Hex Dimensions and Hex Mapping, Proper Motion of Alpha Centauri and Proxima

[sudnadja]

These hex plots presume that the distance between the center of one hex and the center of another is 1.0 parsec, thus the inner radius is 1/2 parsec and the outer radius is 1/sqrt(3) parsec.

Alpha Centauri is moving, and Proxima Centauri, in "far companion" orbit of Alpha Centauri, is moving with it. By Imperial Year (3rd Imperium) 6000 or so, Proxima will be close enough that it will be in our adjacent hex, not the hex after that. Unfortunately, hex maps fall down a little when used this way, as the distance from the far edge of one hex to the most distant edge of the adjacent hex is 2 parsec, though everything with in both hexes is Jump-1 away. So this is for fun, but it shows another difficulty of trying to map the real world into Traveller - it's not just a 3d-2d thing, but a "hex quantization" problem as well.

That said, the scale of a hex is an interesting topic. Here the Sun, the orbit of Sedna (80-800 au orbit around the sun), and Alpha Centauri A+B (barycenter) and Proxima Centauri, presently >12000 AU away from Alpha Centauri) are plotted against the dimensions of a hex.

The leftmost hex is Terra's. You can barely see in the center of the hex the orbit of Sedna - far, far beyond the orbit of Neptune or Pluto yet still a tiny speck compared to the area a hex represents.

The Orange and Red lines represent Alpha and Proxima Centauri, respectively. They are solid lines from their positions now (AD 2017) to imperial year 1116, and then dashed lines representing their paths for the next 22000 years. You can see that the orbital motion of Proxima around Alpha Centauri A+B is so slow that in the 26000 years or so being plotted, it barely moves in relative position to Alpha Centauri. The orbital period of Proxima is about 547,000 years - by the time Proxima completes an orbit it will be dozens of light years away from Terra.

 

[tjoneslo]

This was something I looked at in a larger scale. The idea was that all stars are moving relative to each other, some slower, some faster.

So how often should you need to update the maps across the Imperium or charted space with this same hex quantization problem? My answer was about one or two stars per year shift hexes. I put my work in a post in the IISS forum earlier, and if interested I'll dig it up again.

The second, more interesting question was about the nature of Jump Space. There is a common assumption that jump space is a wavy sheet. This is an explanation of why the maps are flat, and seem to be missing most of the stars. So if stars actually move, can they enter or leave the wavy sheet that is Jump Space? And what happens when they do?

 

[sudnadja]

This was something I looked at in a larger scale. The idea was that all stars are moving relative to each other, some slower, some faster.

Indeed, and the vast majority of the stars are in orbit of the milky way (an a few are on galactic escape). Thus you have to be careful when doing nbody integrations without a model of the galactic potential, the position estimates won't be accurate beyond a million years or so, though I notice that my own position estimates for Gliese 710 and the close encounter with the sun in ~1.36-1.44 Ma were almost exactly the same as that of the esa, and I did not use a galactic potential model.

Most stars have a relative velocity to each other somewhere in the range of 30-60 km/sec to other nearby stars. Barnard's Star being one of the local exceptions at about 141 km/sec, but I'm not sure where you would get a very accurate list of stars and their velocities over such a large volume of stars like the imperium represents - if you take a sphere of radius 200 parsec or so you are in many hundreds of thousands or millions of stars to deal with.

In-game, I do imagine that one of the requirements given by the Imperial Government to the scout service is to catalogue the star positions and velocities and what not.

So how often should you need to update the maps across the Imperium or charted space with this same hex quantization problem? My answer was about one or two stars per year shift hexes. I put my work in a post in the IISS forum earlier, and if interested I'll dig it up again.

I'm certainly interested if you've done the work in the past! If we take the average velocity of stars in the Imperium to be - random guess - 45 km/sec they will cover a parsec in ~22000 years. Presume a star must travel half a parsec to jump a hex and that's a 50% chance that any given star would need to be relocated in 11 ka, - humm, I'll need to think a little more about this, but we can probably presume statistically that the positions and directions of travel of the stars are gaussian. If you've done the math already, yes, it would be interesting to look at.

The second, more interesting question was about the nature of Jump Space. There is a common assumption that jump space is a wavy sheet. This is an explanation of why the maps are flat, and seem to be missing most of the stars. So if stars actually move, can they enter or leave the wavy sheet that is Jump Space? And what happens when they do?

I am of the camp that jump space should be a linear representation of real space and that we're having to do an awful lot of mental gymnastics to promote pure science fantasy into astronomical science fiction. I do understand the simplification needed for the majority of players for simple game mechanics - if you're planning a trip from north america to europe you really only care about your start point and end point and how long it will take, not great-circle complications that arise from the 2d map on your computer screen not being a good representation of the underlying topography. I think though, that one of the things that draws a significant fraction of players to Traveller is the fact that it takes place in space and therefore you're more likely to encounter Real Math in Traveller than you are in D&D, and the players are equipped to deal with it.

I have tried, in the past, to build a multidimensional representation of local space, that would fit both the 2d map and the 3d real positions of the stars, but gave up on that.

It could be an interesting side mechanic to adopt your explanation, and explore the in-game economic crisis that can occur when a hub star is suddenly no longer in the jump-plane. Traveller 5 seems to fully embrace Not As Fast As Light travel, so the star wouldn't be completely cut off, but its status as an economic hub would end overnight. First, perhaps, there would be hints of a shift in the topography as the number of incidents of mis-jumps for inbound starships starts to increase dramatically, outbound ships intending on Jump-5s or so end up with their drive performance halved, or spending a lot of extra time in Jump space. No one *really* understands the differential geometry associated with jump space (it makes general relativity look like grade school math) so there are only speculations about what is happening. Soon, outbound jumps only cover a few AU, and then jump drives cease to work completely.

Probably something that could be fun to explore, but I would still rather that the collective Traveller community ditch 2d jump maps completely.

 

[tjoneslo]

I'm certainly interested if you've done the work in the past! If we take the average velocity of stars in the Imperium to be - random guess - 45 km/sec they will cover a parsec in ~22000 years. Presume a star must travel half a parsec to jump a hex and that's a 50% chance that any given star would need to be relocated in 11 ka, - humm, I'll need to think a little more about this, but we can probably presume statistically that the positions and directions of travel of the stars are gaussian. If you've done the math already, yes, it would be interesting to look at.

I looked though the forum posts and found the one where I made the claim, but mis-rememebered posting the real math. But it was the approach above. Assume a median relative velocity between stars, so stars will cross half a parsec in a few tens of thousands of years. Then apply that over a large number, say 10,000 systems (the third imperium and border regions) or 50,000 - 70,000 (charted space).

A similar approach to yours, but with less mathematical rigidity.

I have tried, in the past, to build a multidimensional representation of local space, that would fit both the 2d map and the 3d real positions of the stars, but gave up on that.

The best map I've seen of real 3D space on a 2D map was in the game Starforce (To boardgamegeek). That works for a subsector (40-80 stars) area. But if you are trying to describe 11,000 worlds of a star spanning empire the various I've not ever seen any way of representing that many systems on a 3D->2D map.