Yeah! To The Demotion of Pluto, But not why…
Updated 9/1/2006 — Added 2 more links, added some more algebra, reformated links to download Emule
Links to some of the Pluto Articles
Original Rules
- (a) is in orbit around the sun
- (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape
- (c) has cleared the neighborhood around its orbit.
- (a) is in orbit around the sun
- (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape
- (c) has not cleared the neighborhood around its orbit
- (d) is not a satellite
My opinion
I agree with booting out pluto, stripping its ‘full planet’ label, but not why. Put mercury in pluto’s position, and it isn’t going to clear out it’s orbit of comet-crap either. Mercury got that for free from the stronger solar wind because of it’s close orbit. I think it should be the ability to retain a carbon dioxide atmosphere at a specific black-body temperature, whether earth’s, a nice round number, the snow-line (as defined by GURPS Space - distance from the star at which water ice could exist during planetary formation), or at the ‘outer limit’ of 40AU (as defined by GURPS Space - Pluto-Centric). This min-RMM / MMWR criteria is also assuming that the atmosphere never freezes way out there in the outer reaches of the solar system.
Revised Rules
- (a) is in orbit around the sun
- (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape (I would like to see some numerical boundaries for this, probably a function of radius and density)
- (c) Has a MMWR (Minimum Molecular Weight Retained) of 44 or less (Retains Carbon Dioxide molecules over geological time) at a black-body temperature of 275 degrees Kelvin.
- (a) is in orbit around the sun
- (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape (I would like to see some numerical boundaries for this, probably a function of radius and density)
- (c) Has a MMWR (Minimum Molecular Weight Retained) of over 44 (Does not retain Carbon Dioxide molecules over geological time) at a black-body temperature of 275 degrees Kelvin.
- (d) is not a satellite
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Planet Test at 44K (GURPS Space 4th Ed Outer-Limit, Approx Pluto mean orbital radius), 126.25K (GURPS Space 4th Ed snow-line), 275K (near freezing and Near Earth’s BlackBody Temperature), 300K (nice round number, summer heat)
Algebra for converting the GURPs Space 4th Ed MMWR formula:
W=MMWR, B=BlackBody Temperature, D=Diameter or Radius in ratio of earth, K=Density in ratio of earth
W = B/(60 x D^2 x K)
W/B=1/(60 X D^2 x K)
B/W=60 X D^2 x K
B / W / 60 = D^2 x K
Carbon Dioxide has a RMM (real molar-mass) / molecular weight of 44 - Carbon-12 + 2 x Oxygen-16 and Sulfur Dioxide has a RMM of 64 - Sulfur-32 + 2 x Oxygen-16.
Retain RMM 64 (Sulfur Dioxide) @ Black-Body Temperature of 44K : Radius^2 * Density > 0.0114583333 Retain RMM 64 (Sulfur Dioxide) @ Black-Body Temperature of 126.25K : Radius^2 * Density > 0.0328776042 Retain RMM 64 (Sulfur Dioxide) @ Black-Body Temperature of 275K : Radius^2 * Density > 0.0716145833 Retain RMM 64 (Sulfur Dioxide) @ Black-Body Temperature of 300K : Radius^2 * Density > 0.078125 (1/12.8) Retain RMM 44 (Carbon Dioxide) @ Black-Body Temperature of 44K : Radius^2 * Density > 0.0166666667 Retain RMM 44 (Carbon Dioxide) @ Black-Body Temperature of 126.25K : Radius^2 * Density > 0.0478219697 Retain RMM 44 (Carbon Dioxide) @ Black-Body Temperature of 275K : Radius^2 * Density > 0.1041666667 (1/9.6) Retain RMM 44 (Carbon Dioxide) @ Black-Body Temperature of 300K : Radius^2 * Density > 0.1136363636 (1/8.8) Radius (D) is in ratio of Earth’s Radius (Target Radius / Earth Radius) - I’m using radius instead of diameter. Density (K) is in Ratio of Earth’s Radius (Target Density / Earth Density) Mercury D^2 x K — (2439.7/6378.137)^2 * (5.427/5.5153) = 0.1439712736 Pluto D^2 x K — (1153/6378.137)^2 * (2.03/5.5153) = 0.012028122 Ceres D^2 x K — (975/6378.137)^2 * (2.08/5.5153) = 0.0088128370262 2003_UB313 (Xena) D^2 x K — (1200/6378.137)^2 * (2.03/5.5153) = 0.0130287186 (Using Pluto’s Density) 2003_UB313 (Xena) D^2 x K — (1200/6378.137)^2 * (0.5) = 0.0176988403 (Using midpoint of 0.5 of density range for icy-core planets in GURPS Space 4th Ed Pg 85)
Planetary Stats are from the Wikipedia - Earth, Mercury, Pluto, 2003_UB313 (Xena), Ceres
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Expansion of GURPS Space 4th Ed planet-size criteria (optional advanced rule) to accomodate the “Dwarf Planet” class
Size- Min- Max- Gas with atomic- Category MMWR MMWR weight at max-MMWR Huge 0 2 Hydrogen (H2) Large 2 4 Helium (He2) Medium 4 18 Water Vapor (H2O) Small 18 28 Nitrogen (N2) Tiny 28 44 Carbon Dioxide (CO2) Planetoid / 44 0 None Dwarf Planet
for a planet to be considered a Gas Giant, it must be ‘Huge’ size (retains hydrogen) and more than 5% of the planet’s mass must be gas/atmosphere (StarGen rule, not GURPs Space).
This does not factor in a fixed black-body temperature that I would want used in the criteria of Planet vs Dwarf-Planet in real life. It just expands the rules of the GURPS Space RPG for the new astronomical happenings. Some of the excerpts below (both the standard and advanced rules section) show that GURPs Space physical size barriers vary by both blackbody temperature and density.
2003_UB313 (Xena) has a semi-major axis of about 67.67 AU, so at 67.67 AU from the sun, it has a black-body temperature of 33.79K, which at that temperature, a D^2 x K of 0.0127992424 or more is needed to retain Carbon Dioxide. Pluto (D^2*K=0.012028122) fail to reach this number, it is still a dwarf planet / planetoid even on a non-fixed black-body temperature based MMWR/44 requirement. 2003_UB313 (Xena) (Pluto’s Density Assumed; D^2*K=0.0130287186), however does pass, so at 2003_UB313 (Xena) with Pluto’s Density assumed qualifies as a Tiny planet under this expanded GURPs Space size categorization system, because it will retain Carbon Dioxide over geological time at the mean orbital radius (I just used the semi-major axis from the Wikipedia as the mean orbital radius). That’s why I would prefer testing at a fixed black-body temperature.
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Algebra to convert to derive the Inner Limit, Snow-Line, and Outer Limit Black-Body Temperatures from GURPS Space 4th Ed’s BlackBody temperature and Inner Limit / Snow-Line / Outer Limit formulas:
(Correcting 77300 to 77284 — 278^2=77284)
Radius of a specified blackbody temperature: R=(77284/B^2) x L^0.5
Radius of the inner-limit: R=0.01 * L^0.5
77284/B^2=0.01
1/B^2=0.01/77284
B^2=77284/0.01
B=(77284/0.01)^0.5
Blackbody temperature of the inner-limit: 2780 K
Blackbody temperature of the inner-limit (rounded): 2780K
Radius of a specified blackbody temperature: R=(77284/B^2) x L^0.5
Radius of the snow-line: R=4.85 * L^0.5
77284/B^2=4.85
1/B^2=4.85/77284
B^2=77284/4.85
B=(77284/4.85)^0.5
Blackbody temperature of the snow-line: 126.2332973538 K
Blackbody temperature of the snow-line (rounded to nearest 0.25): 126.25 K
Radius of a specified blackbody temperature: R=(77284/B^2) x L^0.5
Radius of the outer-limit: R=40 * M (Alter to 40 * L^0.5)
77284/B^2=40
1/B^2=40/77284
B^2=77284/40
B=(77284/40)^0.5
Blackbody temperature of the outer-limit: 43.9556594763 K
Blackbody temperature of the outer-limit (rounded): 44 K
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As you can see, GURPS Space rocks. It is very realistic, has hard physics formulas, and it still keeps that sci-fi feel, and it so does well in simplifying the math to a Junior-High 7th-9th grade level, mostly by converting all the units of measurement to ratios vs Earth or the Sun.
Get GURPS Space
Other cool web links
ED2K links
If you don’t have Emule yet, you can get it through these links (I use MorphXT):
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GURPS Space 4th Edition Page 108 — Placing a Pre-Designed World
If a world has already been designed for the star system using the basic world-building sequence in Chapter 4, then that world should also be placed at a specific distance from one of the stars in the system.
The exact orbital radius for the predesigned world depends on the luminosity of its primary star (as generated in Step 18) and the world???s blackbody temperature (as generated in Step 5). Use the following formula:
R = (77,300/B^2) x square root of L
Here, R is the orbital radius in AU, B is the world???s blackbody temperature, and L is the star???s luminosity in solar units. Compute this orbital radius for each of the stars, and choose one of them to be the predesigned world???s primary.
Note that the proper distance may fall inside the inner limit radius, outside the outer limit radius, or within a forbidden zone for a given star. In this case, the world cannot be placed in orbit around that star.
It???s also possible for the predesigned world to end up being too close to the star???s first gas giant, if any. Determine the ratio between the two worlds??? orbital radii, by dividing the larger radius by the smaller. If the ratio is less than 1.4, then the two worlds are too close together ??C the gas giant???s gravitational influence will tend to make the pre-designed world???s orbit unstable. The pre-designed world cannot be placed in orbit around that star.
Given these two restrictions, it???s possible for a pre-designed world to have no place to go. If this happens, consider returning to Step 15 to generate a new star or set of stars to fit, or choosing a different arrangement of gas giants for one or more of the stars.
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GURPS Space 4th Edition Page 84 — Determining Blackbody Temperature
Another parameter related to a world???s climate is its blackbody temperature. This is the average surface temperature the world would have if it were an ideal blackbody, a perfect absorber and radiator of heat. Of course, real worlds are not ideal blackbodies, so the blackbody temperature is usually different from the world???s average surface temperature.
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GURPS Space 4th Edition Page 113 — Blackbody Temperature
First, the blackbody temperature (p. 84) must be computed for each world. Use the following formula:
B = 278 x (fourth root of L)/(square root of R)
Here, B is the blackbody temperature in kelvins, L is the primary star???s luminosity in solar units, and R is the average orbital radius of the world (or of the planet of which the world is a moon). Note that the blackbody temperature will be the same for a planet and for all of its moons. Record the blackbody temperature for each world, rounded to the nearest kelvin.
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GURPS Space 4th Edition Page 85-86 — Diameter and Surface Gravity
Diameter and Surface Gravity Once the world???s density has been fixed, it is possible to determine its diameter and surface gravity. These two parameters are closely related ??C if you select the world???s diameter, that determines its surface gravity, and vice versa. The following rules will permit the GM to select these two parameters in either order.
Selecting World Diameter First: Refer to the Size Constraints Table for the world???s size class. Multiply square root of (B/K) (where B is the world???s blackbody temperature in kelvins, and K is the world???s density in units of Earth???s density) by the appropriate Minimum value from the table. The result is the minimum possible diameter for the world, expressed in multiples of Earth???s diameter. Similarly, multiply square root of (B/K) by the appropriate Maximum value from the table to get the maximum possible diameter for the world.
Select any value within this range for the diameter. To select a diameter at random, roll 2d-2, multiply by onetenth of the difference between the maximum and minimum diameter values, and add the result to the minimum value. Feel free to vary the final result by up to 5% of the difference, so long as the final value is within the range. To express any diameter in miles, multiply the value in Earth diameters by 7,930.
Once the diameter is known, use the following formula to get the world???s surface gravity:
S = K x D
Here, S is the world???s surface gravity in Gs, K is the world???s density in units of Earth???s density, and D is the world???s diameter in Earth diameters.
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GURPS Space 4th Edition Page 86 — Worlds Big and Little
When designing a world, it???s important to know what volatiles will be available at the world???s surface, defining the environment visitors will experience. Every world begins with a wide variety of volatiles, but some of these will be lost very early in the world???s history. The most common reason for such loss is the fact that molecules of a given volatile that are close to the top of the world???s atmosphere might reach escape velocity and head for deep space!
Molecules in a gas move at random speeds, and the distribution of those speeds is determined by the molecular weight of the gas and by the ambient temperature. Higher temperatures mean that the molecules tend to move faster ??C but the more massive molecules of a gas with high molecular weight will move more slowly at the same temperature. In effect, every world has a minimum molecular weight retained (MMWR) that indicates what volatile substances can be held onto across billion-year time scales. Volatiles with molecular weight higher than the MMWR will stay in the world???s atmosphere and on its surface. Volatiles with lower molecular weight will be lost to space in a relatively short time after the world is formed.
Factors that increase a world???s escape velocity all tend to lower the minimum molecular weight that can be retained. A more massive world will have a higher escape velocity. So will a denser world, even of the same mass.
On the other hand, the temperature at the top of the atmosphere is also critical; higher temperatures mean that more molecules will reach escape velocity. Thus two worlds can have the same MMWR despite being of different sizes, so long as the smaller one is colder. Steps 2-6 of the world design sequence are set up so that the GURPS GM doesn???t need to concern himself with the details of computing a world???s MMWR. Advanced world-builders may choose to work in a more free-form manner, selecting a world???s physical parameters as needed and then checking to make sure the result makes sense. In that case, the following formula may be of use:
W = B/(60 x D^2 x K)
Here, W is the MMWR measured in units of molecular weight, B is the world???s blackbody temperature in kelvins, D is its diameter in Earth diameters, and K is its density in units of Earth???s density.
A world???s physical parameters will fit its selected World Type if its MMWR is legal for its size class. A Large world must have MMWR greater than 2, but less than or equal to 4. A Standard world must have MMWR greater than 4, but less than or equal to 18. A Small world must have MMWR greater than 18, but less than or equal to 28. A Tiny world must have MMWR greater than 28.
For comparison, some of the more important molecular weights are: hydrogen 2, helium 4, methane 16, ammonia 17, water vapor 18, neon 20, carbon monoxide 28, nitrogen 28, nitric oxide 30, oxygen 32, hydrogen sulfide 34, argon 40, and carbon dioxide 44.
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GURPS Space 4th Edition Page 106 — Step 20: Locate Orbital Zones
Inner Limit Radius
Planets will not form too close to a star. Even while a star is on the main sequence, a planet is very unlikely to form in a stable orbit within a certain distance. Once a star moves into the subgiant or giant phases of its evolution, existing planets that find themselves too close may be vaporized by the swollen star???s intense heat.
For each star in the target star system, compute the inner limit radius using both of the following formulae. The inner limit radius that applies will be the larger of the two values. For almost all stars on the main sequence, the first of the two formulae will be the one to apply ??C the second formula becomes dominant for extremely luminous stars.
I = 0.1 x M
I = 0.01 x square root of L
Here, I is the inner limit radius in AUs, Mis the star???s mass in solar units, and L is the star???s luminosity in solar units.
Outer Limit Radius
Planets will also not form too far away from a star. At a large distance, orbital movements are leisurely. Protoplanets will have much less opportunity to sweep up matter before the star ignites and the process of planetary formation is halted.
For each star in the target star system, compute the outer limit radius
using the following formula.
O = 40 x M
Here, O is the outer limit radius in AUs and M is the star???s mass in solar units. Planets will be able to form anywhere between the inner and outer limit radii, so long as no other stars interfere with their gravitational influence.
Snow Line
Next, compute the snow line radius for each star. This is the distance from the star at which water ice could exist during planetary formation, marking the most likely region for the formation of the star???s largest gas giant planet. The snow line radius can be found using the following formula:
R = 4.85 x square root of L
Here, R is the snow line radius in AUs and L is the star???s initial luminosity on the main sequence (the L-Min value from the Stellar Evolution Table).
