Hello everybody
Somebody mentioned that deep space navigation using pulsars (and nearby
stars?) could be accurate to within an astronomical unit.
Thinking about it, I doubt that this accuracy could be achieved with distant
objects alone.
Problem is, we have to know the position of the objects in 3 dimensions and
the measurement is unlikely to be very precise.
Assume we know the pulsars' position to within 1/10th of a Lightyear
(big if) and that no other measurement errors creep in (another big
if). This means we know our spaceships's position to within 1/10th of a
lightyear.
Using many pulsars won't help that much. If you take N measurements, the
accuracy of your result improves with the square root of the
number. 700 pulsars will give an improvement by a factor of 1/26 [
1/sqrt(700) ] that is 1/260th of LY or 1 1/2 lightdays - about enough
to know in which star's system you are.
Greetings
> KH.Ranitzsch@t-online.de wrote:
That was Katy
> Thinking about it, I doubt that this accuracy could be achieved with
Well, on a galactic scale 1/10 ly ain't anything to sneeze at. ;-)
Actually I think, given interstellar travel, we will be able to nail the
positions of other celestial objects (pulsars, et al) down pretty
darn accurately (okay, within 1/10 ly ;-). Right now we are limited
(see an earlier post in this thread) to approx 100 parsecs for parallax
measurements. That's using a 2 AU baseline. Once we start heading out to other
star systems (e.g., Alpha Centauri, Sirius, even Vega), our baseline is going
to grow massively and we ought to be able to extend the parallax measurements
out pretty far. And pretty accurately.
Of course using a parallax measurement from, say Sol and Alpha Centauri
will only cover a portion of the sky - that part being the toroid per-
pendicular to the line subtended by Sol and A-Cen. It would be more
difficult to the extreme to get the same results when looking along
the line between Sol and A-Cen. So you'd have to use other stars as
your baseline there (yielding a different accuracy rating, of course, but hey,
that's what will keep us astronomers in business 200 years
from now! ;-)
> Using many pulsars won't help that much. If you take N measurements,
Which, for most purposes, is all you'd really need. You can repoint your
ship and zip in closer. :-)
In another post Katy said in response to a Karl question:
> It's not /just/ looking at the pulsars. You also know /which one/
> positions and frequencies right. And then there's the fact you're
Well, that's presuming you're moving at such speeds. ;-) I wouldn't
presume that a starship would drop out of FTL and still be moving at
fractional c velocities. But then again, that all works out to whatever scale
you're assuming. I haven't sat down to work out exactly what "interplanetary
speeds" might be. Maybe I'll do that someday. In my copious free time (maybe
this coming weekend...oh, wait, no, can't; got
the ECC to play in :-)
Indy schrieb:
> > Thinking about it, I doubt that this accuracy could be
I guess the 100 parsecs are the range at which measurements are possible,
rather than the error in teh measures location?
> That's using a 2 AU baseline.
Going to Pluto to do parallax measurements would certainly help :-)
Especially if you can do very-long baseline interferometry with Neptune
or Uranus as the other receiver.
> Once we start heading out to other star systems (e.g., Alpha
You would have to know the distance between the sun and your other star quite
accurately. Anay error there gets multiplied massively in parallax
measurements.
> but hey, that's what will keep us astronomers in business
I certainly see an use for the GZG Clarke class survey ships.
> - about enough to know in which star's system you are.
Well, if you are doing multiple jumps through deep space... Probably still
better than dead reckoning (depending on you PSB, of course).
Greetings
> KH.Ranitzsch@t-online.de wrote:
Affirmative. This is the current range of parallax measurements. Technology
will push this out later, but I don't think by a whole lot. We need to
increase the baseline to get much better results.
> > That's using a 2 AU baseline.
:-)
> > Once we start heading out to other star systems (e.g., Alpha
True. But it should not be difficult at all to determine this quite
precisely. We already know to 1/10 ly or better the distances to nearby
stars. Once we actually *travel* to them, all we have to do is turn a
sensitive receiver back toward Earth and pick up signals. From this we can
determine *extremely* well the distance (you know when a given signal
was transmitted - such as, oh, a Weather Channel show which carries the
timestamp in the program - and with calibrated time instruments you can
determine to with lightseconds or tighter accuracy how long it took the signal
to reach your location, and from that, derive the distance to some small
number).
> > but hey, that's what will keep us astronomers in business
More than K'V target practice, that is. ;-)
Indy schrieb:
> True. But it should not be difficult at all to determine
> instruments you can determine to with lightseconds or tighter
You have all this worked out have you?
:-)
> > I certainly see an use for the GZG Clarke class survey
Like the days when the Royal Navy mapped the seas.
Might make for a scenario: UN survey ship in uncharted space with a light
escort boldly going where no man hos gone before...OOPS, wrong show.
Greetings
> KH.Ranitzsch@t-online.de wrote:
Oh yes! I've been collecting and beaming the GZG posts to beta Pictoris for a
couple of years now, in the hopes that by the time we get there we'll have a
signal to work with directly (of course the tricky part is not beaming the
signal directly at beta Pic, but rather beaming it to
where beta Pic will be when we get there - that's taken a bit of
hand-waving to ascertain, what with clairvoyance being such a rigorous
discipline and all).
There are some issues with that.
a) what if you're going to place that doesn't have any signals yet -
i.e. 500LY or more away from Sol? Even early signals won't have a time stamp
(at least I don't think the orignal episodes of I Love Lucy don't)
b) Assuming advanced tech drives, non-FTL speeds could reach an
appreciable portion of the speed of light, how do you correct for the time
shift of the internal chronometers compared to the rest of the universe?
Differences of micro or milli seconds could occur if you stayed at "high"
velocities long enough.
c) Stars, systems and galaxies are all moving - tens, even hundreds of
thousands of miles per hour which would mean some systems are moving a
few light-seconds every day away from Sol. After a year, a decade or
even a century they could be as far 2 light hours per year or 8.3 light days
per century. You'd have to measure the velocity of the star or
system to correct for any red-shift (or blue-shift for that matter)in
your timing signal. The shift in wavelength might add to the imprecision of
the measurements. These velocities would be in refrence to Sol, other systems
might see a different velocity.
d) For a standard map to work, we'd need a good, fixed reference point
to start from - Are we going to use some sort of Galactic North Pole? or
perhaps a "True Galactic Blackhole Center" at or near the center of the
galaxy? Does the Tufflyverse have humans getting to the center of the
Galaxy? Or would we be Sol-centric and make Sol our reference point?
I think that we sometimes forget that we live in a relative world. If you
stand at the equator, you don't feel motion, even though you are traveling
1,000 miles per hour as the earth rotates. In addition, you
are moving 67,0000 miles per hour (+/- a thousand) as the Earth orbits
the sun. Since everything around you is moving at the same rate, you don't
notice the effect. What happens when you jump to another system in another
part of the galaxy?
Some more material to chew on...
--Binhan
> -----Original Message-----
> True. But it should not be difficult at all to determine this quite
> B Lin wrote:
> I wrote:
There are always issues with everything. ;-)
> a) what if you're going to place that doesn't have any signals yet -
I was not addressing jumps of that magnitude. I was addressing the problems
and accuracy range of parallax measurement to other stars. Karl had stated in
order to use stars as a baseline you need to know *exactly* (or damned close)
the distance between your baseline stars. I proposed a method in which this
baseline could be determined. This would be with relatively nearby stars, not
stars like Betelguese.
> b) Assuming advanced tech drives, non-FTL speeds could reach an
Not being addressed in the recent thread/posts.
> c) Stars, systems and galaxies are all moving - tens, even hundreds of
Again, not an issue really addressed in the thread/posts. You are
starting to go out well past what is, er, "reasonable" for space nav in the
vicinity of Sol. IIRC, laserlight postulated a range of about 20 parsecs. I
indirectly expanded on this by stating parallax measurements are [currently]
only good out to 100 parsecs, but in the future we will be able to go further.
How far? Don't know. Don't think it really matters that much for where the
discussion is at this time. Yes, your points are valid, but they take on a
whole new scope and scale that I do not think is easily addressed or dealt
with right now. I say, let the astronomers
of 200 years hence worry about it. ;-) ;-)
> d) For a standard map to work, we'd need a good, fixed reference point
I don't think you can have a "good, fixed reference point" in a universe that
is constantly moving. Any map you make is going to be out of date the moment
you stamp "FINI" on it (much like computers as soon as you buy
them ;-). Whatever reference point you pick is going to have to be a
relative one.
The way I see it (and this is obviously speculation), maps may be modular in
nature. You would create a map of a stellar neighborhood (say, oh, 50
parsecs on a side). Using a particular star (oh, let's say Sol :-) as
the relative center point. Next, make additional map cubes that surround the
local stellar neighborhood cube (I'm stretching the currently accepted
definition of "stellar neighborhood by going 50 pc, btw; change it to 50 ly if
that feels better to you). Each map cube would be more or less centered on a
particular star, whose relative distance away from Sol is well determined (in
some way, shape, or form; if we are mapping the galaxy,
a 50-100 pc distance between stars is a drop in the ocean). After this
next batch of map cubes is done you start on the next "ring" of cubes. Then
the next, then the next, building around the previous. In the end you've cubed
up the galaxy and can make a [temporary] galactic map (I'm
guessing also by this point maps will be 3-D hologram type things that
can evolve as you look at them, not the fixed 2-D pieces of parchment
we have now).
Ya know, thinking about this, I think I have to attribute some of this cubic
mapping to FGU's Space Opera game. IIRC they had their stellar atlases put
together very much this way, with each sector denoted by the relative center
star (Sol Sector, Antares Sector, etc).
> I think that we sometimes forget that we live in a relative world. If
I don't [forget about the relative world, that is; my dice remind me all the
time]. I took all that into account in my earlier postings, but often the
motion of Earth around Sol was such a minute quantity in the scheme of things
that it is lost in the noise and can be ignored. Again, it's all a matter of
scale. If you are worried about a star's position shifting 2 lighthours a
year, the velocity of Earth around the sun is not going to be a significant
factor by any stretch of the imagination. However, a couple lighthours is not
that far. You will already be inside the system of the
star - Uranus, for example, is but 2.6 lighthours from Sol
But, yes, after a while one does have to take into account stellar motions all
around when doing mapping and space navigation. Which is what will make FTL
travel fun. Your database has to continually be updated (or be updating
itself) if you are to not get lost in the vastness of our galaxy. But for most
things within 100 parsecs, it's not going to be that critical an issue in the
space of a dozen years. By then you'll have updated star charts, anyhow
(unless you went "lowest bidder" again!).
Hello Folks,
At present, we are using a 2 AU baseline for measurements of stars. Once we
start using the ships of FT to place automated telescopes in orbit around the
sun, we can expand the baseline easily enough. Anyone care to figure out what
the accuracy will be for determining where stars *were* if the baseline is now
say, 40 AU's?
Also, how accurate does one's position have to be known to establish where you
are precisely? In other words, if I for what ever reason, jump to some
unknown location in space, and I find at least 2 known pulsars -
wouldn't that establish the rough ball park of where I was to the extent that
I at least know which direction to jump back?
That tri-angulation just like you described works just fine in
land-navigation. But that's (sort of) 2 dimensional.
I think you'd need a 3rd pulsar (or other known point) to determine the
unknown point (your location). Otherwise, you could just be anywhere along the
circumference of a circle which is the diameter of the distance you are from
the nearest pulsar... (or something like that, insert Layman's disclaimer
here).
That is, assuming that you're not using light-shift from movement, etc.
and just using the location of the pulsars relative to you.
--Flak
> On Tue, 2002-02-26 at 14:08, Hal wrote:
Once
> we start using the ships of FT to place automated telescopes in orbit
[quoted original message omitted]
[quoted original message omitted]
> Hal wrote:
Once
> we start using the ships of FT to place automated telescopes in orbit
See earlier message in thread re: "copious free time" ;-/
> Also, how accurate does one's position have to be known to establish
You need a minimum of 3 pulsars (fairly seperated) in order to determine your
position. Using 1 point of reference puts you on a sphere (and that is
assuming you know how far away you are). 2 points of reference gives you a
circle of where you might be relative to those 2 points, and nothing else. 3
locks you down. More refines the position. See earlier discussion along this
thread.
> --- Hal <hal@buffnet.net> wrote:
....
> Also, how accurate does one's position have to be
Hal, A roundabout and overly simplistic answer is; 1 point establishes a
sphere that you are on the surface of, I presume the radius can be determined.
2 points establish a line, and therefor you are on the
'surface' of a circle defined by the intersection of the two angles to the two
ends of the line. 3 points determine a plain, and only two locations can
satisify the requirements for the required angles to the determined locations.
(I.E. plus or minus angles) 4 points are needed to determine the plain and
determine if you are above or below the level of the plain.
5+ points are better.
Bye for now,
Hello John L., Thanks for the explanation below, but of course, I've more
questions to ask then...;)
> Hal,
Here is my reasoning...
If you have Pulsar A and Pulsar B, you have two points establishing a line.
You know the distance from A to B as well, since before heading out, you
established A's distance from Earth, and B's distance from Earth, and thus,
A's distance from B.
> From point C, you are at the unknown location. All you can get at C at
> From Point C, you are at the unknown location. All you get at this
Using the angles generated from your bearings to A and B, the only thing you
don't have is distance in your equation right? Hmmm, what about the distance
from A to B which is a known quantity? Now you have a triangle with *all*
angles known, plus one side of the triangle's distance known.
> From that, can you not determine your other two sides? From that, can
I must be missing something. Either that, or I am right, but am uncertain
enough to say why...
> --- hal@buffnet.net wrote:
....
> >2 points establish a line, and therefor you are on
> Here is my reasoning...
-----
Agreed. Now we need to do one thing to make it
more interesting, on the A-B line we place a compass
disk and define 'North' as the bearing from the
centerpoint of the A-B line to earth, I.E. zero
degrees.
hals Logic portion removed...
> Hmmm, what about the
-----
Agreed, you will be able to define your location in
terms of angle/dist fm A and angle/dist fm B. What
this information will not tell you is the difference
between the A-B centerline 'North' and your current
angular location. Or perhaps in a more simplistic case, knowing all the angles
and distances on a triangle will not tell you if the triangle is standing up
or lying down.
> I must be missing something. Either that, or I am
> On 26-Feb-02 at 22:22, John Leary (john_t_leary@yahoo.com) wrote:
> Please note that while I agree with all of the points
Let's see if I can work my way through this.
1. I know the absolute locations of 3 pulsars (A B C).
2. Knowing two (A B) and their angles to my ship I know my location on the
surface of circle.
3. Pick another pair (B C). I get another circle.
4. Pick the remaining pair (A C). Yet another circle.
5. Intersect the three circles. I now know where I am.
6. For safety make it 6 pulsars and find the intersection.
Is this wrong?
> Agreed. Now we need to do one thing to make it
I've got a section of coding from an individual who showed how it is
possible to convert ascention and declination into X,Y,Z co-ordinates.
You do need "distance" to destination to provide for the "Z" aspect of the xyz
system.
> hals Logic portion removed...
You see, this is where you keep getting me confused....
If you have the 3d co-ordinates for Pulsar A, or point A in this three
dimensional space problem, and you have the 3d co-ordinates for Pulsar B
in this problem, and you solve for angles for point C, and you also solve for
distance, it only stands to reason, that you now have the 3d
co-ordinates
for the triangle's third point. This should give you the ability to know
relative to the original co-ordinate system, where you are...
Hello Roger, See, I'm getting confused myself...
> Let's see if I can work my way through this.
Lets say for the sake of argument, that I attempt to take a bearing on Pulsar
A. I get that bearing. At the same time, I have someone else, or the computer
take readings automatically) that gets the bearing on Pulsar B. For this
"exercise" I have the bearings on both known Pulsars, along
with their *known* 3d co-ordinates. From those two known co-ordinates,
I
should be able to compute the third co-ordinate (my location). This is
why I am confused as to why it should require more than *two* pulsars... Mind
you, I'm not saying "exact" co-ordinates down to precision values, but
general ball park at least.
> At 11:10 PM 2/26/02 -0500, Hal wrote:
[snip Roger's explanation]
> Lets say for the sake of argument, that I attempt to take a bearing on
Mind
> you, I'm not saying "exact" co-ordinates down to precision values, but
Nope. Your assumption above is that you know where you are relative to the
origin of the "known" coordinate system, which provides you with the third
point required to relate two volumes. But if you're lost, how do you know that
relation?
For a simplified case, say you are right on the line between the two pulsars,
so one is dead ahead, the other straight aft. How do you know what angle to
rotate the ship so that the origin of the "known" coordinate system is
directly overhead, without a third reference point?
Now, I know that in straight-line cases some examples break down, but
this holds more or less true as you get further away from the line between the
two pulsars. You can establish where you are relative to the two pulsars, and
you know where the origin of the "known" coordinate system is relative to the
two pulsars, but you can not establish a relationship between the
two without a third point to locate by, otherwise you're on a circle of
possible locations around the line between the two pulsars.
I hope this helps, though given the hour I'm not so sure....
> hal@buffnet.net wrote:
> Hello Roger,
Mind
> you, I'm not saying "exact" co-ordinates down to precision values, but
Take a look at this diagram:
http://www.wombatzone.com/images/navexample1.gif
This is a side view of your ship.
You have two pulsars to take a reading from, Pulsar Red and Pulsar Blue.
You take a reading on Pulsar Red. It is 45 degrees below the centerline of
your ship. It is 0 degrees to the left or right of the centerline of your
ship.
You take a reading on Pulsar Blue. It is 60 degrees above the centerline of
your ship. It is 0 degrees to the left or right of the centerline of your
ship.
You attempt to determine your location. As you can see, there are two possible
locations on this diagram (marked A and B) where Pulsar Red is 45 degrees
below the ship and Pulsar Blue is 60 degrees above the ship.
Without a third point of reference, to tell you which way the ship is
pointing, there is no way to determine if you are at point A or B. Even if you
know the distances from your ship to each pulsar, and the distance between the
pulsars, you could still be at either point.
Now, in actuality, the range of possible locations would be a circle of all
the points that lie such that Pulsar Red is 45 degrees below and Pulsar Blue
is 60 degrees above.
[quoted original message omitted]
[quoted original message omitted]
> At 05:06 26/02/02 +0100, Karl wrote:
As they and many other navies continue to do do.
Cheers
Quoting hal@buffnet.net:
> Hello John L.,
Right, look; You need to get at least three bearings.
Bearing one gives you the line you lie on towards the object. This is not
useful. Because you don't know your own orientation, hence that line could in
fact be any line passing through the object.
Bearing two gives you a difference between those two bearings - a flat
angle between them. Assuming you know the location of the two objects, that
resolves you to being somewhere on a circle. (Note that taking the DIFFERENCE
of two bearings removes any dependence on your orientation). That circle
contains all the positions at which the difference of the bearings to the
objects is what you have. It's perpendicular to the line connecting the
objects.
Bearing three, differenced with two, does the same thing, but gets a different
circle.
Unless you're really unlucky, those circles will only touch at one point.
That's you that is.
If they touch at more that one, congratulations. Pick another object.
Actually, they won't touch. They never do, due to measuring inaccuracies.
You're somewhere around their closest approach point.
You don't need to know your distance from the objects - that's why these
are "bearings" and not "positionings". Locating them on a celestial sphere is
enough, assuming, and this is a big assumption, that you pick objects which
are not too far away. I'd suggest picking the bright ones...
{If they're too far away, they won't move against your effective celestial
sphere as you move..}
Determining distance is possible, but a lot more inaccurate than just taking
bearings.
As an aside, I came across a reference somewhere to a new sky survey -
"2MASS will produce the following data products: A digital atlas of the sky
comprising approximately 4 million 8´ à 16´ Atlas Images, having about
4´´ spatial resolution in each of the three wavelength bands. A point source
catalog containing accurate positions and fluxes for ~300
million stars and other unresolved objects. An extended source catalog
containing positions and total magnitudes for more than 1,000,000 galaxies and
other nebulae. "
Their intention is that this wide field survey will allow them to calibrate
the
Another way to look at it: Pulsar A and B form a "known" line of known
distance. So an analogy is a tall pine tree growing on flat ground, Pulsar A
is the base, Pulsar B the top. If I stand somewhere and get an angle to the
base and an angle to the top, in your argument I would know exactly where I
was. The problem is, if I walk in a circle at exactly the same distance away
from the tree, the angle looking down to the base is always going to be the
same and the angle looking up to the top is always going to be same as I
measured before. Does that mean that even though I walked somewhere, I'm still
in the same spot? You need that third point to determine where on the circle
you are.
--Binhan
> -----Original Message-----
> --- Roger Books <books@jumpspace.net> wrote:
> 5. Intersect the three circles. I now know where I
I believe you're missing the point, or I'm missing something.
With one known point (a pulsar for this discussion), you get a sphere of
where you _could_ be.
With only two pulsars, you get one circle of where you could be.
With three, then you get a point where you could be.
If I'm WAY off in bothering to respond as I have to this, then excuse
me, I don't recall the context of points 1-4 of the message you're
responding to point 5 of.
--Flak Magnet
Shooting his mouth off because it's loaded, and he has lots of ammo.
> On Wed, 2002-02-27 at 11:41, John Leary wrote:
> --- hal@buffnet.net wrote:
Hello Folks, I'd like to take this moment to thank those who responded
patiently to my questions and debunking my theoretical thoughts. This has been
a very educational process for me (and fun to boot). Thanks again. From what
I've gotten on this, it would seem that 3 is the minimal number of pulsars to
grab before knowing one's location. Two will give you an idea on how to
eliminate the wildly impossible locations (for ex: if you were travelling
towards X in known space, ended up such that your circle is 90% unlikely to
intersect with any stars - that leaves 10% of the circle that you could
be
at...). Three are needed to get a better idea of where you are, and 4+
gives you enough data to work with to further pin down your location...
All in all, a fun thing to consider. Thanks everyone (especially he
who made the diagram and posted on it web page so quickly!)