nitrogen and thus increase in albedo of the surface of Pluto. This should be easily overcome, as it takes several hundreds to thousands of years for a celestial body to reach a new equilibrium temperature with a significant change in albedo, but nevertheless, it must be addressed in some way here. This decrease in surface temperature of Pluto would then change the mean surface temperature based upon Zubrin and McKay’s equation to roughly 145.579 Kelvin.

This is still well beyond the boiling temperature of N2, and thus should not pose any noteworthy issues. Though, it is possible that during the early stages of Pluto terraforming, N2 ice could sublime into gas, and quickly form back into ice. Until a certain critical point of sublimation rate is reached, Pluto will revert back to a natural state of equilibrium with frozen N2. This is a negative feedback system, but it can be broken with a significant engineering effort. Such an effect is also theorized to be expected in a terraforming effort on Mars [3]. The figure below shows two separate equilibrium temperatures for Mars’ surface.

Fig 9 This graph shows an example of two different equilibrium temperatures on Mars. Such a situation could also be experienced on Pluto, once sufficient frozen nitrogen is sublimated to produce a massive and warmed atmosphere.

It must be understood that Pluto will never have a surface truly similar to that of the Earth in that, because of Pluto’s composition due to its distance from the Sun, its surface will become covered in liquid water. Pluto is comprised approximately of equal parts water ice and silicate rock [18], but its surface in particular has a large amount of frozen water mixed with frozen nitrogen and methane. Indeed, warming Pluto would likely turn it more into a mini-water world, rather than a super-low-gravity Earth. It is possible that small patches of solid rock land formations would be present, but below the rock-ice mantle of Pluto lies what is believed to be a liquid ocean. Any solid landforms would be nothing more than mere floating islands.

Nevertheless, due to the lack of tectonic plate movement on Pluto because of its very small size and low internal heat, such landforms would likely not risk devolution below the liquid layer to any large degree. This is also due to the low amount of solar energy that Pluto receives. With such a low solar energy, the wind currents in an engineered Plutonian atmosphere would be very subtle, perhaps almost non-existent. This is evidenced through the giant moon, Titan, where surface winds at peak intensity reach no higher than 5 miles per hour [7]. This is compared to Earth, where average surface winds are approximately 20 miles per hour. The giant moon, Titan, orbits at a distance approximately 10 times farther away from the Sun than the Earth. This means that a rocky Plutonian surface would not face extreme erosion due to winds, and thus any solid rock formations would remain for an exceptionally long period, perhaps indefinitely.

Fig 10 This figure shows the giant moon, Titan, as viewed in false colour. This image provides a view of the surface of Titan while at the same time clearly showing the massive size of the moon’s atmosphere.

But a water world Pluto does not pose significant problems, and in fact, in some ways it makes terraforming easier. Water has a low albedo compared to other possible surface compounds, such as silicate sand. This means that Pluto would absorb more solar energy, and thus would require less constant heating from greenhouse gas production. So, while the equilibrium of Pluto would be difficult to move past the nitrogen sublimation stage,

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once done, a slow evolution towards a liquid water stage could be a much easier transition.

Fig 11 This figure shows an artist’s concept of a cold water world. As can be seen clearly, this planet has very large polar ice caps and is shrouded in thick cloud layers.

One of the biggest barriers to having a water world is that there is little to no surface for photosynthetic plants to take root. Though, thankfully, water can make up for a large portion of the oxygen issues due to its molecular structure. Water naturally breaks down into its constituent elements over long periods of time, albeit in rather small amounts [4]. But, over several thousands to several millions of years, this can produce enough atmospheric oxygen to render a water world’s atmosphere breathable, perhaps even more so than a planet covered in vegetation.

VIII. LUMINOSITY AND PLANT LIFE ON PH So, we have discussed how to actually make Pluto warm enough

for humans to comfortably survive at the surface without pressure suits or body-heating apparatuses. But how habitable is it to the flora and fauna upon which human society so keenly relies to thrive? At these distances, it truly does start to become very difficult for plant life to proliferate. Unlike PH, a previously designed hypothetical planet over 2 billion kilometres distant from the Sun where light levels were still significant enough for some of the most shade-tolerant plants to thrive, on Pluto, the issue becomes entirely different. Pluto receives only 0.0649% the sunlight that the Earth receives (0.883 watts/m2), and only 16.73% the sunlight that PH receives (5.281 w/m2) [5]. In addition to this, while it may be possible to genetically engineer plants to live in such low light levels, Pluto will likely have no solid surface, as previously stated. This means that any flora would need to be birthed deep beneath the Plutonian surface, in the depths of an ocean. This surface ocean could be anywhere from several hundreds of meters to several hundreds of kilometres thick. At the bottom of such an ocean, even in the shallowest locations, solar luminosity would be practically zero.

Nonetheless, even in these extreme circumstances, there are workarounds. First of all, assuming Plutonian flora would be genetically engineered to endure the low light levels, such photosynthetic flora could float at the surface of a Plutonian ocean, much in the way that seaweed floats through the ocean on Earth. This would mean that any sunlight that Pluto does receive could be absorbed by these floating plants with minimal oceanic diffraction. But beyond even this, intense study of newly discovered organisms

and ecosystems on Earth that do not require photosynthesis even at their lowest trophic levels is being carried out. In the deepest depths of the Earth’s oceans where practically no light can reach, ecosystems have been found that rely exclusively upon bacteria that consume nutrients produced by tectonic activity on the ocean floor, nutrients ejected by hydrothermal vents [22]. These organisms are aptly named extremophiles, for they thrive in what humans consider extreme environments.

Fig 12 This figure shows a scanning-electron image of a water bear. Water bears (also known as tardigrades) are known to be able to survive in environments with literally no atmosphere (i.e. outer space). They can live without water for decades, and can be brought back to life if frozen.

Fig 13 This figure shows a bacterium that has evolved to consume toxic waste.

But once more, beyond even this, there may not be a genuine need for flora to grow on Pluto at all. If sufficient atmospheric oxygen can be produced from the hydrosphere alone, and the ocean covering Pluto produces a significantly large amount of warmth through its increased albedo, then the only issues a human civilization would need to endure are (1) procuring food, (2)

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procuring desalinated water, and (3) developing an efficient and feasible method of producing floating colonies and energy production facilities. Given the long timescales of such an engineering endeavour, these issues could be tackled in perpetuity as they arise.

But what about light levels for humans? The question then becomes, are these light levels on Pluto sufficient for humans to conduct vital day-to-day activities? Let’s put this into perspective. We will use a typical 60-watt light bulb to give us a better understanding of light levels. A 60-watt light bulb produces 840 lumens of brightness through a soft-white-painted glass sheath, whereas a typical candle produces 12 lumens of light. A lumen is a measure of luminous flux. On a typical day at the equator of Earth, the sun provides 93 lumens per watt. From the 60-watt light bulb, we get

840 lumens60 watts

=14 lumenswatt

This means that the Sun provides

93 lumens/watt14 lumens/ watt

=6.6429×thelight intensity

Or, put another way, the 60-watt light bulb provides 15.05% the luminosity of the Sun. To put this into clearer perspective, the luminous energy per watt on the surface of the giant moon Titan is only 1% that of the Earth. The figure below shows the ambient light level of Titan.

Fig. 14 This picture shows the typical brightness at the surface of the moon Titan. While this light level is still some 15 times greater than what would be experienced on the surface of Pluto, it nevertheless is quite bright.

The light level on Titan is approximately 15.4 times that which reaches the surface of Pluto. On the surface of Pluto, the light level is equivalent to a very bright street light, or on average about 250 times as bright as the full moon [23].

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Fig. 15 This picture is a good comparison for the brightness that one may experience on the surface of Pluto at its current distance from the Sun. While much dimmer than daytime, these light levels are more than sufficient to conduct activities that require high levels of visual acuity.

Fig. 16 This picture is a good representation of the light levels that may be experienced on a Pluto with an engineered atmosphere. It is unlikely that wooded plants or large, rocky landmasses would be commonplace on Pluto, but the light levels are quite accurate.

Assuming a human being with normal vision can write in the light of the full moon, these light levels are more than adequate for day-to-day activities. Though it is likely that, for instance, driving a car would require one’s headlights to be on constantly, no matter what time of day.

Through all of this, we can determine that the light levels on Pluto would be in a range that would start to degrade human survivability, unlike PH as shown in the previous paper in this series [5]. Even so, this analysis shows that human survivability on Pluto would not be impossible, and in fact, in many aspects, it would be easier to proliferate on Pluto as opposed to PH or even Mars. In order to really push the envelope of human ingenuity, we require daring and imagination, something that allows you to go beyond the folds of normality, to think outside the box. Impossibility is a concept based in limitations that people put upon themselves. Nothing is impossible. All that one need do is to first believe in possibility. This endeavour is more than within the purview of our civilization; even now, Pluto could be terraformed, though it would likely cost several quadrillion USD.

IX. ANOTHER MEANS TO PREVENT SPUTTERING?As described earlier, sputtering is a serious problem for Pluto,

even at its immense distance from the Sun. Taking into consideration all the factors mentioned in this paper thus far, it would take approximately 4.35 million years for an engineered Plutonian atmosphere to be stripped away back to its current mass. But, there are other methods that can be employed in order to minimize and even entirely eliminate the sputtering effect on Pluto.

Let us take the hypothetical planet, PH, which was designed in the previous paper in this series. PH has a significant magnetic field, one which was engineered primarily to prevent the effects of atmospheric sputtering. This atmosphere can also be used to protect a terraformed Pluto in the same way. This would require engineering not only on a planetary scale, but on an intrastellar scale. That is to say, Pluto could be moved into an orbit around PH

that would allow for the dwarf planet to be protected by the immense magnetic field that PH generates. Not only would Pluto be protected by PH’s magnetic field from sputtering, but less of an effort would be required to heat the surface of Pluto due to its closer proximity to the Sun. Once more, the prospect of photosynthetic plants proliferating on a Plutonian surface re-emerges.

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Fig. 17 This figure shows what a typical day may look like on the surface of PH, with Pluto looming high in the sky. The Sun is far smaller than Pluto in the sky due to its extreme distance from PH. Consequently, the sky is far darker than a typical day on Earth.

It is important to note that if Pluto is put into too close of an orbit around PH, the dwarf planet could face a variety of potential problems. First of all, every celestial body with a significant magnetic field which deflects large amounts of solar wind/radiation, requires that this deflected material go somewhere other than the surface of the body. This usually manifests in the form of large, highly lethal radiation belts that surround the planet. In the case of the Earth, the Van Allen radiation belts are a key example [24].

Fig. 18 This figure is a representation of the Van Allen radiation belts around the Earth. Though not to scale, it illustrates the general shape of the belts quite well. They surround the Earth; this is a cut-out view.

These radiation belts for smaller, Earth-sized planets with magnetic fields of moderate strength typically do not extend

beyond 10 planetary radii above the planet’s surface. In the case of PH, this would be 100,000 kilometres above the surface. These radiation belts pose a number of problems for Pluto. First of all, a radiation belt would make the surface of a non-terraformed Pluto more or less uninhabitable for humans without great measures put in place in order to protect against the harmful radiation. Any extended stay in such a location would be very difficult. Second, placing Pluto in such a radiation belt could actually amplify the atmospheric leeching effects caused by solar wind. This is because the engineered atmosphere of Pluto would react with the excited material in the radiation belts, and would rapidly dissipate. What would normally take Pluto 4.35 million years to have its atmosphere dissipate could be reduced to as little as 10,000 years conservatively.

Again, even with a significant atmosphere on Pluto, having Pluto anywhere near such a radiation belt would drastically increase the probability of getting cancer at the surface. This is because Pluto does not have a magnetosphere itself, and thus cannot deflect the radiation as efficiently as PH. Additionally, the proposed atmosphere on Pluto would only be half as dense at the surface as compared to that of Earth, which indicates itself a vastly reduced capacity to protect against celestial radiation. A clear example of this is the planet Mars. On Mars, the atmosphere is a mere 6 millibars of pressure (1/150th of Earth). In such an environment, it takes roughly 2 years to acquire 60 REM of

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radiation, an amount that would take an airline pilot on Earth an entire lifetime to acquire [3].

Another important issue with which to contend is that of tidal forces. Though Pluto is a tiny celestial body when compared to PH, it nevertheless can exert an impressive gravitational force upon PH. The closer Pluto is to PH, the stronger the force, based upon Newton’s Law of Universal Gravitation. While 100,000 kilometres from the surface would likely produce similar effects on PH to that of what the Moon causes on Earth’s surface, it remains an important issue to be considered in such an engineering design. Moreover, the closer Pluto is to PH, the faster it needs to orbit in order to maintain its altitude. This is due to the conservation of angular momentum. In such an engineering situation, it would require much larger amounts of energy to place Pluto in a shallow orbit around PH, and thus is preferable to give Pluto a larger orbit. These tidal forces and their effects on Pluto and PH will be elaborated upon later.

While placing Pluto into a more distant orbit from PH is preferable, how far is this distance? Clearly, Pluto must be placed somewhere in the vicinity of PH’s magnetic field in order to attain any level of protection from solar wind. The extent of PH’s magnetic field is 392,993.4 kilometres [5].

There are a few more issues with which we must contended before the decision can be made. The first is of the magnetic field lines. Pluto cannot be placed in an orbit that will for any extended period of time put it in the direct path of any of PH’s magnetic field lines, for if Pluto is in contact with PH’s magnetic field lines for any significant amount of time, this can create an induced magnetic field effect on Pluto, which thus can amplify the atmospheric sputtering effect rather than reduce it [25]. The giant moons Callisto and Io of Jupiter can be used as a clear example of the effects of this. Both moons have a induced magnetic fields caused by their interactions with the magnetic field lines of Jupiter as well as potential liquid oceans that at least Callisto may harbor below its cratered surface. Despite Io producing several thousands of tons of material per second due to its high degree of volcanism, a mechanism which should produce a significant atmosphere of some type, Io has almost no atmosphere whatsoever. This is because Jupiter’s magnetic field leeches it away at a faster rate than Io’s volcanism can produce it. Even Ganymede, the only moon in the solar system known to have its own magnetic field, is prevented from having a significant atmosphere for the same reasons [25].

Fig. 19 This picture shows the surface of the giant moon, Io. As can clearly be seen, Io is a highly volcanic world. Despite this, Io has almost no atmosphere. This is because the moon is bathed in high intensity radiation of Jupiter, and is constantly having its atmosphere stripped away by the gas giant’s magnetic field.

Fig. 20 This figure shows the magnetosphere of Ganymede as affected by Jupiter. While Io and Callisto do not have magnetospheres of their own like Ganymede, the induced magnetic field effects are more or less the same. This would strip away significant atmospheres very rapidly.

As one moves farther away from PH, the magnetic field lines become much more dispersed, so much so in fact that an entire celestial body could orbit comfortably within the space between two sets of magnetic field lines. A distance sufficiently far from PH

will thus be chosen that is more than 100,000 kilometres distant, but less than 393,000 kilometres.

The final issue to take into consideration is that of the magnetopause of PH, the point where the solar wind’s strength matches the strength of PH’s own magnetic field. This was already shown to be approximately 393,000 kilometres distant, however,

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this is an important concept to understand. The giant moon, Titan, orbits Saturn at a distance that places it very close to the magnetopause of Saturn, approximately 1,200,000 kilometres. Ironically, Titan is the only known moon in the solar system to have a significant atmosphere. In fact, Titan’s atmosphere has 1.45 times the surface pressure of Earth’s atmosphere. Key to this seems to be the absence of solar wind, or any magnetic field effects at all from either Saturn or the Sun. A similar method can be employed for Pluto. For these reasons, an orbital radius of 390,000 kilometres will be chosen for this design. This orbital distance does not cause excessive tidal issues, prevents interference from any possible radiation belts, and minimizes the risk of intercepting the magnetic field lines of PH for any extended period of time. The magnetic field of PH at this distance is described by

BE ( d )=Bo

d3 =Bo

( d 1d 2 )

3 (13)

Where BE is the magnetic field strength, BO is the magnetic field at a specific frame of reference (in this case, the surface of PH), d1 is the orbital radius of Pluto, and d2 is the radius of PH. Thus, the magnetic field strength is

73.44 nT

( 390,000 km10,000 km )

3 =0.00123 nT

At this distance, the Sun’s magnetic field intensity is 0.00121 nT. This puts the sum of the overall intensity at 0.00002 nT. With such a weak magnetic field effect, this would reduce atmospheric sputtering so much that it would take a Plutonian atmosphere roughly 4.1 times as long to dissipate, putting the longevity of the Plutonian atmosphere at approximately 17.8 million years. This can be reduced even further with more exact orbital placement with relation to PH’s magnetopause. Additionally, this is not even taking into consideration Pluto’s natural rate of atmospheric generation, which is on the order of several thousands of kilograms of material per second [9].

Fig. 21 This figure shows the relative orbit in which Pluto would be placed with respect to PH and its magnetic field. The orbital distance of 390,000 kilometres would put Pluto very close to the magnetopause (if not within it), which would then cause Pluto to experience similar sputtering effects to that of the giant moon, Titan. This figure is not to scale.

A very important thing to understand is that scientists, prior to the Voyager missions which visited Saturn, originally believed that a body with a surface gravity as low as that of Titan could not sustain an atmosphere of any significant mass. In truth, our science has only just begun to scratch the surface of the possibilities.

Without the effects of a magnetosphere on a celestial body, the potential for even a naturally occurring atmosphere on such a small body as Pluto becomes a real one. Placing Pluto as close as possible to the magnetopause of PH could sustain an atmosphere on

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the dwarf planet in perpetuity, with no need for extensive human modification whatsoever.

X. OTHER IMPORTANT FACTORS

Placing Pluto into such an orbit would come with some consequences. First of all, at a distance of 390,000 kilometres from PH’s surface, the orbital velocity of Pluto is described by

vo=√ G(m1+m2)r

(14)

Where G is the gravitational constant, m1 is the mass of PH, m2 is the mass of Pluto, and r is the radius of the orbit itself plus the radius of the celestial bodies. Thus, assuming a perfectly circular orbit with no eccentricity, the velocity works out to be

vo=√ (6.67384 x 10−11 m3

kg ∙ s2) (8.80951 x1024 kg )

(4.1184 x108 m )

¿1.195 km /second

This means that, it would take Pluto 23.73 days to make one complete orbit around PH. Assuming Pluto has no rotational velocity itself, this would add to the difficulty of producing photosynthetic plants. To understand the magnitude of this problem, it is necessary to determine the mechanism of tidal locking on Pluto with respect to PH. The length of time it would take Pluto to tidally lock with PH with respect to distance and starting rotational velocity is approximated through the following equation [26]:

t locked ≈ ω a6 IQ3G mP

2 k2 R5 (15)

Where ω is the initial spin rate in radians per second, a is the semi-major axis of the satellite (Pluto), I is the moment of inertia of the satellite, Q is the dissipation function (which for simplicity purposes is approximated to be roughly 100), G is the gravitational constant, mP is the mass of the planet, k2 is the tidal love number of the satellite, and R is the mean radius of the satellite. These figures or their approximations are straightforward with the exception of the moment of inertia and the tidal love number, so let’s delve into these two concepts before we find the time to tidal locking. The equation to find the moment of inertia of a satellite like Pluto is approximated by

I ≈ 0.4 ms R2 (16)

This makes the moment of inertia of Pluto 7.3176x1033 kg m2. The tidal love number is the tricky one to determine for Pluto, however. The tidal love number is basically a measure of the flexibility of a celestial body, and thus with this you can get a

determination of how much the gravity acting upon the body will affect its spin rate. The equation for the love number of Pluto is approximated as [26]

k 2≈ 1.5

1+ 19 μ2 ρgR

(17)

Where μ is the rigidity of the satellite (3x1010 N/m2 for rocky objects and 4x109 N/m2 for icy objects), ρ is the density of the satellite (2.03 g/cm3 for Pluto), R remains as the radius of the satellite, and g remains as the gravitational pull of the satellite at its surface. For Pluto, since it is theorized to be comprised of a mixture of equal parts rocky and icy material [9], a rigidity of 1.7x1010 N/m2 will be used. This gives a tidal love number of

k 2≈ 1.5

1+( 19 ∙[1.7 x1010 Nm2 ]

2∙[2030 kgm3 ][0.658 m

s2 ] [1.184 x106 m ] )¿0.01455

This falls in line with other celestial bodies close to Pluto’s size. For example, the moon has a tidal love number of 0.0266. The larger the celestial body, the bigger the love number. PH’s tidal love number is 0.59024. Jupiter-sized planets have love numbers in the tens to hundreds of thousands. Let’s assume that Pluto has an initial spin rate that would give it roughly a 24-hour day. This spin rate in radians per second is 7.2722x10-5 radians/second. Thus, the length of time it would take Pluto to tidally lock to P H is 11,320,896 years. This is a relatively short period of time. But it also must be noted that this calculation is a rough approximation. It has been known to be off by as much as a factor of 10. For instance, the time it would take for the Earth to tidally lock to the moon is believed by a consensus of scientists to be roughly 2.1 billion years, but using this approximation, the answer comes out to roughly 20 billion years. As such, this tidal locking time could be anywhere from 110 million years to 1.1 million years. Under any of these scenarios, such a problem would make photosynthesis on the surface of Pluto a highly difficult task. Though, it still is not impossible.

I’m going to push you as far as you can go. Nothing that you can perceive is impossible. There is a way to do it. In this case, to maintain a rotational velocity, large celestial bodies could be used to speed up the orbit of Pluto. Additionally, with such a far-reaching engineering project, there would likely be a plethora of technologies available at the disposal of humanity 10 million years in the future to perpetuate a sufficient rotational velocity for Pluto, such as, perhaps inter-dimensional wormholes used for teleportation and propulsion purposes. The possibilities are endless. Such engineering feats have already been discussed with

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regards to culling entire asteroids into orbits around Earth for mining purposes, so this is not an unimaginable task [27].

XI. A FEW MORE INTERESTING FACTS

As it appears, the development of a habitable Pluto is highly possible, but there are always more variables to take into consideration due to humanity’s ever-limited understanding of the cosmos. One interesting concept to understand is that of barycenters. In Pluto’s current orbit, it has a giant moon relative to its own size, a moon that is over 10% the mass of Pluto itself: Charon. This moon-dwarf planet pair is so close in mass and the celestial bodies far enough away from one another that the barycenter of the system lies outside the surfaces of both Pluto and Charon.

Fig. 22 This figure shows the barycenter of the Pluto-Charon system. As can be seen, the barycenter lies beyond the radius of Pluto.

It brings up an interesting idea: where would the barycenter of a Pluto-PH system be? As it turns out, this is exceptionally easy to calculate. Calculating the barycenter of a planetary system involves taking the mass of the less massive of the two bodies in the system, and dividing by the overall mass of the entire system. You multiply this number by the overall orbital radius of the system, and you get the system’s barycenter. This gives the distance away from the center of mass of the larger of the two bodies. The calculation is as follows:

bsystem=mPluto r

(mPH +mPluto)(18)

bsystem=( 1.305 x 1022kg ) (390,000 km)

( 8.80951 x 1024 kg )

¿577.72 kilometres

In this case, the barycenter would be well within the radius of PH

itself, preventing the possibility of any egregious orbital perturbations. One can do this calculation with any two bodies in the universe, assuming the masses of the two objects are known.

And finally, probably the most interesting artifact of creating a habitable atmosphere on Pluto is the terminal velocity. Due to the far lower gravitational pull on Pluto, the terminal velocity has the potential to be much slower than on Earth (122 miles per hour for a

human being). A good example of this is Titan. On Titan, the terminal velocity is a mere 12 miles per hour, slow enough to fall from the top of the Titanian atmosphere all the way to the moon’s surface and safely touch down without a parachute! A similar effect would be experienced on Pluto, though, since Pluto has only half the surface pressure of Earth, this factor slightly increases the terminal velocity. The overall terminal velocity of Pluto would become roughly 16.4 miles per hour. Typically, a parachutist on Earth will touch down between five and 15 miles per hour. This means that, as with Titan, one would not ever need a parachute to safely touch down on the surface of Pluto!

XII. A FEW MORE LIMITATIONS

It must be noted, there was one assumption not previously mentioned in this analysis with regards to super greenhouse gases that would likely be the most prohibitive. The temperatures on Pluto, even if culled into an orbit around PH are extremely low, so low that very few compounds are scarcely anything more than frozen solid. The boiling point of sulfur hexafluoride is 209 Kelvin, and this paper assumed that sulfur hexafluoride would be gaseous on Pluto. This means that sulfur hexafluoride would likely be solid ice on the surface of Pluto. Nevertheless, the numerical analysis, for the most part, remains valid. In the future, when new types of greenhouse gases are discovered that could potentially be gaseous at low temperatures, the same temperatures that affect a wispy atmosphere on Pluto when it comes close to the Sun, the engineering endeavor can be attempted with a high probability of success. As it is, the next paper in this series will be addressing how to overcome this issue.

Additionally, though sulfur hexafluoride would likely be a solid at these temperatures, a significant vapor pressure could still be present if bulk composition of the compound on Pluto is made to be large enough. For instance, tetrafluoromethane has a boiling point of 145 Kelvin, and methane which is 20 times more effective at trapping heat compared to CO2 has a boiling point of 111 Kelvin. These gases would have a significant vapor pressure even at extremely low temperatures which could potentially increase the equilibrium temperature of Pluto enough to cause a runaway greenhouse effect up to somewhere around 100 Kelvin.

Beyond this, there are other possible ways to affect a temperature on Pluto that would be conducive to a primordial atmosphere of significant enough density to begin retaining higher temperatures for other greenhouse gases. Among these is a planet-wide dome. Not only would this planet-wide dome retain an atmosphere, it would also act in the same way that greenhouses act on Earth, causing the dwarf planet to reach a new, higher equilibrium temperature.

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Fig. 23. The figure above shows an artist’s concept of a potential planet-wide dome on Pluto for atmospheric retention.

XIII. CONCLUSION

Now we have had two papers expanding upon the idea of artificial habitability zones around stars. So, what defines an artificial habitability zone? In truth, it is the human desire to actually make a celestial body habitable—there is no real limit to the human ability to engineer a habitable environment on planets, no matter the distance from a star. Nevertheless, this definition that I am putting forward is due to current limitations in economic and technological feasibility, and is highly subjective.

If it would take more than 6,000,000 MW of power production more than 1,000,000 years to increase the surface temperature enough to sustain life, as well as produce surface atmospheric pressures above the Armstrong limit [28], then the planet falls outside the artificial habitability zone. Additionally, if sputtering effects outpace atmospheric production, the planet falls outside the artificial habitability zone.

True habitability is thus determined less by orbital proximity to the host star and more by the intrinsic properties of the celestial body (i.e. size, gravitational pull, magnetic field, elemental/chemical composition, etc.).

This definition is subject to as much refinement as any third party wishes, and is by no means final. What is artificially habitable is truly a function of the limitations humanity puts in place. As those factors continuously change in the course of human events, assuming humanity does not lose its vision and continues to progress, this artificial habitability zone will continuously push farther and farther out.

One way or another, what was shown in this paper is that if we can as a society eliminate our perceived limitations, the possibilities in the universe expand explosively. Who would have thought that it was theoretically possible to terraform a dwarf planet with minimal gravitational pull? Who would have thought that a planet orbiting the Sun 16.043 times farther away than the Earth would get sufficient solar energy to warm up to habitable temperatures? Once more, who would have thought that a planet such as Venus could be made habitable if the atmosphere were stripped down to Earth pressures, and the albedo were increased to roughly 0.60 Bond (this produces a surface temperature that averages out to be approximately 85 degrees Fahrenheit, as opposed to 58 degrees Fahrenheit for Earth)? Strip away these

limitations and start thinking of grander possibilities. That is what science truly is all about.

Let’s put this engineering thought experiment in perspective. 1,000 years ago, an airplane would have been thought of as impossible; for that matter, the simple technology that is a pocket lighter would have been considered magic. During the 17 th

century, Giordano Bruno was burned at the stake for believing that there were worlds beyond Earth [29]. About a century later, Isaac Newton was a social pariah for many of the same reasons. Galileo Galilei was put on house arrest for explaining the motion of the planets around the Sun and other celestial bodies. All of these people pushed the boundaries of what was considered true or even possible. It is the responsibility of the scientist, or all of us for that matter, to never settle for the currently understood, but continually push back the curtains of ignorance.

Nothing is impossible. The only impossibilities are those created from human-perceived limitations. But, in order for anything to be accomplished, you must first believe that it can be.

ACKNOWLEDGMENTS

1LT William Giguere was integral in the initial review of papers in this series, providing ample support. 1LT Michael K. Seery (MS, CpE.) and 1LT Phaelen French also took part in the review process.

REFERENCES[1] Bate, Roger E., Donald D. Mueller, and Jerry E. White. Fundamentals of

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