World Size and Gravity - Errata?

[far-trader]

Just wondering about the difference between MgT (Core) and the rest of (to my knowledge) Traveller on this. Is there a (good) reason for the change, or is it just errata?

Compare...

Digit     Mong     Olde
World     Trav     Trav
Size:     Gees:    Gees:

  0        neg     0.000
  1       0.05     0.125
  2       0.15     0.250
  3       0.25     0.375
  4       0.35     0.500
  5       0.45     0.625
  6       0.70     0.750
  7       0.90     0.875
  8       1.00     1.000
  9       1.25     1.125
 10       1.40     1.250

An interesting note here, MgT lists Mars as an example of a size 4 world. While the diameter and MgT gravity are a close match, it should be noted that Mars has a lower gravity than its size would indicate because it is also of a lower density than Earth.

Previously Traveller presumed a standard (Earth) density across all world sizes and the gravity was calculated from that. Did Mongoose choose to apply a different (variable?) density and then forget to include that in the book?

 

[far-trader]

Addendumb

Now I see "The values for gravity in the table below assume that the world has a density similar to that of Earth." in the MgT Core book. So, just like olde Traveller, only not?

Add this question then: How "similar" (close) to Earth density? If the olde Traveller values were properly calculated then either MgT got them wrong or "similar" has a wider variation in this usage than I would expect.

 

[DFW]

N.B. Mercury is size 3 and has the same gravity as Mars. I guess we really don't have enough sample of terrestrial planets to know what an average density should be.

 

[far-trader]

N.B. Mercury is size 3 and has the same gravity as Mars. I guess we really don't have enough sample of terrestrial planets to know what an average density should be.

Yeah, which I always figured the olde way of using as example and noting that it was for standard Earth density was the way to go. And MgT seems in agreement by the statement in the book (but then flip-flops? and lists non-standard gravity in the table :? ).

At least if it is noted that the values are for standard density (and correct gravity is given for them) then the ref can choose to modify up or down for higher or lower density worlds. Heck, even give the formula and let the ref calculate it. CT did, it's not that difficult.

I don't get the discontinuity between the stated standard Earth density application and the mismatching table figures for gravity. I wonder too that the discrepancy wasn't raised in playtesting (or do I presume too much) or since, unless I missed it.

I'm hoping for some official explanation. Not overly expectant of it, just hoping

And failing that it could at least open up an interesting side topic. Varying the gravity for world sizes to give players all kinds of fun :twisted:

Anyway, to that end and for the non-math-phobic, the CT formula for calculating surface gravity:

G = K ( D/8 ) (NOTE: I'm not swearing to this as an accurate formula*, it's just what CT used, and it is exceedingly simple math wise )

Where:

G is surface gravity in standard Earth gravities (Earth is 1G, of course)
K is the planet's mean density where Earth's density is 1 (naturally)
D is of course the UWP value for the world size (Earth is 1 again)

For worlds with a mean density greater than Earth: K will be greater than 1 by some fraction. Not by a lot unless invoking some sci-fi like a core with a mini black hole or some abundant superdense element.

For worlds with a mean density lower than Earth: K will of course be less than 1 by some fraction. And again not by a lot without some sci-fi element like a hollow world or something.

* I've long wondered if it properly accounts for volume being it relies on simply the world diameter, though that is what's immediately under your feet I've been too lazy to think much about it It's always been good enough for a game.

 

[DFW]

At least if it is noted that the values are for standard density (and correct gravity is given for them) then the ref can choose to modify up or down for higher or lower density worlds. Heck, even give the formula and let the ref calculate it. CT did, it's not that difficult.

Yes, a simple stand assumption is best for a game system. As you note, refs can then adjust from a common density value.

 

[far-trader]

A bit boredom, a bit insomnia, I figured I'd hunt up and post some values as guidelines for playing with density and gravity

Density (mean I suppose) of planets and gas giants (anddangityesplutotoo ) in our solar system.

Values are in Ks (Earth density) and rounded to 1 decimal point:

Mercury: 1.0
Venus: 0.9
Earth: 1.0
Mars: 0.7
Jupiter: 0.2
Saturn: 0.1
Uranus: 0.2
Neptune: 0.3
Pluto: 0.3 to 0.4

And the densest detected extrasolar planet yet...

55 Cancri e: 1.4 to 2.5 (variable due to error margin) stated as 2.0

So, for our solar system my fractional note is right, but there appear to be those that exceed it, up to 2.0 or 2.5 times Earth density, out there, presumably without sci-fi fantasitic explanation

Oh, and btw, Earth's iron core itself is about 1.5

 

[rust]

Previously Traveller presumed a standard (Earth) density across all world sizes and the gravity was calculated from that.

Well, no.

Traveller New Era, page 190, has a table with different densities and sur-
face gravities for the various diameters of the planets. For example, a
planet with a diameter of 1,600 km / Size 1 has 0.1 G if it has a low den-
sity, 0.15 G if it has an average density and 0.3 G if it has a high density.

In my view TNE had the most "hard science" approach to world building
of all the Traveller versions, almost on the level of the earlier versions of
GURPS Space, but unfortunately many of the data are now no longer in li-
ne with the current state of astronomy and planetology, simply because
there were no data on other systems and planets when it was written,
and it had our system as the only reference.

As with many things Traveller, you can either accept that a Traveller uni-
verse has slightly different laws of nature and use the data from the ru-
les, or prefer a universe that is more like our real one, and use different
sources, like GURPS Space 4.

 

[DFW]

Well, no.

Traveller New Era, page 190, has a table with different densities and sur-
face gravities for the various diameters of the planets. For example, a
planet with a diameter of 1,600 km / Size 1 has 0.1 G if it has a low den-
sity, 0.15 G if it has an average density and 0.3 G if it has a high density.

Sounds like just a slight variation from what F.T. suggested. Average density listed with adjustments for above and below that base. A rose by a different name if you will.

I think I might hunt up a copy of GURPS Space 4 though.

 

[rust]

I think I might hunt up a copy of GURPS Space 4 though.

It is really good, especially because it provides the formulas to calculate
the data, and not only the data itself. This also makes it easier to "update"
it whenever some new discoveries are reported.

Up to now the only problem I ran into is connected with the formulas for
tide locked planets, it seems that they produce less tide locked planets
than they should. Since I normally use F or G stars for my settings, this
does not annoy me enough to search for better formulas, which seem on-
ly necessary when K and M stars are involved.

 

[BP]

...I don't get the discontinuity between the stated standard Earth density application and the mismatching table figures for gravity. ...

Figured out where the MgT values probably came from, but can't recall just now... they are definitely not based on Earth density (error in the statement or table).

BTW: Another really simple equation assuming Earth density (should match CT):

• gs = diameter / 1280
  
  where gs is the surface gravity in manuever drive g's of 10 m/s^2 and diameter is number in km. This is basically the same as the CT formula (see below) - using diameter instead of UWP and setting K = 1.0.

With Earth quite dense as planets go (in our system), it might have been preferable to have more primary planets larger for purposes of 'adventuring' away from high-TL cities, but CT did not...

...G = K ( D/8 ) (NOTE: I'm not swearing to this as an accurate formula*, it's just what CT used, and it is exceedingly simple math wise )
...
* I've long wondered if it properly accounts for volume being it relies on simply the world diameter, though that is what's immediately under your feet I've been too lazy to think much about it It's always been good enough for a game.

Yes, actually it does. This is only counter intuitive when not thinking in 3D space (gravity applying to a volume)

My crude summary:

• Surface Gravity g = 4/3 * pi * G * p * r
  
  Where:
  g = nominal surface gravity
  pi = ratio circumference to diameter of a circle, or area to radius squared (Euclidean - unitless) ~ 3.14159
  G = measured gravitational constant (i.e. empirical) ~ 6.674 * 10^-8 cm^3/(g * s^2)
  p = mean density (mass/volume); Earth's ~ 5.515 g/cm^3
  r = nominal radius (Earth's ~ 6,371 km)
  
  Note that everything but g and r are constant values - so g varies proportionately to distance r. So things simplify using a constant C for everything but g and r to:
  • g = C * r
  Playing with the units, one ends up the earlier equations ( C = 1 / 1280 for MgT gs...)