Refining the 100D Jump limit

[RogerD]

I was thinking about the 100D Jump limit. It is described as a distance where gravity is weak enough to allow the Jump drive to work. IMTU, I'm thinking about using an adjustment factor based on this limit, but adjusting for the actual mass of the planets.

The basic idea is to use a formula like:
2.56 Gm * sqrt(M)
Where M is in earth masses.
This was derived from Newton's Law of Gravitation and uses the 100 diameter limit for Earth as a benchmark. With this, you can jump when the acceleration due to gravity is less than .25mm/s^2

With this formula, you would get jump distances from:
A 250 Solar mass star - 116780 Gm (78 au = about orbit 10)
The Sun - 739 Gm (4.94 au = about orbit 6
Jupiter - 228 Gm
Earth - 2.56Gm (dominated by the sun, but 8.54 light-seconds)

You could change the constant to shorten the time to accelerate to jump point if you wanted. Cutting to about 0.5 Gm would bring the jump point for the Sun in to below Earth's orbit. You can roughly just divide the listed values for each body by 5. This does also make it easier to jump from small worlds outside the gravity well of a star though. It all depends on what effect you're going for.

As usual with changes I think about - the math works out better, but it's a bit harder to use. I like verisimilitude.

 

[whulorigan]

I was thinking about the 100D Jump limit. It is described as a distance where gravity is weak enough to allow the Jump drive to work. IMTU, I'm thinking about using an adjustment factor based on this limit, but adjusting for the actual mass of the planets.

The basic idea is to use a formula like:
2.56 Gm * sqrt(M)
Where M is in earth masses.
This was derived from Newton's Law of Gravitation and uses the 100 diameter limit for Earth as a benchmark. With this, you can jump when the acceleration due to gravity is less than .25mm/s^2

With this formula, you would get jump distances from:
A 250 Solar mass star - 116780 Gm (78 au = about orbit 10)
The Sun - 739 Gm (4.94 au = about orbit 6
Jupiter - 228 Gm
Earth - 2.56Gm (dominated by the sun, but 8.54 light-seconds)

You could change the constant to shorten the time to accelerate to jump point if you wanted. Cutting to about 0.5 Gm would bring the jump point for the Sun in to below Earth's orbit. You can roughly just divide the listed values for each body by 5. This does also make it easier to jump from small worlds outside the gravity well of a star though. It all depends on what effect you're going for.

As usual with changes I think about - the math works out better, but it's a bit harder to use. I like verisimilitude.

Another possibility is to use the tidal acceleration due to gravity as the basis, which goes as gT = -GM/R^3 (i.e. in g's per meter). I believe Hemdian on this board first worked out or published this method.

He has two methods (the page is tabbed) on his website: https://hemdian.com/traveller/book2/minimum-safe-distance/

• Original “Gravity” Model
• Revised “Tidal Force” Model

The rational for the gravitational effect on Jump is clearer with the Tidal Force Model: It is not so much the presence of a gravitational field, per se, but rather the difference in gravitational acceleration between one end of the ship and the other (in other words the bow of the ship has a slightly different jump-field value than the stern of the ship due to the difference in tidal acceleration across the length of the ship. Beyond a certain tolerance this creates problems for a uniform jump-plot. Another interesting possibility with it (if you want the increased math) is that larger ships would be more sensitive to jump than smaller ones (since they have larger dimensions, the tidal force in g's per meter for a larger ship with dimensions of "x" number of meters is greater than for a ship of smaller dimensions).

 

[whartung]

The Sun - 739 Gm (4.94 au = about orbit 6

Honestly, this is probably the most impactful issue with this change. It greatly enlarges the "jump shadow" in many systems. Right now, most 'main worlds' are not trapped within the 100D of their primary, which makes travel "reasonable". But start shrouding more of them, it make space travel kind of a real pain in the neck.

but rather the difference in gravitational acceleration between one end of the ship and the other

I kind of love the idea of a ship turning parallel (tangential?) to the affecting mass in order to jump sooner. Neat bit of color.

 

[Spinward Flow]

Honestly, this is probably the most impactful issue with this change. It greatly enlarges the "jump shadow" in many systems. Right now, most 'main worlds' are not trapped within the 100D of their primary, which makes travel "reasonable". But start shrouding more of them, it make space travel kind of a real pain in the neck.

The biggest effect of this change would be that it would make Maneuver Drives more relevant to ... uh ... Space Travel.

I don't exactly see that as a bad thing ...

 

[MichaelSTee]

While my Pilot character can do this kind of math with one hand tied behind his back, I can't. :/ So for my house rules, for a long time I've said that it's 100 diameters from a solid planet, 50 diameters from a star, GG, or brown dwarf, and at least 200 diameters from a white dwarf (not that many would want to jump close to one of those). I won't even speculate on black holes...

 

[mike wightman]

Try this - safe jumping distance = 100D/g

were g is surface gravity

 

[Condottiere]

If you have an anti gravitational field that rejects gravity matching external gravitational influence, couldn't your starship wormhole it's way through one or more gravitational shadows, and jump?

 

[RogerD]

Thanks for the feedback, all - it is always fun to see that others have had similar thoughts.

The tidal stress idea is interesting, and I'll think about how that might play in.

You could probably re-express this idea in terms of surface gravity, but I don't think the 100D/g fomula does what I want - that actually lets you jump in closer to more massive objects, and mass really is the key. The question about a black hole is actually quite simple, and a benefit of this system - the limit is based strictly on the mass of the black hole. Small black holes are maybe 10 solar masses, and the one at the center of the galaxy is roughly 4 million solar masses. At 330000 earth masses per solar mass, you get a jump shadow of 3 million Gm, or 3 Pm - only about 0.1 parsec.

I did also consider the notion that the gravitational force would be important (vs. acceleration). The modification there would be that the mass of the ship would be a factor as well. That formula looks like K*sqrt(M*m) where M is the mass of the planet/star and m is the mass of the ship. If we handwave mass = tonnage, you can pick a benchmark ship (say 100 tons for the scout/courier) and then express the mass in 100 ton units. A 1600 ton ship would have to be 4x the distance away as a scout! A jump-capable million ton ship would have to jump in 100x further away than a 100 ton scout. Space is big though, and that might actually be an interesting effect (possibly reducing the constant from the 2.56Gm somewhat).

I also thought about the idea you might be able to jump at the lagrange point between two bodies where the gravity cancels out, but I decided that such a location would end up being locked in. I suppose you could technically jump at such a point and re-emerge at the same point a week later. That might make for an interesting surprise at some point.

 

[mike wightman]

You may want to watch this video for a better explanation of gravity than anything else I have seen so far:

The TL;DR version - gravity is an imaginary force while tidal forces are real forces.

 

[RogerD]

The TL;DR version - gravity is an imaginary force while tidal forces are real forces.

True - everything travels in a straight line, it's just that time-space is warped. One measure of curvature is in the equation theta = 4GM/(rc^2), which measures the angular deflection of light by a body at radius r. This is how gravitational lensing works. If you took a constant theta as the minimum safe jump distance, you get an equation that is directly proportional to mass (vs. the sqrt idea in the original post). A step in the wrong direction from a canon POV.

i see how the tidal force model fits with Traveller canon better. Essentially you get a MSD = K*(M*d)^1/3, and from that you can get MSD=100*D*(rho*d)^1/3. d is this size of the ship here. With the cube root, the million ton ship still needs to jump 21.5x further out than the scout, which is interesting. The density effect actually pulls in the limit from stars by maybe a factor of 0.6 vs a rocky planet.

I feel like the tidal model makes the limit be a little more about the ship's capabilities and a little less about the shape of the universe. Not sure if this is quite what I want, but I'm considering it.

What benchmark ship do we think the Imperium would use in coming up with the 100D guideline?

 

[mike wightman]

With a couple of exceptions Traveller has always pegged drive performance to ship volume rather than mass. Unless you use one of the design systems that mentions ship mass (which give different values for the type S scout for example) you are forced to approximate ship mass.

 

[whartung]

With a couple of exceptions Traveller has always pegged drive performance to ship volume rather than mass.

But, save for Jump, that's just a simplification. As a general rule, bigger things have more mass and thus need bigger drives. In this simple world volume == mass, but volume is the most dominant design factor for a ship, since we need a big box to put stuff into. Far easier to design around volume than mass.

TNE calls this out in FF&S when a ship become, essentially, "heavier than average", to the point that it would be justified to jump through the math to take into account the extra mass.

 

[whulorigan]

What benchmark ship do we think the Imperium would use in coming up with the 100D guideline?

Seems to me the Type-S Scout/Courrier would be ideal. It represents the minimum possible starship size, it is ubiquitous and a long-standing design (including all of its minor variants), and is by design an "explorer" charting worlds, systems, and their spatial characteristics and anomalies for Imperial databases. It is the kind of ship you most want to know how it should be "typically" affected by routine spatial and jump considerations. From that basis you can develop theoretical jumpspace modelling.

 

[BlackBat242]

Try this - safe jumping distance = 100D/g

were g is surface gravity

Having plugged a few numbers in, I question this.

100d/2g = 50
100d/1g = 100
100d/.5g = 200

So the LESS the gravity the GREATER the safe jump distance?

I read the rules as saying that it is the effect of the gravity distorting the space-time curvature that affects jump - with a greater gravity field causing more distortion.

I think your formula should be 100d x g.

Thus:
100d x 2g = 200
100d x 1g = 100
100d x .5g = 50

Making the safe jump distance from a lesser gravity source a smaller distance.

 

[mike wightman]

You are neglecting the fact that a 2g body is likely to be a gas giant with a greater diameter,

Plug in the D bit...

Planet	Mercury	Venus	Earth	Mars	Jupiter	Saturn	Uranus	Neptune
g	0.4	0.9	1	0.4	2.5	1.1	0.9	1.1
D	4880	12100	12800	6800	142000	120000	51000	49500
safe jump	1220000	1344444	1280000	1700000	5680000	10909090	5666666	4500000

And for the sun - 1400000 and 28 for a jump distance of 5000000,

It mostly does what I want it to.

 

[kilemall]

You are neglecting the fact that a 2g body is likely to be a gas giant with a greater diameter,

Plug in the D bit...

Planet	Mercury	Venus	Earth	Mars	Jupiter	Saturn	Uranus	Neptune
g	0.4	0.9	1	0.4	2.5	1.1	0.9	1.1
D	4880	12100	12800	6800	142000	120000	51000	49500
safe jump	1220000	1344444	1280000	1700000	5680000	10909090	5666666	4500000

And for the sun - 1400000 and 28 for a jump distance of 5000000,

It mostly does what I want it to.

Ummm I don’t see how when Earth and Mercury are about the same and Venus is more with smaller diameter and less surface G.

 

[mike wightman]

It makes the rocky planets have a similar safe jumping distance, while gas giants and stars have bigger safe jumping distances but not so great. The real outlier is Saturn.

 

[Enoki]

Well, to be fair, if you are doing this, you should really also calculate the velocity and vector of the star and planets relative to ship motion. That is, the ship will reach the appropriate limit faster if it moves away from the direction the star and planets are moving. For example, our Sun is circling the Milky Way at about 217 km/s or 486,000 mph. If you are moving in the other direction...

If you plan things correctly, you could just get into a stable location away from the planet you took off from and wait for the solar system to move away from you...

 

[whulorigan]

Well, to be fair, if you are doing this, you should really also calculate the velocity and vector of the star and planets relative to ship motion. That is, the ship will reach the appropriate limit faster if it moves away from the direction the star and planets are moving.

You would have the exact same circum-stellar and circum-galactic momentum vectors as the planet that you just took off from; you would be in the exact same free-fall orbit frame-of-reference around the central star that the planet has. It wouldn't make any difference which direction you took off from. Your concern would be the relative momentum vectors of your destination, not your origin.

For example, our Sun is circling the Milky Way at about 217 km/s or 486,000 mph. If you are moving in the other direction...

But as noted above, you are NOT initially moving either in the other direction nor "at rest", but at the same speed and direction as the originating world. You would have to accelerate in the opposite direction first to bring yourself to rest with respect to the new reference frame.

If you plan things correctly, you could just get into a stable location away from the planet you took off from and wait for the solar system to move away from you...

See note above.


Of course, you could get a "boost" to orbit by taking off in the same direction as the planet's rotation about its own axis (the closer to the equator the better . . . ) .

 

[Enoki]

That doesn't change that it might be better, and quicker, to stop and let things move away from you than you try to move away from them...