The 100-Diameter Limit

This article originally appeared in the September/October 2019 issue.

“Canon” (i.e., the extant body of official rules in the ‘default’
setting) specifies that Jump drives work far less reliably within 100
Diameters of a body more massive than themselves than in “open space”.
There is an increased chance of misjump if the drive is activated in
this region and a moving ship will precipitate out of jump space if it
tries to move inside this region. However, there are some strange
implications and no basis in science, even weird science, for this rule.
Consider: you are in a starship some 13,982,000 km from a Jupiter-sized
large Gas Giant. Somehow the drive or jump-space itself knows that the
ship is just within 100 diameters and if you were to move 200 km further
away a jump would work. That is a variation of 2km in the diameter of
the gas giant. How does the drive know this? It isn’t really measurable.
It also isn’t because of gravity. At this point the ship is experiencing
a 6.5×10^{-4} (0.00065) m/s^{2} acceleration towards the planet. At a safe
jump distance from a star of 1 Solar Mass/Size a ship would experience a
force from gravity of 6.8×10^{-3} (0.0068) m/s^{2} – count those zeros (or
compare the exponents) carefully; the force is 10 times as much at a
safe jump point away from the star as at a safe jump point away from a
Large Gas Giant. The weak force can’t act at that
distance and electromagnetism is at best inconsistent, and absent in
some cases.

Why is 100D an issue? Let’s take a look at some other factors that come from a phenomenon that can measure diameter at a distance and even measure it from within jump-space (theoretically a different dimension) to an object in normal space:

Consider an extreme example, a neutron star of 1.6 solar masses has a
diameter of about 21 km, and therefore a 100 D limit of 2100 km. So, a
starship could jump in to 2100 km of the surface without issue (it can’t
jump out as we will see). Calculating the force at 101D (2121 km), we
get 4.8 *million* G. Everyone will die, however, before the ship crashes
into the star at 5% of light-speed, as the tidal forces will shred
everything “long” before impact (which is only in 0.3 seconds) – but
*theoretically* the ship *could* have jumped away.

Let’s look at a different example. Saturn is a very gaseous gas giant. It has a very high oblateness. The equatorial diameter is 120,536 km while the polar diameter is 108,728 km – a 10% difference. So a starship in a very large polar orbit at 11,000,000 km (still inside the orbit of Phoebe) will be able to jump when it is near the poles, but not while it passes over the equator as the 100D limit is 12,000,000 km there. While the average diameter could be used, what mechanism could be in place to measure that?

Let’s look at smaller effects. A 500,000 dton battleship, the Tigress class is essentially a 500 ft. sphere with a 250 ft box on the back. As a Tigress is likely more massive than most ships, it can be expected to have a jump limit of its own. If we assume the same 100D limit as for planets or stars, it will affect jumping out to 15 km of a ship to either side (or above or below). If, however, the Tigress is facing directly toward or directly away from the jumping ship, jumps within 22.8 km are prohibited.

The Kokirrak 200,000 dton dreadnought is 1,484×371×185 ft. The 100D limit goes from 5.6km above/below to 11.3 km at the sides to 45 km to the front/back. One could imagine creating a ship 20-30m in diameter and 20 km long. That would prohibit jumping within 2,000 km of anything it is pointing towards – not a huge distance in space terms. But that brings up another point in the calculation of diameter at a distance. What happens if you bring two ships together? Let’s say you have 2 Tigresses 10m apart. Your ship is 25 km in front of the first ship and 25.2 km in front of the one behind that. So, OK to jump. What if they touch? Is the jump interference now 45.6 km? What if they docked and were now physically essentially one ship?

Finally, 14 AWG wire is fairly stiff (used as in-wall house wiring for 15 A circuits). A ring of this around the Sun just past the orbit of Neptune would have a diameter of 10,000,000,000 km. At 18.4 kg/km a circle of this would weigh 552 million tons – a lot but not impossible amount of resources – about the equivalent of 75 Tigress battleships. Would two of these rings perpendicular to each other constitute a structure for jump interference? If so, it could prohibit jumps within 1/10 of a light year. That would be a 233 day trip for a 2G ship.

I think I have presented enough points to question the validity of the
100 Diameter jump limit as any actual physical limit; perhaps it should
be treated more like a general guideline to an underlying gravitic
physical constraint. The problem with this is (as mentioned previously)
the difference in force experienced at valid jump points from different
types of bodies (G at a safe jump point from a star is 10× that from a
gas giant, and 25× that from a rocky planet (Earth is 2.46×10^{-4} m/s^{2})).

How can this be addressed (besides ignoring it completely)? We can say that the jump distance is based on mass and gravity experienced by the ship. So as long as the referee doesn’t actually provide a number for that force and says that the 100D is an easy approximation and the players don’t try the math themselves then one can ignore the issue. But unfortunately the force exerted on a ship by gravity at 100D is wildly different between an iron planet, a silicate planet, a gas giant, and a stellar mass.

We could pick one of the values as correct and recalculate the jump distances, throwing away the 100D rule. However, calculating based on the stellar gravity at 100 stellar diameters would make planetary travel to the jump point quite a bit shorter (10 minutes vs 4 hours at 2G), but this wouldn’t be a huge issue. The opposite is not true. Using the planetary force at 100 planet diameters the stellar jump zone would be 25× larger, the majority of planets would be masked by their star, and it would make all journeys extremely long (237 hour flight time in and again back out at 2G).

The proposed solution: Jump space (or the jump ‘bubble’) is supposed to
be a different dimension, which allows light-speed in ‘real space’ to be
circumvented. Why can we not change other physical factors? Gravity in
‘real space’ follows the inverse-square law (f=Gm/r^{2}; if you double the
distance the force is ¼ as strong (2^{2} = 4). If we tweaked this a bit,
and decided that jump space interacts slightly differently with ’real
space’ masses, it should not be noticeable to a ship that is alone in
its jump bubble with no masses around. In fact, if we used an inverse
power 2.7 law (f=Gm/r^{2.7}), and decided that the safe jump distance is
where f≤10^{-10} m/s^{2}, we could almost replicate the 100D guideline for
jump distances with a real math-based formula. (In the formulae, G is
the gravitational constant 6.67408×10^{-11} m^{3}/kg-s^{2}, m is the mass of the
body in kg, and r is the distance in meters.)

Why go to the effort? Even this method lets us approximate by using 100 diameters in many cases. However, using this new rule most of the exceptions listed above go away. Jumping to a neutron star will precipitate out at a safe distance (black holes, too). Oblate planets will have one distance as it is purely mass based. Two objects near-touching/touching will act like their combined mass, regardless of how much contact they do or do not have (planets can be treated as point masses, irregular bodies – such as a pair of ships, would be the sum of the effects of multiple point masses). Huge low mass structures will not affect jumping any more than a large asteroid. The new formula, being optimized for both stellar and Iron planets, does noticeably differ for silicate planets (Asteroids) and smaller gas giants. Ships, too, have 25% of the former 100D jump interference, so it is not without some effects. In the end however, there is a reasonable science-based formula underlying the 100D “rule”, previous references can be maintained (with a reasonable margin of error), and special cases (e.g., neutron stars) are calculated as needed.

The following table shows the old and new safe jump limits (in km) for some examples and the travel time to the limit assuming mid-point turn-around.

Safe Jump Limit (km) | Time (hrs:min) turn-around | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Body | Type | Mass | Old (100D) | New (g=10^{-10}) |
% | M1 | M2 | M3 | M4 | M5 | M6 |

Sol | Stellar | 1.99×10^{30} |
139,268,400 | 143,348,474 | 103.0 | 67:00 | 47:00 | 39:00 | 34:00 | 30:00 | 27:00 |

Earth | Med Iron | 5.97×10^{24} |
1,274,200 | 1,292,143 | 105.0 | 6:24 | 4:30 | 3:42 | 3:12 | 2:54 | 2:36 |

Mars | Low Iron | 6.42×10^{23} |
677,900 | 565,578 | 83.4 | 4:12 | 3:00 | 2:24 | 2:06 | 1:54 | 1:42 |

Jupiter | LGG | 1.90×10^{27} |
13,982,200 | 10,915,645 | 78.1 | 18:30 | 13:06 | 10:42 | 9:18 | 8:18 | 7:36 |

Saturn | LGG | 5.68×10^{26} |
11,646,400 | 6,983,513 | 60.0 | 14:48 | 10:30 | 8:36 | 7:24 | 6:36 | 6:06 |

Neptune | SGG | 1.02×10^{26} |
4,924,400 | 3,701,725 | 75.2 | 10:48 | 7:36 | 6:12 | 5:24 | 4:48 | 4:24 |

Ceres | Silicate | 9.39×10^{20} |
94,600 | 50,427 | 53.3 | 1:18 | 0:54 | 0:42 | 0:36 | 0:36 | 0:30 |

Tigress | Ship | 7.38×10^{09} |
15 or 22.8 | 3.89 | 25.9 | 40s | |||||

Neutron Star | Special | 3.20×10^{30} |
2,100 | 185,804,434 | 88,478.0 | 76:00 | 54:00 | 44:00 | 38:00 | 34:00 | 31:00 |

(remember the formula gives distance in meters) To calculate the values for other bodies, use the following formulae and tables:

World Mass (M) in kg (S=Size Code, d=density): M=(2,145×10^{18})×d×S^{3}

Select a density (g/cm^{3} [=tonnes/m^{3}]) from the table below.

World Type | Low Density | Medium Density | High Density |
---|---|---|---|

Gas Giant | 0.825 | 1.100 | 1.375 |

Icy body (e.g., Pluto) | 1.100 | 1.925 | 2.750 |

Rocky body (e.g., Ceres) | 2.750 | 3.575 | 4.400 |

Molten Core (e.g., Earth) | 4.400 | 5.500 | 6.600 |

Heavy-metal Core | 6.050 | 8.250 | 11.000 |

The above table represents common ranges of densities; you may choose
other values within the indicated ranges.

100 Diameters in km: D=S×160,000

Safe Jump Distance (km where g=10^{-10} m/s^{2}) (M=world mass in kg; uses
modified relationship): D=(3.369×10^{-11})×M^{1/2.7}

Travel time (hours) to safe jump (D=safe jump (km); M=drive maneuver
rating): T=(D/M)^{½}/360

The above formulae are simplified; constants and scale factors have been
combined and reduced where possible.