Gravity: Hg Lg Codes?

[kilemall]

I'm not sure where you get that idea. Shaun's post includes a scaling factor between mass and radius (this factor would be proportional to density) and his table includes a density column as well.

He has atmospheric density which is a gold mine I didn't know about especially for those exotic atmospheres, but near as I can tell the chart assumes a consistent density for the planetary mass itself, rather then what I am contending, that the same size/radii could yield different masses with different compositional densities.

Perhaps planetary formation follows a universal formula and our solar system already reveals proper proportions of typical densities- perhaps not.

But at least for exceptions to the rules, I have to think more dense planets have greater mass and therefore G and atmo retention then a straight size definition, and vice versa, lighter density planets can have lower G.

Of course I'm skipping over all that core or no-active core/magnetic field/distance to star stripping atmosphere/atmospheric pressure ala Venus parts that would be major factors as well.

I'm shooting for the generic atmosphere/G results with size to atmo ratio, and the exotic/insidious/corrosive ones can get the special attention to their genesis and unique conditions separately.

 

[Magnus von Thornwood]

Because I am weird.

Magnus von Thornwood used it that way in his PbP. It may have been one of his house rules, but I'm not sure, you'd have to ask him.

I used the SysGen from T5.00 and that gave me some Big Worlds as MainWorlds and so I kept them, but then I read McCaffery and she turned me on to heavy worlders as a minor human race and I have some in my ATU so I use BigWorlds for my ATU.

I know that when I asked Don to give them a pass through his SysEgn validation tools I had to let him know that I was using MainWorlds that were Size A+, so the standard OTU may not use them.

Also, in the BBB on page 447 (page 440 in T5.09 PDF) has World Dimensions which I have found to be awesome for calculating Denisty and Gravity.

 

[77topaz]

I know that when I asked Don to give them a pass through his SysEgn validation tools I had to let him know that I was using MainWorlds that were Size A+, so the standard OTU may not use them.

Yeah, worlds with sizes larger than A don't appear anywhere in Traveller 5 Second Survey, apart from the Paranoia Press sectors and Far Frontiers Sector (and those sectors are still in review, not official yet).

 

[77topaz]

Rob,

*** What do you think are the most important factors in determining gravity? ***

Shalom,
Maksim-Smelchak.

Well, if all else fails, you can use Newton's law of universal gravitation. For that, you only need the radius of the planet and its mass, which would be equal to its density to its volume, which is proportional to its radius.

 

[shaunhilburn]

Shaun, you are telling me composition means nothing and raw volume is everything for gravity?

I have a bit of a problem with that.

In the context of solid planets, composition appears to mean very little. I too was skeptical at first.

There was an article somewhere on the 'net that had illustrations comparing the sizes of iron, rock-iron, and carbon planets; claiming that earth-mass exoplanets all have approximately the same size regardless of composition. There are obvious exceptions; e.g. Mercury, or pelagic exoplanets composed largely of water.

Mass and radius are strongly related, and you can derive mass from radius alone. If you look at the formula for mass I posted earlier, r³×2^r/2, you can cross-check it by calculating masses for the various terrestrial planets:

            Radius    r³×2^r/2       Actual Mass    Variance
Venus       0.9499    0.827850776    0.815         0.012850776
Earth       1.0000    1.0000         1.0000        0
Moon        0.2728    0.012263574    0.0123       -3.64255E-05
Mars        0.5332    0.10968373     0.1079        0.00178373
Io          0.286     0.014261417    0.015        -0.000738583
Europa      0.245     0.008714061    0.008         0.000714061

You can see that this relationship is accurate for terrestrial planets of differing compositions over a wide range of size and mass, with very little variance.

 

[shaunhilburn]

Shaun,


I don't have the column header here.

*** What do these numbers mean? 0.265? And how do they relative to standard gravity ratings (e.g. 1.0G, which correlates to Earth at 0.257)? ***

Thanks!

Those numbers are the planet's scaling exponent, found by taking x = log(r)/log(m); typically lying somewhere between 0.24 (for icy worlds) and 0.3 (silicate with large iron core). Take Ganymede, for example. r=0.413 earth radii and m=0.025 earth masses, and x = Log(0.413)/Log(0.025) = 0.239722576



Also, m = r^(1/x) and r = m^x.

 

[77topaz]

In the context of solid planets, composition appears to mean very little. I too was skeptical at first.

Those numbers are the planet's scaling exponent, found by taking x = log(r)/log(m); typically lying somewhere between 0.24 (for icy worlds) and 0.3 (silicate with large iron core). Take Ganymede, for example. r=0.413 earth radii and m=0.025 earth masses, and x = Log(0.413)/Log(0.025) = 0.239722576



Also, m = r^(1/x) and r = m^x.

But, isn't the scaling exponent proportional to the planet's composition/density?

 

[shaunhilburn]

But, isn't the scaling exponent proportional to the planet's composition/density?

No. It's proportional to the radius and mass. Density is an effect and not a determinant.


A planet accretes a certain amount of mass from the protoplanetary disc, which compacts down under self-gravity to yield a certain radius, determined by the net modulus of compression of the constituent accretion materials. Density and gravity are just the products of the accreted mass and consequent radius.

Many refs get hung up on density. While it's true that density can be used to derive mass, gravity or radius, it's really a back-solving exercise. For most worlds of interest to Travellers, density falls in a range of 0.5 to 1.5 earths. There are some exceptions, but such worlds are oddities and not the norm.

 

[shaunhilburn]

But, isn't the scaling exponent proportional to the planet's composition/density?

Okay - you *could* say it's proportional to density. Dense bodies have higher scaling exponents than low-density bodies.

Take Tarsus (SM/District 268). The Tarsus boxed adventure lists only gives the world's diameter as 8014 km, but there are clues in the module that yield it's density - the geostationary period of it's largest satellite. It works out to a mass of 0.3025 earths, gravity 0.7664 G and suspiciously high density of 6.727 g/cc - far too high for a body this small.

The scaling exponent of this world is log(0.629)/log(0.3025) = 0.387751194. This value is even higher than Mercury with a scaling exponent of (log(0.3829)/log(.055) = 0.330979902.

It can only mean that Tarsus has a grossly over-sized core and shallow mantle, probably resulting from ancient collision. If it were normally accreted world like Venus or Mars, it would have a mass of 0.1924 earths and a scaling exponent of 0.281320191.

 

[Garnfellow]

Curious, I collapsed shaunhilburn's table and compared the sizes and resulting atmosphere ranges to T5 and Mongoose Traveller's "Hard Science" world creation variant:

Size	Atm	T5 Range	MGT Hard Science
0	0	0	0
1	0	0-6	0
2	0	0-7	0
3	1-	0-8	1-, A
4	1, A+	0-9	1-, A
5	1+	0-A	0-A
6	2+	1-B	1-B
7	2+	2-C	2-C
8	4+	3-D	3-D
9	6+	4-E	4-E
A	6+	5+	5+
B	8+	6+	6+
C	8+	7+	7+
D	B+	8+	8+

This suggested to me a revised procedure for generating atmosphere. Once size is determined, roll flux and consult the following table:

Size	-5	-4	-3	-2	-1	0	1	2	3	4	5
0	0	0	0	0	0	0	0	0	0	0	0
1	0	0	0	0	0	0	0	0	0	0	0
2	0	0	0	0	0	0	0	0	0	0	0
3	0	0	0	0	0	1	1	1	1	1	1
4	1	1	1	1	1	A	A	A	A	A	A
5	1	1	2	3	4	5	6	7	8	9	A
6	2	2	3	4	5	6	7	8	9	A	B
7	2	3	4	5	6	7	8	9	A	B	C
8	4	4	5	6	7	8	9	A	B	C	D
9	4	5	6	7	8	9	A	B	C	D	E
A	5	6	7	8	9	A	B	C	D	E	F
B	8	8	8	9	A	B	C	D	E	F	F
C	8	8	9	A	B	C	D	E	F	F	F
D	B	B	B	B	C	D	E	F	F	F	F

 

[77topaz]

Curious, I collapsed shaunhilburn's table and compared the sizes and resulting atmosphere ranges to T5 and Mongoose Traveller's "Hard Science" world creation variant:

(table snip)

This suggested to me a revised procedure for generating atmosphere. Once size is determined, roll flux and consult the following table:

(table snip)

You're not the first person to devise such a method - there is a house rule for it at the Zhodani Base, and I think Don McKinney had one as well, which was used for the Traveller 5 Second Survey.

 

[Maksim-Smelchak]

For solid bodies, mass and radius are logarithmically coupled; they are not independent values. You can determine the scaling exponent for any solid body taking x = log(r)/log(m). In our solar system, this yields values of x between 0.24 and 0.3.

     Large icy moons      0.239 - 0.242    0.240   Callisto, Ganymede, Titan
     Superterrestrials    0.265 - 0.275    0.270
     Plutinos, KBOs       0.271 - 0.285    0.280   Triton, Pluto, Charon
     Icy moonlets         0.265 - 0.290    0.278   Dione, Rhea, Mimas, Iapetus
     Large Terrestrials   0.257 - 0.283    0.281   Mars, Earth, Venus
     Small Terrestrials   0.292 - 0.298    0.295   Io, Europa, Moon
     Asteroids            0.292 - 0.324    0.309   Pallas, Juno
     Mercury              0.300 - 0.350    0.332

Mercury is the outlier here because of its over-sized core.


I produced the following table using this principle. It shows the various formulae used for each column. Units are earth masses, earth radii, earth gravity where Earth = 1. The first column is the Traveller size digit, and the second is earth radii based on Size/7.9175, because Earth is not precisely Size 8.

Calculated mass m, density d, gravity g of silicate or carbon planets with FeNi or FeS cores and 32.5% core mass fraction.
Note: Icy planets with silicate cores have 33% to 66% of the calculated mass and gravity.

                         r³×2^(r-1)  2^(r-1)    r×2^(r-1)
             S/7.9175    r³×2^r/2    2^r/2      r×2^r/2    10/(m/r)  HZ
     Size S  Radius r    Mass m      Density d  Gravity g  MMWR    Atmosphere
     ------------------------------------------------------------------------
      0.2    0.0253      0.0000      0.5088     0.013                0         semi-spherical
      0.3    0.0379      0.0000      0.5133     0.019                0         smallest spherical bodies
      0.4    0.0505      0.0001      0.5178     0.026                0
      0.5    0.0632      0.0001      0.5224     0.033                0
      0.6    0.0758      0.0002      0.5270     0.040                0
      0.7    0.0884      0.0004      0.5316     0.047                0
      0.8    0.1010      0.0006      0.5363     0.054                0
      0.9    0.1137      0.0008      0.5410     0.062                0
      1.0    0.1263      0.0011      0.5457     0.069                0
      1.5    0.1895      0.0039      0.5702     0.108                0
      2.0    0.2526      0.0096      0.5957     0.150                0
      2.5    0.3158      0.0196      0.6223     0.197      159.6     1-
      3.0    0.3789      0.0354      0.6502     0.246      106.1     1-        retains sulfur hexafluoride
      3.5    0.4421      0.0587      0.6793     0.300       74.6     1
      4.0    0.5052      0.0915      0.7097     0.359       54.7     1, B+     retains sulfur dioxide
      4.5    0.5684      0.1361      0.7414     0.421       41.3     1, A+     retains carbon dioxide, argon, hydrogen sulfide
      5.0    0.6315      0.1951      0.7746     0.489       32.0     2+        minimum habitable mass, retains oxygen, acetylene, ethylene
      5.5    0.6947      0.2713      0.8093     0.562       25.4     2+        retains nitrogen, ethane
      6.0    0.7578      0.3679      0.8455     0.641       20.4     2+
      6.5    0.8210      0.4887      0.8833     0.725       16.6     2+
      7.0    0.8841      0.6377      0.9228     0.816       13.7     2+        retains methane, ammonia
      7.5    0.9473      0.8195      0.9641     0.913       11.4     2+
      8.0    1.0104      1.0391      1.0072     1.018        9.6     4+
      8.5    1.0736      1.3021      1.0523     1.130        8.2     4+
      9.0    1.1367      1.6148      1.0994     1.250        7.0     6+
  A   9.5    1.1999      1.9842      1.1486     1.378        6.0     6+
     10.0    1.2630      2.4178      1.2000     1.516        5.2     8+        superterrestrial planet
  B  10.5    1.3262      2.9241      1.2537     1.663        4.5     8+
     11.0    1.3893      3.5125      1.3098     1.820        3.9     8+        retains helium
  C  11.5    1.4525      4.1931      1.3684     1.988        3.4     8+
     12.0    1.5156      4.9774      1.4296     2.167        3.0     8+
  D  12.5    1.5788      5.8775      1.4936     2.358        2.7     B+        maximum terrestrial planet size
     13.0    1.6419      6.9073      1.5604     2.562        2.4     B+        gas giant core, chthonian planet

Shaun,

Isn't planetary density also a significant factor?

Shalom,
Maksim-Smelchak.

 

[shaunhilburn]

Shaun,

Isn't planetary density also a significant factor?

Shalom,
Maksim-Smelchak.

The table in the previous post has a density column, along with the formula to derive it.

LBB Book 2 (and other sci-fi worldbuilding sources) use a density constant along with size to derive the other values - assuming that density is independent of size.

It doesn't appear to be the case. Among the solid bodies in our solar system, density, mass, and gravity increase with size.