Navigating in 3D

IsaacKuo wrote:
> I don't understand the popularity in this thread of using
> these relatively rough distinctions, when binary orbit
> period should be pretty fine.

It can be, if you're able to make very fine measurements in a short
period of time. A lot of binaries have a long enough period that we
can't yet make those determinations in a timely fashion. Of course, one
could say that about just about any characteristic of individual stars.

> A decent fraction of stars out there are in binary
> star systems, right? And the orbital period can be
> calculated very precisely from a wide variety of angles.
> For orbits fast enough for spectral analysis, any direction
> except roughly along a pole will do.

It's not the velocity you need to measure, but the change in velocity.
With our current technology, you need to measure that change over a
significant fraction of an orbit to determine the period to enough
precision to distinguish it from any of the billions of other binaries
in the galaxy. A similar problem plagues anything based on stellar
characteristics like mass or temperature.

Also, note that this thread has comprised a number of different though
related problems--all of which have to do with navigating the galaxy,
OK, but there have been a few different sets of rules to play against.

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Nyrath the nearly wise wrote:

> Star catalogs not only document a star's position,
> but also its "proper motion".

Although it's worth noting that the "proper motion" has two components,
along the line of sight (Doppler shift) and perpendicular to the line
of sight (much tougher to establish, especially for objects further
away). Actually, the same problem plays for exact positions as well
(Hip made things much MUCH better, but still not perfect... especially
for FTL jumping near a star/planet). You could do far far better if you
had even *one* other telescope with a long baseline relative to
Earth... which brings up one of the main tasks for the cruise phase of
STL ships, and perhaps a very good task for short-jump FTL types as
well: establishing very accurate positions and proper motions.

--
Brian Davis
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Brian Davis wrote:

> Although it's worth noting that the "proper motion" has two components,
> along the line of sight (Doppler shift) and perpendicular to the line
> of sight (much tougher to establish, especially for objects further
> away). Actually, the same problem plays for exact positions as well
> (Hip made things much MUCH better, but still not perfect... especially
> for FTL jumping near a star/planet). You could do far far better if you
> had even *one* other telescope with a long baseline relative to
> Earth... which brings up one of the main tasks for the cruise phase of
> STL ships, and perhaps a very good task for short-jump FTL types as
> well: establishing very accurate positions and proper motions.

Also, those give you the _instantaneous_ velocity vectors, not their
future paths. Any interaction is going to make that rapidly inaccurate;
take, for instance, the current velocity of Proxima Centauri as a
predictor of its future position.

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Brian Davis wrote:
> Although it's worth noting that the "proper motion" has two components,
> along the line of sight (Doppler shift) and perpendicular to the line
> of sight (much tougher to establish, especially for objects further
> away).

In the astronomical usage I'm familiar with, "proper motion" refers to
just that (angular) motion that is perpendicular to the line of sight.
"Radial motion" is used to refer to motion along the line of sight.

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Erik Max Francis wrote:
> Also, those give you the _instantaneous_ velocity vectors, not their
> future paths. Any interaction is going to make that rapidly inaccurate;
> take, for instance, the current velocity of Proxima Centauri as a
> predictor of its future position.

I'm not sure what interaction you're speaking of, but the gravitational
interaction is pretty small. Motions in the local neighborhood relative
to the Sun are pretty good approximations to straight lines, I believe.

It is true that as an object gets close, perspective effects cause the
motion to change in terms of yearly speed and direction on the celestial
sphere, but the apparent paths are, I think, still pretty close to great
circles.

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Brian Tung wrote:

> In the astronomical usage I'm familiar with, "proper motion" refers to
> just that (angular) motion that is perpendicular to the line of sight.
> "Radial motion" is used to refer to motion along the line of sight.

That's right. It's not usually called "radial motion," though; it's
called by how it's measured, which is _radial velocity_. Combined with
its position in the sky and its distance, they can be combined to
determine its real velocity vector in 3D space. Usually it's overall
motion in space is distinguished from the proper motion or radial
velocity by the term _peculiar motion_.

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Erik Max Francis wrote:
> That's right. It's not usually called "radial motion," though; it's
> called by how it's measured, which is _radial velocity_.

Right, motion, velocity, that's what I said. (Translation: I had a
brain-o; thanks.)

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Brian Tung wrote:

> I'm not sure what interaction you're speaking of, but the gravitational
> interaction is pretty small. Motions in the local neighborhood relative
> to the Sun are pretty good approximations to straight lines, I believe.

Sure, but we're talking about arbitrary distance travel around in the
Galaxy without taking into account the implicit time travel that is also
involved, even if the travel is instantaneous.

To first order the peculiar motions of stars that you can compute is the
way they'll move, but that's only to first order. Second-order effects
will come into play over longer timescales, namely due to the
interactions between the stars. Stars do _not_ move in straight lines;
that is only an approximation that is true over short timescales.

The disclaimer was already given that if you take into account long
enough timescales where galactic rotation comes into play, then needless
to say positions are hard to predict. My point is that the timescale
where you need lower-order corrections comes into play long before that.

Proxima Centauri is an obvious example; whether or not it is bound to
the Alpha Centauri system proper, it is _not_ moving in a straight line.
Failure to take that account when trying to observe the system from a
great distance will result in errors.

--
Erik Max Francis && max RemoveThis @alcyone.com && http://www.alcyone.com/max/
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Brian Tung wrote:
> Brian Davis wrote:
>> Although it's worth noting that the "proper motion" has
>> two components...
>
> In the astronomical usage I'm familiar with, "proper
> motion" refers to just that (angular) motion that is
> perpendicular to the line of sight.

Yes, which is why I used the term in quotes. My point was if you wanted
an accurate location for a star to "jump" to, that's not very well
known even now, let alone at some other time.

--
Brian Davis
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Brian Davis wrote:
> Yes, which is why I used the term in quotes. My point was if you wanted
> an accurate location for a star to "jump" to, that's not very well
> known even now, let alone at some other time.

True, though the main problem is not the proper motion, but the parallax
(the distance, in other words). As an illustration, typical errors in
parallax are on the order of 1 mas (milliarcsecond). On a star like
Proxima Centauri, about 4.3 light-years (1.3 parsecs) away, that amounts
to a distance error of 1/500 of a parsec, or about 1/150 of a light-year.
That isn't much--only about 400 AU. But the transverse accuracy is even
better; with also an angular error of about 1 mas, the linear error is
only 20 *billionths* of a light-year. That is a mere 4/10,000 of an AU,
or just 60,000 km. Pretty spectacular.

What's more, the error in distance goes up as the square of the distance
(more or less), whereas the error in transverse position only goes up
linearly as the distance. So by the time you're talking about objects
100 parsecs away, say (with a parallax of 10 mas), the error in distance
is 10 percent or 10 parsecs, but the error in transverse position is
still only 0.03 AU, or about 5 million km.

The proper motion has an error of about a mas/yr, so that those errors
do build up, but even so, the transverse error will still be much less
than the distance error, unless you are travelling much slower than the
speed of light (say, on the order of 3 km/s).

The ESA's GAIA satellite is supposed to improve parallaxes by 2 or 3
orders of magnitude, so the errors will be on the microarcsecond (uas)
level. Personally, I think that's darned amazing.

--
Brian Tung <brian RemoveThis @isi.edu>
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 >> Stay informed about: Navigating in 3D 

Brian Tung wrote:
> IsaacKuo wrote:
> > I don't understand the popularity in this thread of using
> > these relatively rough distinctions, when binary orbit
> > period should be pretty fine.

> It can be, if you're able to make very fine measurements in a short
> period of time. A lot of binaries have a long enough period that we
> can't yet make those determinations in a timely fashion. Of course, one
> could say that about just about any characteristic of individual stars.

Yes, but if you restrict your search just to binaries with
relatively short periods, then that should be good enough.

Naturally, this depends on how eager you are to get on with
the next "jump". I'm imagining a scenario where each jump
makes you go a very, very, long distance, so your typical
journey won't take many jumps. Otherwise, it seems
strange for you to get lost so easily.

> > A decent fraction of stars out there are in binary
> > star systems, right? And the orbital period can be
> > calculated very precisely from a wide variety of angles.
> > For orbits fast enough for spectral analysis, any direction
> > except roughly along a pole will do.

> It's not the velocity you need to measure, but the change in velocity.
> With our current technology, you need to measure that change over a
> significant fraction of an orbit to determine the period to enough
> precision to distinguish it from any of the billions of other binaries
> in the galaxy. A similar problem plagues anything based on stellar
> characteristics like mass or temperature.

Yes, but if you wait for an entire orbit or two, then you'll
get a very good measure. So you spend the first couple
hours scanning for a thousand candidate binaries.
Then just keep observing them for the next several
hours or days until you've got sufficient accuracy on
a sufficient number of them for definitive identification.

Isaac Kuo
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