Stellar System Generator, Part 4

Copyright RMF Runyan © 2011

Edited by Aaron Smalley for The Guild Companion

"Besides, if you truly want a corrosive atmosphere, an atmosphere like Venus will do nicely. "

Editor's Note: The following is the fourth chapter of the documentation provided by the author. This as well as the previous three and next installment (five in all) are intended to provide background information as to the science and reasoning behind the application that RMF Runyan has put together. Once we publish the last installment (tentatively planned for December of 2011), we will also provide the entire documentation in the form of a pdf, which will include all of these article installments as well as a table of contents. In the meantime we are also publishing the "SSG Users Guide" put togehter by RMF Runyan which includes a link to download the application that he is developing. He is continuing to work on the application to improve it and create more functionality within it, and as such he is looking for comments and suggestions from users, which can be posted on the appropriate forums at RealRolePlaying.com. We will release each updated and improved version of the application through the end of the series of articles in December of this year.

Chapter 4: Planets

Generating Orbits

Before going into generating parameters for the planets, we need to first determine if the system has a Prime Jovian or not. Jupiter is the Prime Jovian of our system. Prime Jovians will always outmass all other planets in the system combined. However, due to recent discoveries of stellar systems close to ours, we have been finding that systems with a Prime Jovian are perhaps more rare than systems without a Prime Jovian. Currently only about 1 in 5 systems we have discovered have a Prime Jovian. You can simply choose whether your system has a Prime Jovian or not, or you can use the below for random determination. Prime Jovians will be a Jovian with a minimum mass equal to Jupiter. For purposes of generating orbits, Giants are O and B spectral class stars, and stars of Luminosity Class III or greater. Majors are Main Sequence stars of A, F, G, and K spectral class, and Luminosity class IV and V. Minors are all others.

Star Type Determination
Giant 01-90 = non-Jovian; 91-00 = Prime Jovian
Major or Minor 01-75 = non-Jovian; 76-00 = Prime Jovian

Orbital Paths

This is the number of possible planets the star may have. Luminosity class will modify the roll due to the fact that the larger a star is, the more massive it is, and the more massive it is, the less matter will be left behind to form planets. Although main sequence, the same holds true for the O and B class stars. All modifiers are cumulative.

Roll Result Luminosity Class Modifier
01-25 none 0 -50
26-50 d5 Ia -50
51-75 d8 Ib -50
76-94 d10 II -25
95-97 d10+2 III -10
98-99 d10+5 IV -5
00 2d10 all others -0
Spectral Class Modifier
O -25
B -15
For non-Jovian system, add +25 A -5
For Prime Jovian system, add -6 all others -0

System with a Prime Jovian

For a system with a Prime Jovian, we first need to determine where it is located in the system. All systems have five orbital density zones: epistellar, inner system, middle system, outer system, and deep system. For this generator, Prime Jovians cannot be in the deep system orbits.

You may use the table below to determine randomly where the Prime Jovian is, or you may simply choose.

Roll* Result - Notes
01-15 Epistellar orbit - planets cannot form in this orbit, but are dragged here by friction with the proto-planetary disk as the system is forming.
16-30 Inner System orbit - planets can form here rather easily. There is not as much material here as in the Middle System orbit, but it is closer together, allowing planets to form here easily.
31-90 Middle System orbit - the proto-planetary disc is at its thickest in this region and is the best region for a Prime Jovian to form. Though Prime Jovians can end up anywhere.
91-00 Outer System orbit - this is the outermost region for the formation of planets. Although the material in this region is more widespread, planets can still form here easily enough. If the Prime Jovian is in this region, there will be no other planets further out, only Kuiper objects.

* For Giant star systems, add +15 to this roll.

Beyond the Outer System orbits are the Deep System orbits. Outer Deep System orbits are reserved for extra-Kuiper and Kuiper objects since, most likely, these objects will primarily be ice balls. Another rule-of-thumb to keep in mind with any stellar system is that the closer to the star a planet is, the denser it will be. Only Venus (95% as dense as Earth) in our stellar system disobeys this general rule, and it is still not understood why. For example, Mercury is as dense as the Earth (and I forget where I read this on a NASA-JPL webpage). Mars is slightly more than two-thirds as dense as Earth. And the other planets just keep getting less and less dense. Remember, this is just a general rule-of-thumb. Generally, terrestrial type planets will be much denser than Jovian type planets. In fact, Saturn has such a low density (687 kg/m3) that it would actually float on water (1000 kg/m3). Now wouldn't that be a sight?

Now that we know where the Prime Jovian is, we can determine where other orbits will be. As always, you can simply choose. But do use the below for a guideline.

Number of orbits inside the Prime Jovian:

If the Prime Jovian is in an epistellar orbit: d4; 1-3 = 0, 4 =1.

If the Prime Jovian is in an inner system orbit: d4; 1-2 = 0, 3 = 1, 4 = 2.

If the Prime Jovian is in a middle system orbit: d4; as rolled.

If the Prime Jovian is in an outer system orbit: d6; as rolled.

Now we need to figure out the mean orbital radius for the Prime Jovian. The table below lists the ranges for the five general orbit zones. The values in the below table are for a Sol-like star. For other stars, multiply the below listed values by the star's mass in Sol units. If not recorded, divide the star's mass by 1.98892e30 to convert to Sol units. All values are listed in AUs.

Orbital Zone Minimum Maximum
Epistellar 0.02 0.2
Inner 0.2 2
Middle 2 8
Outer 8 20
Deep 20 Oort Cloud

If desired, you can choose an orbital radius from within the above ranges. Or, you can use the below table for randomness. Remember to multiply the rolled value by the star's mass in Sol units.

Epistellar Inner Middle Outer
Roll Result Roll Result Roll Result Roll Result
01-10 0.02 01-10 0.2 01-07 2 01-07 8
11-30 0.04 11-20 0.4 08-15 2.5 08-15 9
31-50 0.07 21-30 0.6 16-23 3 16-23 10
51-70 0.1 31-40 0.8 24-31 3.5 24-31 11
71-90 0.15 41-50 1 32-38 4 32-38 12
91-00 0.2 51-60 1.2 39-46 4.5 39-46 13
61-70 1.4 47-54 5 47-54 14
71-80 1.6 55-62 5.5 55-62 15
81-90 1.8 63-69 6 63-69 16
91-00 2 70-77 6.5 70-77 17
78-85 7 78-85 18
86-93 7.5 86-93 19
94-00 8 94-00 20

Alright, now we know exactly where the Prime Jovian is. Now we can determine where the other planets' orbits are. Remember, we already determined the number of orbital paths above and how many are inside the Prime Jovian. However, if you generated a Prime Jovian in the 0.02 AU orbit, then there will be no planets inside. Additionally, if you did generate a planet inside an epistellar Prime Jovian, then that planet is at the 0.02 AU orbit and the Prime Jovian will be at the 0.04 AU orbit. Please remember that the 0.02 and 0.04 AU orbits may be further out or closer in since they are modified by multiplying by the star's mass in Sol units.

To determine the orbits for the other planets, use the Prime Jovian as the Foundation Planet. Then, use the below listed method for calculating where the other planets are.

For planets inside the Prime Jovian, begin with the next orbit inside and divide the Prime Jovian's orbit value by (1.3 + (d12÷10)). Record this value and use it as the basis for the next orbit inside and repeat until you have determined the orbit values for all planets inside the Prime Jovian. If any planet's orbit ends up less than the 0.02 AU orbit, then disregard and move it outside the Prime Jovian. Please remember the 0.02 AU orbit may be of a different value modified by the star's mass. (Old writer's law: Tell the reader three times to make it sink in.)

For planets outside the Prime Jovian, begin with the next orbit outside and multiply the Prime Jovian's orbit value by (1.3 + (d12÷10)). Record this value and use it as the basis for the next orbit outside and repeat until you have determined the orbit values for all planets outside the Prime Jovian.

System without a Prime Jovian

Generally, systems without a Prime Jovian will tend to have more planets than systems with one. This is mainly due to more stellar matter being available for more planets. For a non-Jovian system, the most important planet orbit is the Foundation Planet. For this type of system, it is the innermost orbit. Use the below method for calculating planet orbits.

Foundation Planet Mean Orbital Radius (MOR)

1) Roll d1000, summing results until total is >= 500.

2) Divide result of Step 1 by 1000.

3) Multiply result of Step 2 by the star's mass in Sol units.

4) Result is the MOR in AUs. To convert to meters, multiply by 149,597,870,691.

Now that we know where the Foundation Planet is, the remaining planets are fairly easy. Using the MOR of the Foundation Planet, simply multiply its orbit value by (1.3 + (d12 ÷ 10)). Record this value and use it as the basis for the next orbit outwards and repeat until you have determined the MOR values for each of the Orbital Paths determined above.

Now we're ready to generate the data for our planets. Remember, if all you want is the data for your focus planet; just simply skip all the other planets.

Physical Characteristics

Type

Planets come in a myriad of types. Basically there are two broad categories of planets: terrestrial and Jovian. Terrestrial planets are similar to Mercury, Venus, Earth, and Mars. Jovian planets are similar to Jupiter, Saturn, Uranus, and Neptune. After I first read about the Kuiper belt and Kuiper objects, way back in 1976, I ceased to consider Pluto a planet. Instead I classified it as a Kuiper object. My logic was based on Pluto's orbit when I once commented in class, "Because of its orbit, Pluto looks like a giant captured comet." To which the teacher replied, "Or it's a Kuiper belt object." Which in turned caused me to study up on what the Kuiper belt was. Since then, in 2006, the IAU has now classified these larger Kuiper objects as Plutoids. Here is a decent article on planet classification at Wikipedia.

The Deep System

Beyond 20 AUs (modified by star's mass) is the Deep System. This is a region where, normally, planet formation is improbable. However, planets can be found out here due to a phenomenon known as "scattering." During the Newborn and Young phase of a star, planetary orbits are highly susceptible to change. Close encounters with other planets or gravimetric resonance interference from more massive planets can throw or push other planets into deeper regions of the stellar system. I once read a theory that suggested Uranus and/or Neptune may have started in the region now occupied by the asteroids and was pulled out by Jupiter/Saturn. Later, Jupiter/Saturn flung them out into the deep system, where they currently reside. If true, this could easily explain the asteroids since they were left behind and shepherded by Jupiter and Mars. This could also explain why Uranus rotates on its side with an axial tilt of almost 98°. As it was flung outwards, it was also pulled over onto its side. There are also theories that Uranus and Neptune were once a single planet and were pulled apart by the same flinging that threw them into the deep system. My theory is that all planets form within the Inner, Middle, and Outer System orbits, with orbits that are much closer than now, then later scatter themselves inward/outward, following the Keplerian Laws of Planetary Motion.

Asteroid Belts

Asteroid belts deserve some special mention. An asteroid belt cannot exist as the outermost orbit. If you generate such in the outermost orbit, simply ignore the result and reroll until you get a planet. Two asteroid belts cannot be generated in two successive orbits. Once you generate an asteroid belt, ignore any asteroid belt results in the next orbit.

Note: Always remember that you can choose which type you desire at each orbit. Also remember that no Jovian may be larger than the Prime Jovian .

Planet Type

Epistellar Orbits Inner System Orbits Middle System Orbits
01-27 Lunan 01-24 Lunan 01-19 Lunan
28-46 Terran 25-44 Terran 20-31 Glacial2
47-62 Pyrosubjovian 45-55 Pelagic 32-44 Terran
63-92 Pyrojovian 56-60 Oceanic 45-55 Pelagic
93-00 Pyrosuperjovian 61-65 Vesuvian 56-60 Oceanic
66-70 Furian 61-65 Vesuvian
71-73 Asteroid Belt 66-70 Furian
74-82 Subjovian1 71-73 Asteroid Belt
83-92 Jovian1 74-82 Subjovian3
93-98 Superjovian1 83-92 Jovian3
99-00 Hyperjovian1 93-98 Superjovian3
99-00 Hyperjovian3

Outer System Orbits Deep System Orbits Transplanetary Region
01-23 Lunan 01-23 Lunan 01-67 Lunan
24-44 Glacial 24-44 Glacial 68-00 Glacial
45-54 Pelagic4 45-58 Pelagic4
55-62 Asteroid Belt 59-64 Asteroid Belt
63-82 Cryosubjovian 65-00 Cryosubjovian
83-92 Cryojovian
93-98 Cryosuperjovian
99-00 Cryohyperjovian

Footnotes in Above Tables

1 - Pyro type in the inner third of region; Cali type otherwise.

2 - Only in the outer two-thirds of region; treat as Terran otherwise.

3 - Cali type in the inner third of region; Frigi type otherwise.

4 - As Glacial type, just more massive.

Special Note: No other Jovian type may be more massive than the Prime Jovian. Largest acceptable mass is ×0.5 that of the Prime Jovian.

Explanation of Planet Types

Planetary bodies come in many myriad forms. They come in many different sizes and chemical makeup, from immense spheres of fluidic gas massive enough to outmass all other planets in their systems, arid and dusty rock balls, to oceanic worlds brimming with life. Planets are divided into two broad categories: Terrestrial and Jovian.

Jovian Planets

Jovian planets are usually called "gas giants." The term "gas giant" was coined by science fiction author James Blish in 1952 in his story Solar Plexus. Arguably the term is something of a misnomer since throughout most of a Jovian's volume; all of the constituents are above the critical point. Therefore, there is no clear-cut difference between ices, liquids and gases. Fluidic planet is a more accurate term. Generally, Jovian planets have no solid surface except for a small core of rock and metal. The rather misleading term of "gas giant" has caught on because planetary scientists tend to use the terms "rock," "gas," and "ice" as catch-all terms for the constituent elements contained within the planet, regardless of what phase (gas, liquid, solid) the matter is in. Especially in the outer system, hydrogen and helium are referred to as "gases"; water, methane, and ammonia as "ices"; and silicates and metals as "rock". When considering the deep interiors of Jovian planets, "ice" means oxygen and carbon, "rock" means silicon, and "gas" means hydrogen and helium. Jupiter is an exception since it has a metallic hydrogen outer core which generates a lethal magnetic field much stronger than the Earth's. The Earth's magnetic field measures about 0.3 gauss at the surface while Jupiter's measures about 4.28 gauss (about 14 times as powerful).

Jovians come in four types: subjovian, Jovian, superjovian, and hyperjovian. They also come in four subtypes based on temperature: pyro-, cali-, frigi-, and cryo-. Since all Jovians share similar compositions, only temperature makes a difference to their prime chemical makeup. Nomenclature plus the prefix differentiates the Jovian types. Mass Ranges are listed in multiples of Jupiter masses (1.8986e27 kg) and abbreviated by "Mj."

Subjovian

Mass Range: 0.03 to 0.3 Mj

Uranus and Neptune in our stellar system are examples of this type of planet. Although subjovians have a smaller core than a Jovian, that core makes up more of its overall mass and volume. The predominance of hydrogen and helium is usually replaced by ammonia and methane and other hydrocarbons. Like Uranus and Neptune, this will tend to cause subjovians to have a greenish or bluish tint. Subtypes: pyrosubjovian, calisubjovian, frigisubjovian, and cryosubjovian.

Jovian

Mass Range: 0.3 to 3.5 Mj

Saturn and Jupiter in our stellar system are examples of this type of planet. These planets are dominated by hydrogen and helium, but can possess other gases in minute amounts. For example, Jupiter is composed of 89% molecular hydrogen, 10% helium, 3000ppm methane, 260ppm ammonia, 28ppm hydrogen deuteride, 6ppm ethane, 4ppm water, and in minute amounts, the aerosols of ammonia ice, water ice, and ammonia hydrosulfide. Saturn has a very similar composition. Depending on either the amount of energy received or energy produced in the core, these planets can have the most monstrous weather of any planet, excepting the super and hyperjovians. If there is very little energy, then the weather will be more subdued like the subjovians Uranus and Neptune. Subtypes: pyrojovian, calijovian, frigijovian, and cryojovian.

Superjovian

Mass Range: 3.5 to 8 Mj

With no contemporary examples, these planets are still similar to Jupiter, just more massive. Superjovians will only be about up to 2 times the size of Jupiter. Planets tend to become denser with a smaller size than expected when they become more massive. This same tendency also holds true for terrestrial planets. As a general rule-of-thumb, take the fourth root of the planet's mass in Jupiter units (or Earth units for terrestrial) to get the size increase. Please note that this rule-of-thumb does not work for planets with a mass factor <= 1. Subtypes: pyrosuperjovian, calisuperjovian, frigisuperjovian, and cryosuperjovian.

Hyperjovian

Mass Range: 8 to 15 Mj

These are the true giants of planets. More often than not, if a stellar system has one of these, it will rarely have any other planets, or the other planets will be of much less mass. Additionally, hyperjovians will tend to have a highly elliptical orbit which cause them to sweep away almost the entire protoplanetary disk as the stellar system is forming, leaving little matter for other planets to form. The 13 Mj mass is the generally accepted upper limit for a gas giant. However, the difference between a hyperjovian and a brown dwarf is very subtle and not very easy to determine. Essentially, the main difference between a hyperjovian and a brown dwarf is whether it is fusing deuterium in the core. Also, there are some hyperjovians currently believed to have masses up to 20 Mj. Thus, I set the maximum at the lower end of the 13 to 20 Mj range. Subtypes: pyrohyperjovian, calihyperjovian, frigihyperjovian, and cryohyperjovian.

Pyro-

From the Greek "pyro" meaning "fire." This prefix is used for Jovian types within the epistellar zone. Jovian type planets will evolve into a Lunan or Terran type terrestrial planet. However, this can take 8 to 15 billion years. Thus, if the star is Newborn, Young, or Mature, the Jovian type planet will still exist. Jovians and larger can begin to take on the visual characteristics of brown dwarfs, but they still may not be fusing deuterium.

Cali-

From the Latin "calidus" meaning "warm." This prefix is used for Jovian types within the inner system zone. Subjovians can evolve into Terran, Pelagic, or Oceanic type terrestrial planets, or become "gas dwarfs." Jovians and larger tend to take on a deep azure color as more of the constituent elements are forced to form more methane from the increased energy (object flux) received.

Frigi-

From the Latin "frigidus" meaning "cold." This prefix is used for Jovian types within the middle and outer system zone. All Jovian types will be characterized by banded cloud layers from various ices of water, ammonia, and methane as well as the formation of other hydrocarbons and dioxides. These planets can range from whitish, through yellowish to reddish-brown or orangish-brown. You can use Jupiter and Saturn for example appearances.

Cryo-

From the Greek "kryos" meaning "ice cold." This prefix is used for Jovian types within the deep system zone, although some can lie within the outermost outer system zone. This subtype of Jovians is also called "ice Jovians." The deep chill of the deep system zone causes thick atmospheres with little structure since there is little energy (heat) to generate weather. Cirrus-like clouds of water and/or ammonia ice crystals can form and last for weeks, months, perhaps years.

Terrestrial Planets

Terrestrial planets may be the most common type of planet in the universe. Most of these terrestrial exoplanets discovered are referred to as "superearths" due to their mass and size. Currently, we are probably unable to detect anything other than these superearths. But that may not remain so for long. Even using our stellar system as an example, there are only 4 Jovian types compared to 9 terrestrial planets. Although the Moon, Callisto, Ganymede, Io, and Titan are satellites themselves, they qualify as terrestrial planets since their mass is within the lower limit of 0.01 Me (5.9736e22 kg). The Moon is a special case since it has less mass than its size would suggest. The main hypothesis that may explain this fact is the " giant impact hypothesis." This hypothesis states that a Mars sized planet (named Theia) may have formed in Earth's L5 Lagrange Point and drifted into the Earth. This impact caused much of the less dense crustal material of both planets to be ejected into space which later formed the Moon. The denser metal core material sank into the Earth, giving Earth its current dynamic nickel-iron outer and inner cores. Mass, composition, and location in the system play a large role in the formation of the terrestrial type planet. They also come in a larger variety than the Jovian type. A general rule-of-thumb for terrestrial type planets is the closer to the star a terrestrial is, the more dense it will be, and thus richer in metals. Mass Ranges are listed in multiples of Earth masses (5.9736e24 kg) and abbreviated by "Me."

Lunan

Mass Range: 0.01 to 0.25 Me

From the Latin "luna" meaning "moon". Mercury, Mars, and the Moon are good examples of this type of terrestrial planet. Most often, this type of planet is too small to hold onto any appreciable atmosphere. Any atmosphere that does exist will be much too thin to support any kind of life, except perhaps some of the hardiest bacteria and/or protozoa. These planets are also characterized by having little or no geological activity. Landforms are usually very ancient, perhaps dating almost back to the very beginnings of the stellar system. Some of the larger lunans may still have some geological activity if the system is Young or Newborn.

Glacial

Mass Range: 0.01 to 0.5 Me

From the Latin "glacialis" meaning "ice". Ganymede, Callisto, and Titan are good examples of this type of terrestrial planet. Europa is a borderline glacial and very small pelagic/oceanic. Although the name of this type derives from "ice," it does not mean that this type of terrestrial is completely frozen. Ones in the deep system zone may be completely frozen. Glacials will usually have a lot of water, which forms an icy crust over the inner rocky mantle. Some may even have enough internal heat, either due to tidal forces or their own internal heat, to form oceans below the icy crust. The "ices" need not be water. Ices also include methane, as with Titan, ammonia (no contemporary example), carbon dioxide (perhaps Pluto-Charon), and oxygen, amongst others. This also depends on the temperature of the glacial planet. Here is a partial list of the temperatures (approximate) which form ices: Water 273K (0C, 32F); Methane 90K (-183C, -297F); Ammonia 195K (-78C, -108F); Carbon Dioxide 195K (-78C, -108F); Hydrogen 14K (-259C, -434F); Ethane 89K (-184C, -299F). [K = Kelvins, C = degrees Celsius, F = degrees Fahrenheit]

Terran

Mass Range: 0.5 to 1.25 Me

From the Latin "terra" meaning "ground". Terrans are a more massive version of the Lunan type terrestrial. The major difference between terrans and pelagics is water. Terrans usually have very little water, if any. Terrans usually form in the innermost Inner System zone, or are dragged into the outermost epistellar zone. Due to their proximity to the system's star, terrans will usually form into hellish greenhouses like Venus. Since terrans have little standing water, it does not play a large role in the geological processes of the planet. Plate tectonics are virtually impossible on a terran since the crust tends to be thick, except on hotspot locations. Where vulcanism does exist, it is usually in the form of shield volcanoes over hotspots. Even if there is little geological activity, the searing flux some of these planets receive can still turn a terran into a hellish greenhouse since only the heaviest gases can be held by the planet's gravity. Mars is another example of a smaller terran.

Pelagic

Mass Range: 0.5 to 1.5 Me

From the Greek "pelagus" meaning "sea". Pelagics are virtually like our Earth with oceans that can cover 30 to 90% of the planet's surface. Pelagics will be fairly geologically active since the water lubricates the crustal layer generating plate tectonics. The crust will usually be fairly thin and broken into plates. These plates tend to move across the surface of the planet creating convergent and divergent boundaries and seafloor spreading zones. This recycling of crustal material means the land will be relatively young (usually less than 500 million years old).

Oceanic

Mass Range: 1.5 to 3 Me

From the Latin "oceanus" meaning "ocean". Oceanic type planets are usually the remains of a subjovian. They are more massive than the pelagic type, and are usually covered in their entirety with water (>=90% oceans). However, there may be chains of islands formed from volcanoes due to subduction zones with the underlying rock/metal core. These planets can be teeming with life, even more so than our Earth. Of course, all vulcanism can be hidden beneath tens to hundreds of kilometers of ocean. Oceanics can be larger than Vesuvian due to the layer of water which is less dense than rock and metal.

Vesuvian

Mass Range: 3 to 8 Me

From the Latin "vesuvius" meaning "volcano". Terrestrial planets beyond 3 Earth-masses loose all pretense of Earth-like behavior. The crust becomes much thinner as the planet is in turmoil of barely contained heat. Vesuvian planets are massive enough to have an overall mean density approaching that of lead or greater. This greater density means the vesuvian will tend to possess a much greater amount of actinide metals than the less massive terrestrials. This greater amount of actinides produces a greater amount of internal heat. This means vesuvian types possess constant vulcanism and megavulcanism. The atmosphere tends to be thick and dominated by carbon dioxide, sulfur dioxide, hydrogen sulfide, and hydrogen cyanide. If there is any water on a vesuvian, it is invariably in the form of vapor. Standing water is not impossible on these hellish worlds, just highly improbable. However, some vesuvians may possess some small seas in which only the hardiest primitive life can exist.

Furian

Mass Range: 8 to 14 Me

From the Latin "furia" meaning "rage". These truly hellish worlds are the most massive, most dense, and largest of the terrestrial type planets. The furian planet makes a vesuvian type look pleasant by comparison. If there are any crustal rafts on this type of planet, it is paper thin (1 to 5 km thick) and fairly small in area (a few million square kilometers). Usually, a furian is nothing more than ball of blistering and boiling lava. The atmosphere is similar to the furian, except it is denser and thicker and more like a blast furnace with temperatures that could almost approach the melting point of iron (1811K, 1538C, 2800F). No life can survive on a furian unless it is a life form that can exist in the molten environment.

Some terrestrials massing 5 to 10 Me may also evolve to be gas dwarfs. The term "gas dwarf" has been used to refer to planets smaller than gas giants, but possess thick hydrogen and helium atmospheres. Usually, a gas dwarf is the remains after a higher mass vesuvian or furian that has lost the nuclear fission furnace of the heavier actinide metals which have broken down to lighter metals and minerals. Once enough cooling has occurred, their atmosphere will settle down into a composition similar to a Jovian type planet. However, it is calculated to take about 10 to 15 billion years for this to happen. If the star is Newborn, Young, or Mature, there will be no gas dwarfs. If the star is Old, you may change any Vesuvian or Furian to a gas dwarf if desired.

Asteroid Belts

Is there anyone who does not know what an asteroid belt is? Especially after the film The Empire Strikes Back? There are many methods by which an asteroid belt may form.

• A particular region of the protoplanetary disk could have simply failed to coalesce into a planet.

• Debris from elsewhere in the system could be shepherded into the region where a planet never formed.

• Two bodies of near same size could have begun to form and later impacted, completely disrupting both. FYI: It would take a planet about 60% the size of the Earth to completely disrupt both into an asteroid belt.

• A forming planet could have been torn apart by another more massive.

• A subjovian could have begun forming here and was flung out into the deep system leaving the debris behind.

However it formed, what is left is an asteroid field. Although asteroids can exist anywhere in the system, this belt is a major object in the system. We only have our asteroid belt as an example. Our asteroid belt has enough mass to make a planet perhaps the size of the Moon. This does not mean an asteroid belt could have even more mass. Perhaps even enough to have formed a furian. However, the SSG only generates asteroid belts with a total mass up to two Earth-masses.

Roll Belt Size and Orbit Coverage Belt Density Mass Range (Me)
01-20 Tiny (45°) Sparse 0.001 to 0.01
21-40 Small (90°) Light 0.01 to 0.1
41-60 Medium (180°) Moderate 0.1 to 0.5
61-80 Large (270°) Dense 0.5 to 1.0
81-00 Huge (360°) Very Dense 1.0 to 2.0

Roll for each aspect separately.

Special Note: There is an app included (SSGCalc.exe) that will calculate the next several parameters. All you will need is a working Volumetric Mean Radius, working Density, and Rotational Period. You can also enter a Land Percentage but only if you wish Land Area and Ocean Area calculated for you. The list of parameters that CelBodCalc.exe will calculate are: Mass, Volume, Mean Density, Equatorial Radius, Polar Radius, True Volumetric Mean Radius, Oblateness, Inverse Flattening Ratio, Surface Gravity, Escape Velocity, Total Surface Area, Land Area, and Ocean Area. I also include the equations with each of these parameters below .

Mean Density

This is fairly easy to calculate. First, determine the planet's mass and volume. Then divide mass by volume to get overall mean density. Remember, this is the overall mean density. All planets will vary in their density through the layers from surface to core.

\[D=M/V\]

Where \(D\) = mean density in kg/m3; \(M\) = mass in kilograms; \(V\) = volume in cubic meters.

Some sample Density Ranges; listed in kg/m3 (for use with CelBodCalc.exe)

Terrestrial Type Density Ranges Jovian Type Density Ranges
Lunan 2500-4000 Subjovian 500-1800
Glacial 1500-3000 Jovian 500-2000
Terran 2500-5000 Superjovian 1500-4000
Pelagic 3500-6500 Hyperjovian 2500-5000
Oceanic 4000-7000
Vesuvian 5500-9000
Furian 7500-12,000

Oblateness

All celestial bodies that rotate are actually oblate spheroids. Oblateness is simply the amount of flattening of a planet caused by centrifugal force. An oblateness of 1 indicates a perfectly flat disk, where an oblateness of 0 indicates a perfect sphere.

Oblateness from Equatorial and Polar Radii: \[f=\frac{a-b}{a}\]
Oblateness from Density and Rotation: \[f=\frac{3\pi}{GT^2D}\]
Oblateness Constant: \[ q= \frac{r^3\left(\frac{2\pi}{T}\right)^2}{GM} \]

Where \(f\) = oblateness; \(q\) = oblateness constant; \(a\) = equatorial radius; \(b\) = polar radius; \(G\) = Gravitational Constant (6.67428e-11 m3/kgs2); \(T\) = rotational period in seconds; \(D\) = mean density of object; \(r\) = volumetric mean radius; \(M\) = mass of object in kilograms.

Special Note: An oblateness of 1 is impossible; for the object would be rotating so fast that it would have torn itself asunder long before it could achieve an oblateness of 1. One of the NCSU students in our Udava campaign (back in 1982-1997) convinced me that the maximum oblateness is 0.5. He argued (although not precisely accurate, but close enough) that the Polar Radius would be 2/3 and the Equatorial Radius would be 4/3, meaning the Equatorial Radius is twice that of the Polar Radius. It is at this point that the object would begin to tear itself apart. Thus, for the purposes of the SSG, the maximum oblateness for any celestial body would be 0.48.

Inverse Flattening Ratio

This is simply 1 ÷ Oblateness. This parameter is primarily used for GIS. If you do not plan on using GIS software (such as Quantum GIS, GRASS, etc.), then you can skip this step.

Radii

There are three different radii for a planet: Equatorial, Polar, and Volumetric Mean. Which ones you determine is dependent upon how accurate you wish to be. All celestial bodies that rotate are actually oblate spheroids. The most accurate is to compute the Equatorial and Polar Radii. For simplicity, you can just use the Volumetric Mean Radius. The CelBodCalc.exe app will also calculate these for you. Volumetric Mean Radius is simply the radius of a perfect sphere that has the same volume as the planet. If you know an oblate spheroid's volume, you can use the below equation to calculate its volumetric mean radius. The tables below generate volumetric mean radii.

\[r=\sqrt[3]{\frac{3V}{4\pi}}\]

Where \(r\) = volumetric mean radius; \(V\) = volume.

Here are the equations for equatorial radius and polar radius once volumetric mean radius and oblateness are known. However, once you use the below equations, you will have to recalculate the oblateness.

\[E_r=V_r \times (1+f)\] \[P_r=V_r \times (1-f)\]

Where \(E_r\) = equatorial radius; \(P_r\) = polar radius; \(V_r\) = volumetric mean radius; \(f\) = oblateness.

It must be remembered that an increase in a planet's mass will not mean a proportional increase in a planet's size. For example, a planet with three times the mass of Earth may only be about 1.3 times as large. Also, looking at the equation for mass (M = DV), you can see that size (volume) is directly proportional to mass. However, density plays a part to cause volume to increase at a smaller increment than 1:1. Below are the three forms of that equation.

\[M=DV,\; D=M/V,\; V=M/D\]

For random radius, use the below table (next page). Remember, the radius generated below is volumetric mean radius. For the terrestrial planets, radius is listed in 100s of kilometers. For Jovian planets, radius is listed in 1000s of kilometers. If any die roll for radius yields a negative number; treat it as a zero (0).

Volumetric Mean Radius
Mass Radius Mass Radius Mass Radius
Lunan Glacial Terran
0.01-0.1 16+(d10-1) 0.01-0.1 16+(d20-2) 0.5-0.75 50+(d12-1)
0.1-0.25 24+(d12-1) 0.1-0.25 33+(d20-2) 0.75-1 60+(d12-1)
0.25-0.5 50+(d20-1) 1-1.25 70+(d12-1)
Pelagic Oceanic Vesuvian
0.5-0.75 50+(d10-2) 1.5-2 86+(d20-5) 3-4.5 78+(2d8-2)
0.75-1 58+(d10-2) 2-2.5 100+(d20-4) 4.5-6 90+(2d8-2)
1-1.25 66+(d12-2) 2.5-3 115+(d20-4) 6-8 103+(2d8-2)
1.25-1.5 75+(d12-2)
Furian Subjovian Jovian
8-10 116+(d6-1) 0.03-0.1 15+(d20-4) 0.3-1 60+(d12-1)
10-12 120+(d6-1) 0.1-0.2 30+(d20-4) 1-2 70+(d12-1)
12-14 124+(d6-1) 0.2-0.3 45+(d20-4) 2-3.5 80+(d12-1)
Superjovian Hyperjovian
3.5-5 80+(d12-1) 8-11 95+(d12-1)
5-6.5 85+(d12-1) 11-15 105+(d12-1)
6.5-8 90+(d12-1)

Mass

The masses listed in the below tables are in multiples of Jupiter or Earth. For the Jovians, they are listed in multiples of Jupiter masses. For the terrestrials, they are listed in multiples of Earth masses. To convert to kilograms, multiply the planet's mass factor by the below listed values.

Jovian Mass

Subjovian Jovian Superjovian Hyperjovian
01-09 0.03 01-09 0.3 01-10 3.5 01-07 8
10-18 0.06 10-18 0.5 11-20 4 08-14 8.5
19-27 0.09 19-27 0.7 21-30 4.5 15-20 9
28-36 0.12 28-36 0.9 31-40 5 21-27 9.5
37-45 0.15 37-45 1.1 41-50 5.5 28-34 10
46-54 0.18 46-54 1.3 51-60 6 35-40 10.5
55-63 0.21 55-63 1.5 61-70 6.5 41-47 11
64-72 0.23 64-72 2 71-80 7 48-54 11.5
73-81 0.25 73-81 2.5 81-90 7.5 55-60 12
82-90 0.27 82-90 3 91-00 8 61-66 12.5
91-00 0.3 91-00 3.5 67-73 13
74-80 13.5
81-86 14
87-93 14.5
94-00 15

Terrestrial Mass

Lunan Glacial Terran Pelagic
01-07 0.01 01-07 0.01 01-07 0.5 01-09 0.5
08-15 0.03 08-15 0.03 08-15 0.55 10-18 0.6
16-23 0.05 16-23 0.05 16-23 0.6 19-27 0.7
24-31 0.07 24-31 0.07 24-31 0.65 28-36 0.8
32-38 0.09 32-38 0.09 32-38 0.7 37-45 0.9
39-46 0.11 39-46 0.11 39-46 0.75 46-54 1
47-54 0.13 47-54 0.13 47-54 0.8 55-63 1.1
55-61 0.15 55-61 0.15 55-61 0.85 64-72 1.2
62-69 0.17 62-69 0.17 62-69 0.9 73-81 1.3
70-77 0.19 70-77 0.2 70-77 0.95 82-90 1.4
78-84 0.21 78-84 0.3 78-84 1.05 91-00 1.5
85-92 0.23 85-92 0.4 85-92 1.15
93-00 0.25 93-00 0.5 93-00 1.25

Terrestrial Mass

Oceanic Vesuvian Furian
01-07 1.5 01-09 3 01-07 8
08-15 1.6 10-18 3.5 08-15 8.5
16-23 1.7 19-27 4 16-23 9
24-31 1.8 28-36 4.5 24-31 9.5
32-38 1.9 37-45 5 32-38 10
39-46 2 46-54 5.5 39-46 10.5
47-54 2.1 55-63 6 47-54 11
55-61 2.2 64-72 6.5 55-61 11.5
62-69 2.3 73-81 7 62-69 12
70-77 2.4 82-90 7.5 70-77 12.5
78-84 2.6 91-00 8 78-84 13
85-92 2.8 85-92 13.5
93-00 3 93-00 14

For those wishing to convert mass to kilograms: Jupiter = 1.8986e27 kilograms; Earth = 5.9736e24 kilograms

Volume

Simply, this is the cubic measure of the amount of space the object occupies. The Sphere Volume equation is simpler, but the Oblate Spheroid Volume is more accurate.

Sphere Volume: \[V=\frac{4\pi r^3}{3}\]
Oblate Spheroid Volume: \[V=\frac{4\pi a^2 b}{3}\]
Error Margin = ±0.037%

Where \(V\) = volume; \(r\) = volumetric mean radius; \(a\) = equatorial radius; \(b\) = polar radius.

Surface Gravity

This is the gravitational attractive force of the planet at sea level, or mean altitude. To convert the value into cm/s2, multiply by 100.

\[g=\frac{GM}{r^2}\]

Where \(g\) = surface gravity in m/s2; \(G\) = Gravitational Constant (6.67428e-11 m3/kgs2); \(M\) = mass of planet in kilograms; \(r\) = volumetric mean radius in meters.

Ballistic Escape Velocity

Contrary to popular belief, this is not the velocity an object needs to maintain to escape a planet's gravity well. As said on this Wikipedia page, "It is the speed needed to break free from a gravitational field without further propulsion. The term escape velocity is actually a misnomer, as the concept refers to a scalar speed which is independent of direction whereas velocity is the measurement of the rate and direction of change in position of an object. A rocket moving out of a gravity well does not actually need to attain escape velocity to do so, but could achieve the same result at walking speed with a suitable mode of propulsion and sufficient fuel. Escape velocity only applies to ballistic trajectories." Thus, the reason why I added ballistic to the term.

\[V_e=\sqrt{\frac{2GM}{r}}\]

Where \(Ve\) = escape velocity for the ballistic object in m/s2; \(G\) = Gravitational Constant (6.67428e-11 m 3/kgs2); \(M\) = mass of planet in kilograms; \(r\) = volumetric mean radius in meters

Astronomical Albedo

Also called visual geometric albedo, this is the ratio of the body's brightness at a phase angle of zero to the brightness of a perfectly diffusing disk with the same position and apparent size. Another way of looking at this, it is the amount of sunlight reflected by the body.

Since this parameter is extremely difficult to randomize and requires quite a bit of complex math, I usually just arbitrarily choose a number between 0.42 to 0.31 ((d12 + 30) ÷ 100) for an Earth-like planet. Earth's astronomical albedo is 0.367 ( JPL Planetary Fact Sheet). Just use some logical reasoning when choosing this parameter.

Albedos of typical materials in visible light range from up to 0.9 for fresh snow, to about 0.04 for charcoal, one of the darkest substances. Deeply shadowed cavities can achieve an effective albedo approaching the zero of a perfectly black body. When seen from a distance, the ocean surface has a low albedo, as do most forests, while desert areas have some of the highest albedos among landforms. Most landform areas are in an albedo range of 0.1 to 0.4. The average albedo of the Earth is about 0.37. This is far higher than for the ocean primarily because of the contribution of clouds. Thus, depending upon your world's cloud cover, you could make the +30 modifier above as low as +15, up to as high as +40.

Human activities have changed the albedo (via forest clearance and farming, for example) of various areas around the globe. However, quantification of this effect on the global scale is difficult.

Two common albedos that are used in astronomy are the (V-band) visual geometric (or astronomical) albedo (measuring brightness when illumination comes from directly behind the observer) and the Bond albedo (measuring total proportion of electromagnetic energy reflected). Their values can differ significantly, which is a common source of confusion.

Some Sample Albedos
Surface Typical Albedo
Fresh asphalt 0.04
Worn asphalt 0.12
Conifer forest 0.08-0.15
Deciduous forest 0.15-0.2
Bare soil 0.17
Green grass 0.25
Desert sand 0.4
New concrete 0.55
Ocean ice 0.5-0.7
Fresh snow 0.8-0.9

Bond Albedo

Also called planetary albedo, this is the fraction of incident solar radiation reflected back into space without absorption. Another way of looking at this, it is the amount of energy (object flux) reflected by the body.

As with visual geometric albedo, Earth-like planets will have a bond albedo of 0.37 to 0.26. Since this parameter, like astronomical albedo, is extremely difficult to randomize and requires some complex math, I usually just arbitrarily choose a number between 0.33 to 0.26 ((d8 + 25) ÷ 100). Earth's bond albedo is 0.306 (JPL Planetary Fact Sheet). Just use some logical reasoning when choosing this parameter.

Sol System Albedos
Planet Astronomical Bond
Mercury 0.142 0.068
Venus 0.67 0.9
Earth 0.367 0.306
Mars 0.17 0.25
Jupiter 0.52 0.343
Saturn 0.47 0.342
Uranus 0.51 0.3
Neptune 0.41 0.29

As can be seen by the above table, desert planets (Mars) will have a slightly lower bond albedo and even lower astronomical albedo. Cloud covered planets like Venus will have a much higher bond albedo. Ice ball worlds (like Hoth in Empire Strikes Back) will have a very high visual geometric albedo and a slightly higher bond albedo, dependent upon how clean or dirty the ice is.

Object Flux

This is the total amount of energy received by the object.

\[F=\frac{L}{4\pi d^2}\]

Where \(F\) = amount of energy received in W/m2; \(L\) = luminosity of emitter in Joules; \(d\) = distance (mean orbital radius) from emitter in meters.

Land/Ocean Ratio

This is simply a listing of a ratio of the percentage of land to the percentage of ocean. For example, Earth's is 29/71, meaning there is 29% land to 71% ocean. You are not restricted to listing this as land/ocean. If desired, you could list it as ocean/land. Just be consistent and annotate how you list it.

Total Surface Area

This is the total area of the planet. There are two different methods. One is for an oblate spheroid using the equatorial and polar radii. The other is for a perfect sphere. Of course, the first is the more accurate, but the second is simpler. Also remember, you can get this value using the CelBodCalc.exe app which calculates total surface area using the first equation.

Oblate Spheroid Surface Area: \[A=2\pi \left(a^2 + \frac{b^2}{\sin \alpha} \ln{\frac{1 + \sin \alpha}{\cos \alpha}}\right) \] Error Margin = ±0.01371%

Sphere Surface Area: \[A=4\pi r^2\]

Where \(A\) = area; \(a\) = equatorial radius; \(b\) = polar radius; \(a = \arccos(b/a)\); \(r\) = volumetric mean radius.

Land Surface Area

This is nothing more than converting the land percentage into a decimal and multiplying it by the total surface area. Most often, I never bother with listing ocean area since it is the land area (livable surface without special habitation constructs) I am more interested in.

Orbital Characteristics

Orbital Period

This is the time it takes the object to orbit the primary one full revolution. Time is in total seconds. Also see the appendix article, Creating Your Own Time Units.

\[T=2\pi \sqrt{\frac{a^3}{G(M+m)}}\]

Where \(T\) = total time in seconds; \(a\) = mean orbital radius; \(G\) = Gravitational Constant (6.67428e-11 m 3/kgs2); \(M\) = mass of central body in kilograms; \(m\) = mass of orbiting body in kilograms.

Orbital Eccentricity

No planet orbits a star in a perfect circle. Kepler's First Law states: "The orbit of every planet is an ellipse with the star at one of the two foci." This is the measure of the planet's orbital circularity. An eccentricity of 0 indicates a perfect circle, which is highly improbable, but not impossible. Reason: The constant tug-of-war of the sun, planets, and moons (if any) will have enough of an effect to prevent an orbital eccentricity of 0. Only a stellar system with a single planet could possibly have the planet's orbital eccentricity equal to 0. Unless the planet is highly eccentric, most orbits about a mature or older star will usually have an eccentricity = 0.1 to 0.01. I usually arbitrarily choose this, especially for the focus planet. If you desire randomness, use below.

Roll d100:

01; circular; (d12 - 1) ÷ 10,000.

02-66; near circular; (2d8) ÷ 100.

67-00; eccentric; (2d20 + 20) ÷ 100.

For Newborn stars, add +50. For Young stars, add +25. For all others, add +0. This depicts the orbital flux of younger stars compared to older ones. For a single planet, add -25. All these modifiers are cumulative.

If periapsis, apoapsis, and mean orbital radius are already known, orbital eccentricity may be calculated using the below equation.

\[\frac{a-p}{2r}\]

Where \(a\) = apoapsis; \(p\) = periapsis; \(r\) = mean orbital radius.

Author's Note: Before you email me and tell me that the two below parameters are actually perihelion/aphelion or perigee/apogee, read this article at Wikipedia . You will see that the generic terms for these parameters is in fact periapsis/apoapsis. The -helion and -gee actually refer to the sun and Earth, respectively. But, we aren't talking about either anymore.

Periapsis

This is the measure of the planet's closest approach to the star.

Periapsis = MOR × (1 - e); where MOR = Mean Orbital Radius, e = orbital eccentricity. Units are dependent upon units used for MOR.

Apoapsis

This is the measure of the planet's furthest excursion from the star.

Apoapsis = MOR × (1 + e); where MOR = Mean Orbital Radius, e = orbital eccentricity. Units are dependent upon units used for MOR.

Special Note: Once you calculate the periapsis and apoapsis, you will have to recalculate the orbital eccentricity.

Orbital Inclination

This is the askewment of the planet's orbital plane away from the ecliptic. In our stellar system, the ecliptic is the plane of Earth's orbit. You may use the plane of the focus planet of your stellar system as the ecliptic. Thus, for only the focus planet, its orbital inclination would be 0.0°. Otherwise, choose the inclination. If you want randomness, then see below.

Orbital Inclination:

01-95 = Ecliptical: inclination = 2d12 ÷ 10; then, 01-50 = positive, 51-00 = negative.

96-00 = Eccentric: inclination = d100; then, 01-50 = positive, 51-00 = negative.

Orbital Obliquity

The technically accurate term for this is Obliquity to the Ecliptic. Most often called axial tilt, this is the measure of the planet's rotational axis in respect to its orbital plane. Remember, there are many factors for considering obliquity. The more upright (0° obliquity) a world is, the less seasonal changes there will be, and the smaller the regions where these changes occur. Unless the planet has a highly elliptical orbit, at 0° obliquity, there will be no seasonal changes, for the entire surface of the world will receive the same amount of energy throughout the planet's orbital period. The more sideways (90° obliquity) a world is, the more drastic the seasonal changes will be. For some parts of the world's revolution (orbital period), one pole would receive constant sunlight for half the revolution. I usually arbitrarily choose this, especially for the focus planet. If you want randomness, use below.

Roll d100:

01-20 = none; axial tilt = 0.

21-40 = small; axial tilt = 2d10.

41-60 = moderate; axial tilt = 2d10 + 20.

61-80 = large; axial tilt = 2d10 + 40.

81-00 = severe; axial tilt = 4d10 + 60.

Mean Orbital Velocity

This is the overall mean velocity the object has in its orbit about the primary. For km/s, multiply by 0.001.

\[V_o=\frac{2\pi r}{T}\]

Where \(V_o\) = mean orbital velocity in m/s; \(r\) = mean orbital radius in meters; \(T\) = orbital time in seconds.

Rotational Period

When first forming from the protoplanetary disk, a planet begins spinning. This is due to conservation of momentum. Ever seen those ice skaters who spin faster as they pull their arms in? That is conservation of momentum. Even slowly pulling their arms inward imparts a great amount of radial inertia. Over the aeons, this spinning can be altered by major impacts and tidal tugging. If within a certain distance, tidal forces can lock the rotation of a planet so that its rotation is equal to its orbital period. In other words, one face of the planet will always face the star. A little further out, resonance between the planet and star will force a rotation that is two-thirds of its orbital period. This means the planet will rotate once every two orbital periods. Mercury has a rotational period like this. If such an orbit is elliptical enough, this can also lead to "double sunrises." Here is an excellent video of this phenomenon by T0R0YD @ YouTube. This video also shows how such a phenomenon would look like on Earth. Beyond this inner region, rotational periods become more chaotic since they are influenced by other forces besides the star's gravitational tides. As always, you may choose the rotational period, or you may use either of the below tables for random determination. Please remember that the AU distances listed are modified by the star's mass in Sol units.

<= 0.25 AU Locked rotation: rotation period = orbital period.
0.25 to 0.5 AU Resonant Rotation: rotation period = (orbital period × (2 ÷ 3))
>= 0.5 AU Terrestrials roll 3d6; Jovian roll 2d6
2-5 2d6 hours
6 3d6 hours
7 4d6 hours
8 5d6 hours
9-10 3d6 × 2 hours
11-12 3d6 × 3 hours
13 3d6 × 5 hours
14 1d6 days (= 86,400 seconds)
15 2d6 days
16 5d6 days
17-18 3d6 × 5 days

Alternative Rotational Period

01-10 Very fast 2d10 ÷ 2 hours
11-30 Fast 2d10 hours
31-70 Moderate 4d10 + 2 hours
71-90 Slow 1d100 × 1d10 hours
91-00 Very slow 1d100 × 1d100 hours

Longitudinal Orbital Parameters

Special Notes: Virtually none of these will ever be in the same location. The actual chance of any two of these parameters being at the same location was once calculated to be 1 in 1e24 (equivalent to rolling 12 straight "00" on a d100).

Randomizing these parameters is not possible, for one will affect the range in which the others may be located. If you do not have a good understanding of orbital mechanics, then skip this section of parameters. Otherwise, you have to use some really brutal mathematics to calculate these parameters. Usually, I do not include these parameters, unless I want to create a .cel or .celx file for use in Celestia for the entire system.

All of these parameters are measured in degrees ranging from 0 to 359.999… Of course, this means that an arbitrary 0° direction must be chosen. As mentioned, if you do not understand orbital mechanics well enough, then just skip this. However, if you choose to create these parameters, I usually choose the 0° point as being when the planet is directly in line between the star and the galactic center at a particular point in time known as the Epoch. Also, check this article at Wikipedia. There are some external links. Also do a web search for "Keplerian Elements". Just remember to visit the scientific and university sites.

Contrary to common logic, a planet's Ascending Node and Descending Node may not be 180° apart. The same holds true for Periapsis and Apoapsis. See images below for a visual representation for why not. The third image below gives a three dimensional visual representation. Of course, the images are exaggerated for emphasis. However, periapsis and apoapsis will be very close to 180° apart, and no greater than ±2.5° away from 180°.

OrbitSide.png
Side View of a Planet's Orbit (Ascending/Descending Nodes)
Green is the ecliptic, Blue is planet's orbit
OrbitOver.png
Obverse View of a Planet's Orbit (Ascending/Descending Nodes)
To exact same scale as above image
3DOrbit.png
3-D View of a Planet's Orbit

Longitude of Ascending Node

This is the point in the planet's orbit when the planet rises above the plane of the ecliptic.

Longitude of Descending Node

This is the point in the planet's orbit when the planet sinks below the plane of the ecliptic.

Longitude of Periapsis

This is the point in the planet's orbit when the planet is at its closest approach to the star.

Longitude of Apoapsis

This is the point in the planet's orbit when the planet is at its farthest excursion from the star.

Longitude of Mean Orbital Radius

This is the point in the planet's orbit when the planet is at the mean orbital radius distance from the star. Contrary to logic, there will be only one location in the planet's orbit where this will be true. One would think it would happen twice. However, using the Earth as an example, it only happens at 100.46435°. You'd figure it would also happen at close to 280°, but it does not.

Atmospheric Characteristics

Scale Height

This is altitude above sea level, or mean altitude, by which the atmospheric pressure decreases by a factor of e ( Euler's Number = 2.7182818…).

\[H=\frac{RT}{mg}\]

Where \(H\) = scale height in meters; \(R\) = Universal Gas Constant (8.3144621 J/mol K); \(T\) = GAST in K; \(m\) = mean molecular weight in kilograms; \(g\) = surface gravity in m/s2. Note: To get mean molecular weight in kilograms, multiply the mean molecular weight by 0.001.

Surface Pressure

For an Earth-like planet with an Earth-like atmosphere, you can calculate the mean surface pressure by converting your planet's atmosphere's mean molecular weight and surface gravity into Earth units. Divide your planet's atmosphere's mean molecular weight by 28.96728. Divide your planet's surface gravity by 9.80665. Multiply these results together. Multiply this result by 760. The result is your planet's mean atmospheric surface pressure in mmHg.

Conversions: 1 mmHg = 1.333223684 millibars = 133.3223684 pascals = 0.1333223684 kilopascals = 0.039370079 inHg.

Surface Density

As in Surface Pressure above, except multiply by 1.225. This is the mean atmospheric surface density in kilograms/meter3.

Conversions: 1 kg/m3 = 0.062427961 lb/ft3 = 0.001 g/cm3 = 0.000578037 oz/in3.

Please Note that the above methods (pressure and density) only work for Earth-like planets with an Earth-like atmosphere.

GAST

This is the global average surface temperature (GAST) across the entirety of world's surface. It is the average of day and night temperatures also. Just because a planet has a GAST of only 284K (11°C, 52°F) does not mean the world cannot also have some very hot temperatures. Remember, Earth's GAST is about 289K (16°C, 61°F) and has some temperatures that hit 333K (60°C, 140°F).

Special Note: You probably chose the planet's astronomical albedo. Just remember this, the lower it is, the higher the GAST.

\[T=\left( \frac{L(1-A)}{16\pi \sigma D^2} \right)^{0.25}\]

Where \(T\) = temperature in Kelvins; \(L\) = luminosity of emitter in W/s; \(A\) = object's astronomical albedo; \(\sigma\) = Stefan-Boltzmann Constant (5.6704e-8 W/m2K4); \(D\) = mean orbital radius in meters.

Diurnal Temperature Range

Also called daily temperature range, this is the average range of diurnal temperatures the planet experiences during one rotation. Remember, this is just an average, not the extremes. For example, Earth's DTR is 283 to 293 K (10 to 20 °C, 50 to 68°F). Also remember this is the temperature range and is not added to the GAST.

Wind Speeds

This is the range of wind speeds. The upper limit of this is the extremes that can only be experienced during violent weather such as some thunderstorms, tornadoes, and hurricanes. Earth's wind speeds are 0 to 100 meters per second (0 to 360 kph, 0 to 224 mph). Most often, the average wind speed will be one-tenth the maximum. Your best choice for an Earth-like planet is just to choose the same value (0 to 100 m/s). Then again, if you wanted to create another Arrakis, the upper limit of wind speeds could be as high as 200 m/s (720 kph, 447 mph).

Conversions: 1 m/s = 3.6 kph = 2.236936292 mph

Mean Molecular Weight

For your convenience, I have included an app which will help greatly in this step. It is named SSGCalc.exe. Explaining how to calculate mean molecular is worthy of a few pages of text and actually quite simple. However, since I have included a calculator program to do it for you, why waste the paper?

Atmospheric Composition

Use the AtmosCalc.exe app for this step. You will be able to fiddle around with the numbers in parts per million until you get what is desired.

Halogens

I have seen many persons wanting to make an exotic and corrosive atmosphere by using other natural gases such as: fluorine, chlorine, bromine, hydrofluoride, hydrocyanide, nitric oxide, ethane, fluoromethane, hydrogen sulfide, hydrogen chloride, sulfur dioxide, and/or sulfur trioxide. Only problem with these gases is that all of them are highly reactive with other substances, even in the absence of oxygen. In any atmosphere much like Earth's, these gases will rarely exist beyond a lifetime of a few months, perhaps a year at most, easily combining with water vapor, and thus raining out of the atmosphere to be easily broken down in the oceans and other environments. Besides, these gases will only exist in large amounts in an atmosphere of a highly volcanic planet. And if the planet is volcanic enough to have these gases in large amounts, it would hardly support any life except in the extreme (such as some bacteria and some algae).

Besides, if you truly want a corrosive atmosphere, an atmosphere like Venus will do nicely. Venus's atmosphere is composed of 96.5% Carbon Dioxide, 3.5% Nitrogen, 150ppm Sulfur Dioxide, 70ppm Argon, 20ppm Water, 17ppm Carbon Monoxide, 12 ppm Helium, trace of others. Although water is rather scarce, there is still enough to create carbonic acid, which is the prime ingredient for sodas (called carbonated water). Combined with a pressure over 90 times that of Earth and temperatures averaging around 730K (457C, 854F), this creates a very hostile environment for almost anything we can currently build. The longest lasting lander probe (Venera 13) only survived for 127 minutes. Atmospheres with some water vapor will create carbonic acid from carbon dioxide, sulfuric acid from sulfur dioxide, nitric acid from nitrous oxide, hydrochloric acid from hydrochloride, and hydrofluoric acid from hydrofluoride. Exotically corrosive enough?

Also, remember that the most reactive gas known is oxygen. Oxygen will react with every other element or substance, even the noble gases. No other element or substance is as reactive as oxygen. Although it may take quite a bit longer, oxygen will even rust stainless steel. Only gold is the least reactive substance with oxygen. But, like stainless steel, given enough time, oxygen will react and combine with even gold. Now you know why gold is considered the most precious of metals.