"jump masking" based on gravity

[Malenfant]

Since RainOfSteel asked, here's a table showing jump limits based on the mass of the object you're jumping from (using the strength of the gravitational field - you can't jump in a gravitational field that is stronger than 0.01 m/s2.).

If you want to use a higher or lower field strength as the limit, you need to multiply the distance in metres on the tables below by 1/(SQRT(R)), where R is the ratio of the new g-limit to the old one. So if you want to set the limit at 0.02m/s2, you multiply the existing 0.01m/s2 limit by 1/(SQRT(2)), which moves the limit closer to the star.

The full formula is:

D = SQRT(GM/g)

where D = distance of jump limit from centre of body (in metres), G = 6.672559e-11, M = mass of object in kg, and g is the local g-field strength in m/s2.

In all cases, this is distance from the centre of the body. If the limit is smaller than the object's radius, then jump can occur from any distance beyond its surface.

Note also that since it is related to mass, the limit doesn't change through any stellar evolutionary stage (unless the star loses mass, as it would when it became a white dwarf or neutron star).

Note that the jump limit for white dwarfs here remains around 0.5 AU, not a few million km - and for giants and supergiants the jump limit is usually within the star's radius. It also means that the jump limit for brown dwarfs increases as they become more massive - in the old system, it would stay the same since they keep the same radius as they get more massive.

For stars:
</font><blockquote>code:</font><hr /><pre style="font-size:x-small; font-family: monospace;">Solar limit/metres limit/AU
masses
15 4.46179E+11 2.97 Antares
14 4.3105E+11 2.87
13 4.1537E+11 2.77
12 3.99075E+11 2.66
11 3.82085E+11 2.55
10 3.64304E+11 2.43
9 3.45609E+11 2.30
8 3.25843E+11 2.17
7 3.04798E+11 2.03 B3 V
6 2.82188E+11 1.88 B4 V
5 2.57602E+11 1.72 B5 V
4 2.30406E+11 1.54 B7 V
3 1.99537E+11 1.33 B9 V
2 1.62922E+11 1.09 A5 V
1.75 1.52399E+11 1.02 A8 V
1.5 1.41094E+11 0.94 F1 V
1.25 1.28801E+11 0.86 F7 V
1.1 1.20826E+11 0.81 G0 V
1 1.15203E+11 0.77 G2 V (Sol)
0.9 1.09291E+11 0.73 G7 V
0.8 1.03041E+11 0.69 K1 V
0.7 96385703793 0.64 K3 V
0.6 89235821902 0.59 K5 V
0.5 81460787656 0.54 K7 V
0.4 72860743480 0.49 K8 V
0.3 63099254792 0.42 M0 V
0.2 51520325797 0.34 M4 V
0.1 36430371740 0.24 M5 V
0.08 32584315062 0.22 M9 V</pre>[/QUOTE]For Jupiter masses (Brown dwarfs, superjovians, and LGGs):
</font><blockquote>code:</font><hr /><pre style="font-size:x-small; font-family: monospace;">Jupiter limit/metres limit/AU
masses
70 29774421720 0.20 Largest BD
60 27565758087 0.18
50 25163979198 0.17
40 22507347229 0.15
30 19491934472 0.13
20 15915097852 0.11
10 11253673614 0.08 Smallest BD
5 7957548926 0.05
2 5032795840 0.03
1 3558724067 0.02 Jupiter</pre>[/QUOTE]For Earth masses (SGGs, large terrestrials):
</font><blockquote>code:</font><hr /><pre style="font-size:x-small; font-family: monospace;">Earth limit/metres limit/AU
masses
100 1996577120 0.01331 Saturn
50 1411793221 0.00941
25 998288560.2 0.00666
15 773270993.7 0.00516 Uranus/Neptune
10 631373122.5 0.00421
9 598973136.1 0.00399
8 564717288.4 0.00376
7 528244653.4 0.00352
6 489059517.7 0.00326
5 446448216.4 0.00298
4 399315424.1 0.00266
3 345817301.4 0.00231
2 282358644.2 0.00188
1 199657712 0.00133 Earth</pre>[/QUOTE]For Earth masses (small terrestrials):
</font><blockquote>code:</font><hr /><pre style="font-size:x-small; font-family: monospace;">Earth limit/metres limit/km
masses
0.8 178579286.5 178579 Venus
0.5 141179322.1 141179
0.4 126274624.5 126275
0.3 109357032.7 109357
0.2 89289643.27 89290
0.1 63137312.25 63137 Mars
0.05 44644821.64 44645 Mercury
0.01 19965771.2 19966 Moon</pre>[/QUOTE]EDIT: Added some explanation

 

[RainOfSteel]

Well, just right off the bat, I like it.

More study is needed, but a quick glance at Book 6's Table of Zones charts and the Planetary Orbits chart clearly shows that under this model, worlds found in the habitable zone of many stars will lie outside the Jump Limit of those stars.

This is great news.

 

[RainOfSteel]

Mal,

Sorry.

Tomorrow (or maybe it was yesterday), you are scheduled for &#147redeployment&#148 via closed time-like curves to 1975, where your new identity as a member of the staff of GDW awaits you!

Wait! That either means that Mal will work on CT/MT for at least 16 years, or TNE will start in 1977! The horror!


But at least the worldbuilding sections of the game will get a leg up.

 

[Malenfant]

Nah, tomorrow is when Marc pulls off his mask to reveal... me!

If you excuse me, my head will explode now


Anyway, your observation is why I like this limit. Makes more sense in a physical sense too - it always struck me as being a bit barmy to base a jump limit like this on something as changeable (and relatively meaningless) as radius.

The "tidal limit version" that IIRC Anthony Jackson came up with is based on the cube root rather than the square root - basically, the limit is determined by the rate of the change of gravitational field, not the gravitational field itself. I like my version better because it's easier to visualise .

 

[RainOfSteel]

Originally posted by Malenfant:
Nah, tomorrow is when Marc pulls off his mask to reveal... me!

If you excuse me, my head will explode now


Anyway, your observation is why I like this limit. Makes more sense in a physical sense too - it always struck me as being a bit barmy to base a jump limit like this on something as changeable (and relatively meaningless) as radius.

Well, IMNSHO, it was originally based on "getting out of the gravity well." The 100 Diameter limit was an abstraction used to avoid mathematical gravity calculations.

Any definition based on real science and gravity is, by definition, superior.

Doubly especially sinces it preserves Marc's original vision of how "things work". Which Jump Masking based on Stellar Radii x 100 destroys.

Originally posted by Malenfant:
The "tidal limit version" that IIRC Anthony Jackson came up with is based on the cube root rather than the square root - basically, the limit is determined by the rate of the change of gravitational field, not the gravitational field itself. I like my version better because it's easier to visualise .

Well, guess what? So do I. It also appears to involve fewer calculations, to boot.


This material has been saved away, and you can be sure, is (for the moment, at least) now considered "official" IMTU.

 

[Malenfant]

Originally posted by RainOfSteel:
This material has been saved away, and you can be sure, is (for the moment, at least) now considered "official" IMTU. [/QB]

Mwahahahaaaaa. The corruption spreads!

 

[LordVince]

I gotta agree with RainOfSteel. This is something that I've been puzzling over for some time -- but I suck at the mathematics.

Like RainOfSteel, I, too, have copied this data, and filed it away as part of IMTU.

Thank you, Malenfant.

 

[TheEngineer]

Hi folks !

Actually I am trying to improve my solar system viewer software in order to show "real" jump limits based on the calculations shown above.

Just doing that I realized, how drastically the usage of the 0,01 m/s2 limit decreases travel times of typical planets (as the limit of an earth sized planets is now roughly at 16 diameters). Is that intended ?
Mal, why didnt You choose that 0,00027 m/s2 representing earths 100 D limit gravitation ?

Well, I guess I will leave the g limit editable anyway.

Best regards,

Mert

 

[rancke]

Originally posted by Malenfant:
The "tidal limit version" that IIRC Anthony Jackson came up with is based on the cube root rather than the square root - basically, the limit is determined by the rate of the change of gravitational field, not the gravitational field itself. I like my version better because it's easier to visualise .

I like the tidal model better because it is linear, which means that given a specific density, the result match those of the original rules. I.e. if the limit is 100 diameters for a world with a density of (say) 5.5, the limit will be 100 diameters for all worlds with a density of 5.5, regardless of what that diameter is.

That means that while you get radically different numbers for suns and gas giants, you get numbers very close to the original for world. Which is, I submit, the most important part. Also, all you need to get the figures for suns and gas giants is a list of the most common densities and the corresponding number of diameters.


Hans

 

[tjoneslo]

Add another vote for the tidal model.

From a handwave standpoint, gravity warps space and tides measure how much space is warped by gravity. The jump drive also warps space, and the two interefere with each other.

About a year or two ago this discussion occured on the TML. Tim Little produced an interesting movie. Based upon the tidal forces, if you have a planet right at the 100D limit, the tidal forces combine to produce an torus of stability much closer to the planet than either the star or planet's 100D limit. The theory was if you knew where this stability was, you could jump safely from very close to the planet.

As a simplification, if rocky planets have about a 100 diameter safe limit, gas giants and ice planets have about 60 diameters, and stars, well it ends up being inside the habitable zone. For some red giants, the safe limit is inside the star itself. Be real careful about jumping to that system.

Edit: Found the original TML disucssion: November 2001. Look under Timothy Little and Anthony Jackson. The discussion gets real math heavy, but raises some very interesting points.

 

[Malenfant]

Mert - Well, I chose 0.01 m/s2 as the limit because it worked for my purposes (and it produces results similar to the 100D limit for sun-like stars). You can set it to whatever you like, but your 0.00027 m/s2 would only be equal to the 100D limit of Earth, not anything else with a different mass.

Yes, large masses makes dents in the "rubber sheet" of spacetime. Gravity is represented by the slope of the sheet - flat means no gravity, very steep means high gravity. IMSFU, the slope of the dent in space-time is what prevents the jump drive from working - if the slope of the sheet is too far off horizontal, then it can't work. You're literally jumping ballistically off the sheet from one point to another - if the slope of the sheet is such that you're pointing upwards, then it gets that much harder to land properly again.

The tidal force is the rate of change of gravitational field - it's the gravitational gradient. If it's large, the gravity changes dramatically over a small difference in space. If it's small, then it changes more gradually.

Whichever model works depends on what you think restricts jump in your sf universe.

 

[Anthony]

Originally posted by RainOfSteel:
Well, guess what? So do I. It also appears to involve fewer calculations, to boot.

Appearances can be deceptive. The tidal limit is typically Diameter * 100 * (Density/5.5 ^ 1/3). As density is not very variable for terrestrial planets, this really just works out to Diameter * 80-100. That's simpler than the equivalent G limit, which is Diameter ^3/2 * Density^1/2 * K (not sure what value K has).

 

[TheEngineer]

What bugs me a bit, is that if I choose 0,01 m/s2 its ok the stars but very different for the planets.
If I choose those 0,000027 m/s2 it works well for planets (in order to be similar to the 100D limit) but extents stars limit quite far...
Life is so complicate

Anyway, Mals method fits perfect to my "thrusters revision" regarding energy consumption where I need shorter travel times to jump limit

 

[aramis]

I've always been a fan of the tidal model, as well. But I run in the OTU for the most part, and therefore, assume something about massive objects causing a 100x size gravity shadow on Jumpspace; the shadow is transparent to normal J-space material (if there is any), but not to extra-dimensional matter thrust to the J-space planes.

 

[Malenfant]

assume something about massive objects causing a 100x size gravity shadow on Jumpspace

That's exactly the problem though - the jump limit has nothing to do with how massive the object is. A sunlike star with one solar mass, a red giant with one solar mass, and a white dwarf with one solar mass have wildly different 100D limits, simply because the red giant is larger and the white dwarf is smaller - yet the total mass inside them is the same.

As an aside, does it really matter to the game in practise if you use a tidal model, a gravitational field model, or the radius-based 100D limit?

 

[kurtis]

I am currently making design decisions about MTU (semi-heretical), and am considering the impact of using tidal gravity boundries on the design. I am leaning heavily against using "plate" gravity drives that work everywhere, favoring a gravitic manuever drive that only works slightly beyond the jump limit. I'd also like a jump limit that reflects a realistic gravity footprint for the stars themselves.

However, I also want to avoid rubbing my own nose in near-C rock handwaving (part of the idea behind nixing the T-plates). So, does a 1AU+ sized jump limit give even gravity-well-limited manuever drives enough room to achieve high fractions of C?

 

[TheEngineer]

Hi !

Mal stated:

As an aside, does it really matter to the game in practise if you use a tidal model, a gravitational field model, or the radius-based 100D limit?

To honest, IMHO it does not.
It causes variation of in-system travel times a bit. Perhaps the most severe impact here might be, that the jump limit caused by the main star opens or closes parts of a system or not, depending on the system used.
But all in all its just a taste thing.

Taking the "practise", I just do it the pure Traveller way. Non of my players ever seriously had a problem with the simple 100D limit. Its a kind of fun to find some pseudo techno-explanations for that limit, e.g. as Aramis

Somehow the assumption, that the existence of matter itself shadows jumpspace, or the existence of a 5th force, which causes such effects is as "correct" as any other assumption or like the jumpspace concept itself.

If I would set up an alternate revised "TU", I surely would use a basic gravitic model combined with thrusting technology sensibel to local gravity and preservation of energy (speed/distance only depends on the energy put into the system).
The near-c rock problem is less likely to occur here

As this increases in-system travel times drastically, I really need lower jump limits to keep traffic going

Regarding the sytemview software I will implement every option noted in this thread.

Best regards,

Mert

 

[aramis]

Yes, It does make a difference whether I use the mass shadow (all masses over X cause a shadow with 100x the diameter of the object, no matter the density), or the tidal, or the gravity threshold.

In case one, other ships are viably threats, and thus jumping has less to do with mass, and more to do with displacement; if I set the threshold at a megaton, only BIG ships (100KTd+) become threats.

Under the tidal model, I have less chance of being j-blocked by a star; such interactions add days, or even weeks, to trips, and so those extra times are lost.

Under the gravity threshold model, ranges for small worlds drop a lot, making them more likely to be trade ports... likewise, big worlds lose travel time; this reduces terrain effect upon travel.

Not that these are bad interactions, but they would invalidate some of the better stories I've told, by negating the mass-shadow (which is not a shadow caused by the mass, but a shadow that exists because the object is possessed of mass) and its long-trip-time effects on certain systems.

(I've used Mass-shadow interaction to explain certain non-route A ports, in the past!)

 

[TheEngineer]

Hi !

Well Vhela, it is a basic defintion of the Traveller rulesets, that the JLimit applies to every object, like planet, gas giants and also moons or stars, too

The JLimit effect itself is perhaps not so complicate. Maybe its more complicate to do the choice, which model to choose, and to consider all the consequenses.

I just had to deal with this jump limit problem in order to get the effects programmed in my system viewer software.
Just like Aramis, I currently consider 3 different JLimit modes:
- central body diameter related
- gravitational effect based
- gravitational "slope" based

The central body diameter system should be considered to be a rule over the tumb method to easily calculate the distances, where gravitic effects are low enough for doing jumps.
Taking solar systems sun the diameter is 1400000 km. So a 100D jump limit would be around 140 million km.

Using pure gravitational effect, I calculated the effective gravitational force at 100D from the unit system earth. To specify to corresponding Jlimit for other astronomical bodies I reverse the calculation to get the distance, where the
graviational force equals the one calculated above.
Earth reference gravitational g rating at 100 earth diameters distance is
(G*Earth mass)/(earths diameter*100)^2, which results in something around 0,000275 m/s^2.
Distance to sun has to be around 670 000 000 km, to reach a similar value.
Well, this would stretch the jump limit beyond solar systems planetoid belt.
In a result many habitable mainworlds would be located deep inside the jump masked regions of the star.

So, another reasonable method to fix this a bit and to keep on using a gravitational model is to use the distance related derivation of the gravitational force.
The derivation of a = G*m/r^2 is da = -2*G*m/r^3, which describes the amount of decay of the gravitation, namly the slope of the function ,when moving away from the star.
Using this approach shifts the calculated JLimit to something around 83 million km, which should be more practical (hey and it kicks Venus out of the jump masked regions).
This is in fact my favorite model and I use it IMTU.

Well, regardless which method You might prefer in YTU, it might be reasonable that this universe (mainworld location, location of trade centers, defense strategy) is adapted to this situation.
And if its about actual gaming these astrographical impacts IMHO are mostly ignored anyway (Player: "Guess, we're going to Gitosy next". Ref: "Ok. You're there...").
If You're a trader/merchant is might be reasonable to find a trading outpost at a location, where it makes sense for logistics, thus near or outside of a jump limit, and so You can follow standard procedures, too.

So, unless You want to use "solar system astrography" (jlimits included) as inspiration and spice for in-system adventuring, you might simply ignore it.

Vhela, if You would like to get a visual impression about the Traveller astrography of a system, those different jlimit modes and all those nifty details, Youre very welcome to take a look at the SystemView software

New version will be uploaded today evening....

Regards,

Mert

 

[RainOfSteel]

Originally posted by TheEngineer:
[...]if You would like to get a visual impression about the Traveller astrography of a system, those different jlimit modes and all those nifty details, Youre very welcome to take a look at the SystemView software

New version will be uploaded today evening.... [...]
Mert

Mert,

Your site is written in German, and while I can puzzle out a few words, I can't really navigate it.

Can you please post a link to the appropriate page?