Limits of Sensor Technology

[Sifu Blackirish]

The TRAVELLER bug is nibbling at my brain again. I figured out a way to simulate my version of the Terran Exodus on paper, and was just about to create a sector map using Harold D Hale's Solomani Rim star analysis when i happened to read a part of the Zhodani Aliem module.

Specifically, it was the section of charting unknown space that made me stop and reboot.

Hale's addition of the uncertainty factor makes sense (paraphrasing...the father away you are from Sol, the less likely you are completely correct about a star's location). But what are those limits? A subsector, a sector, a domain? Surely Sol-system based observatories, studying the sky for decades, have things pretty accurate.

How about detecting gas giants and planets? I know it takes finiky and long-term measurements from here, but what are the the limits for TL-9 ships? Could the analysis from space be more accurate if compared to the Sol system database?

Ah, you see my difficulty. My future players or readers of stories may not care, but I want a logical, consistent backstory.

Help would be greatly appreciated.

 

[TheEngineer]

Hi !

Guess the key factor is, that once you are able to get along in space well (thats quite true at TL9), the oppertunities to set up vast detector arrays (VLBI) are striking.

So, I would not think of a simple advanced antenna on the surface of a TL 9 ship, which is always limited because of very physical reasons.
My imagination is more directed to a set of remote controllable sensor drones, which spread out to form a virtual mega-sensor. Maybe this is combined with other ships, which do the same.

This technique would allow very very long ranging views into uncharted space.

Regards,

TE

 

[Icosahedron]

There are a number of different ways of detecting things at those distances, but take direct observation as an example.

The problem boils down to the size of your base line compared with the viewing distance. It is not sideways location that is a problem, but figuring out whether a given star is twenty subsectors away, or thirty.

Imagine a triangle, whose base is the diameter of your telescope and whose apex is at the viewed star. That is one very long triangle, and the only way to know just *how* long without getting there is to measure the angles at the triangle base. Stars at different distances will create different angles, but at stellar distances the differences will be almost unmeasurable. If you have a bigger telescope, giving the triangle a wider base, there will be a greater difference in angle measurement and you can tell the distance to a star more accurately.

Today, we use linked arrays so that our effective baseline is no longer the diameter of a mirror, but the diameter of the planet. Later, we will be able to link to sensors on spacecraft or other planets and maybe our baseline will be the diameter of the solar system.

In a starfaring setting, presumably we could use the diameter of our pocket empire as the baseline, leading to considerably better accuracy in judging the distance to stars.

I think the TL7 accuracy is about 15 percent at 100pc, (someone will correct me) so a star ten subsectors away might not be in the subsector you think - it might not even be in the one next door!
You'll figure its direction quite accurately, but not its distance.

Hope that helps.

 

[GypsyComet]

To some extent, the length of your baseline is also dependent on how patient you are. Hang in a planet's orbit long enough and the planet itself will drag you through millions of kilometers for free. Multi-ship expeditions can also seperate ships by huge distances and still retain enough linkage to get good distance data.

Then there is the parsec level baselines that jump drive makes possible. For gross distances you don't even need to be time synchronized. An index of stars in given positions at one end of a jump compared with the same data for the other end of the jump will answer most of your raw distance questions pretty quickly, though the data itself might be a lengthy process to collect if you are trying to be comprehensive.

 

[marvo]

Yeah the longer your baseline, the more accurate your results are going to be.

The only problem I can see is that your observations are still constrained by the speed of light. You can get a very accurate reading on a system/planet that's jump 1 away, but your results are based on where that object was 3.262 years ago. You will need to have some base space/time reference to predict where the planet is now if you want to jump close to the 100 diameter distance.

 

[Straybow]

Doppler effects tell you how the star is moving relative to your position.

But you wouldn't be doing that from a ship, anyway. It will be done from your home planet centuries before your campaign.

On Earth we can reliably locate all but the dimmest stars within a thousand LY. With a suitable orbital telescope you can locate every star within a thousand parsecs. That limit is proportional to baseline, so with a set of three telescopes moving outsystem we can extend that to tens of thousands of parsecs.

 

[Icosahedron]

I'm not sure about you figures there, Straybow, and it depends on your definition of 'reliably locate'
Locating in the sense of finding or discovering a star is not the same thing as being able to place its exact position on a 3D map.

Trying to place a star within a single parsec hex at 1000Pc distance using the Earth's 2AU baseline would require a resolving accuracy of the order of 10^-10 degrees!

I don't think current instruments have anywhere near those resolutions. In fact, I'm not even sure it's physically possible given the wave nature of light.

I could be wrong, but...

 

[Straybow]

To locate an object with a precision of ½ Pc at a distance of 1000 Pc requires angular precision of 1.7 arc-minutes, which is trivial. The challenge is measuring the distance to within ½ Pc.

1" is 3x10^-4 degrees, so for 1000 Pc we only need 3x10^-7 degrees divided by field width. So, ¼-wavelength (100nm) on Palomar's 5m Schmidt with 4° field is already at that precision, mechanically. The atmosphere prevents Palomar from achieving this theoretical resolving power.

Our other problem is brighter stars swamping out dimmer stars near the same line of sight. But the ones we can see we can easily place accurately enough to map to the precision of a generalized sector map out to ~300 Pc.

That's why I said:

With a suitable orbital telescope you can locate every star within a thousand parsecs.

Even at present tech (TL8-ish) we can build orbital telescopes with greater light gathering and field suitable for measuring parallax at 1000 Pc.

 

[Icosahedron]

Originally posted by Straybow:
To locate an object with a precision of ½ Pc at a distance of 1000 Pc requires angular precision of 1.7 arc-minutes, which is trivial. The challenge is measuring the distance to within ½ Pc.

1" is 3x10^-4 degrees, so for 1000 Pc we only need 3x10^-7 degrees divided by field width. So, ¼-wavelength (100nm) on Palomar's 5m Schmidt with 4° field is already at that precision, mechanically. The atmosphere prevents Palomar from achieving this theoretical resolving power.

I can't be sure without getting the calculator and tables out again (which is more trouble than it's worth) but I think we're saying the same thing here.

I agree that fixing _lateral_ position at 1000Pc is do-able, but as you say, the trick is trying to use parallax to fix the _distance_ of a star at that range; and that's what I don't think we can do.

As I say, I can't figure out whether your Scmidt figures are disproving me or not without going to altogether too much trouble. Are you saying that current telescopes can fix _distance_ to 0.5 Pc at 1000Pc using parallax alone?
(That's tens of times times further away than I figured was possible.) Or are you just talking about fixing _lateral_ location if you're 'given' the distance?

 

[Scott Martin]

remember that you aren't trying to hit *any* 10d limit until you're within 6 parsecs, so the inability to resolve at that resolution at 1,000 parsec distance is irrelevant.

For the 3I (or even the Zhodani) the empires are hundreds of parsecs wide, so bearing data on stars will give reasonably accurate fixes for stars out to hundreds of millions of parsecs based on parallax alone, with our current (TL-8?) measurement technologies.

Gravitic focusing (which gives many orders of magnitude better resolution than optical focusing) will also extend this: grav focusing appears "formally" in TNE, as the appropriate handwavium to allow beam weapons to hit LS range targets...

Scott Martin

 

[Straybow]

Originally posted by Icosahedron:
As I say, I can't figure out whether your Scmidt figures are disproving me or not without going to altogether too much trouble. Are you saying that current telescopes can fix _distance_ to 0.5 Pc at 1000Pc using parallax alone?
(That's tens of times times further away than I figured was possible.) Or are you just talking about fixing _lateral_ location if you're 'given' the distance?

1" (at 1Pc) = 3e-4 degrees
.001" (at 1000Pc) = 3e-7 degrees
100nm = 10^-7m
Palomar 5m Schmidt with 4° field = 1.25m/degree
¼-wavelength mirror surface precision on a large telescope is ~10^-7°

That means we could resolve parallax at 1000Pc with a 1AU baseline if it weren't for atmospheric effects. So at our TL we could easily assemble a space telescope of similar dimensions and achieve 2000Pc distance measurements to the precision needed for Traveller maps by parallax from Earth orbit's 2AU baseline.

 

[Anthony]

At a distance of 1,000 parsecs (206,264,806 AU) and a baseline of 1 AU, parallax is 4.848136816903e-9 radians. At a distance of 1,000pc + 0.5 AU, parallax is 4.848136805151e-9 radians. The difference is 1.175e-17 radians. At a wavelength of 5e-7 meters, resolving that requires a diffraction-limited lens with a size of ~6e9 meters. No, we can't build that, or anywhere even close (10^-7 degrees = 1.74e-9 radians -- so we could build a telescope that can determine the distance to an object at ~1,000 pc to within a few hundred parsecs).

 

[Straybow]

Originally posted by Anthony:
At a distance of 1,000 parsecs (206,264,806 AU) and a baseline of 1 AU, parallax is 4.848136816903e-9 radians. At a distance of 1,000pc + 0.5 AU, parallax is 4.848136805151e-9 radians...

Ah, there's the problem. You've just specified measurement to ±0.25AU instead of ±0.5Pc.

x1 = 999.5 Pc = 999.5/sin(pi/648000) = 206,161,673.845
x2 = 1000.5 Pc = 1000.5/sin(pi/648000) = 206,367,938.651
pax = arcsin(2/x1) = 9.701124184245e-9
pax = arcsin(2/x2) = 9.691427908199e-9
∆pax = 9.696276046221e-12

That's 5 orders of magnitude easier!

Note: I used "2" in the parallax calculation because while we define the parsec based on a 1AU baseline our orbit gives us a 2AU baseline to work with.

 

[Straybow]

The field is determined by lens diameter and focal length. The longer the focal length, the narrower the field. It is relatively easy to get the field down to a small fraction of a degree. Now the wavelength limited precision is perhaps 2 orders of magnitude better.

We'd never get the measurement error small enough using single-image techniques. We would build an inventory of images and reduce measurement error by a factor of √n. In addition we use "mixel" analysis: measuring the image intensity and color in adjacent pixels (very easy to do with digital images). The position of the star is interpolated between the pixels. Measurement error is further reduced by √n.

Next we build a database of relative parallax measurements. You know star X is farther than star Y. Star Z is farther than star Y. You try to determine if X or Z is farther of the pair. Now with each such pair you can further reduce parallax error by √n (as long as the intrinsic precision is preserved).

Spectrum and luminosity studies help refine the relative distance measurements as well. Over time the distances are narrowed considerably.

From the presumptive starting precision of 1e-9 we jumped 2 orders of magnitude with scope design to 1e-11. Our 9.69e-12 is marginally within reach. With say 50 images of each star, and 50 image pairings, we reduce error by a factor of √100, and now we have the extra digit of precision we need to confidently place the star's distance to ±½Pc.

 

[Merxiless]

I posit that as you jump out there, you look for yellow stars, and orange stars. Jump there, you got your target systems.

From A good ways off. I.e.

It's all in game fiction. It's as accurate as you want it to be.

I used to handroll sectors, that never got used...no more. All i need is a subsector or two and I am good for nearly a year of gaming.

 

[Plankowner]

The Aslan Alien Module (Alien Module 2) has rules for "exploration". It gave detection ranges for Gas Giants etc.