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Date: 23 Sep 2007 21:27:36
From: Paul Ciszek
Subject: Stellar velocity question: Can anyone help?
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A friend sent me this question:
>Paul,
>
>How's your celestial mechanics? I'm having trouble understanding
>astronomerspeak. Epsilon Indi ("Home" in Niven's Known Space) is 11.83
>ly from earth and has a radial velocity of -40.4 km/s (meaning, I think,
>that the redshift indicates that it's headed toward us at that speed).
>But I'm trying to figure out where it will be, distancewise, in 50,000
>years, which should require all three relative motions. Wikipedia lists
>these as "U=-77, V=-38, W=+4". I don't know what the three letters stand
>for, and I don't understand why none of them correspond with the radial
>velocity (unless the V is a slightly different value for the same
>thing). Any ideas?
I posted this in rec.arts.sf.science, and there seems to be some
confusion as to whether the velocity is given in a co-ordinate system
in which the Sun is stationary or moving. So I thought I would start
from scratch in this newsgroup. I would be grateful if anyone could
tell me:
* What units go with the numbers?
* Is the co-ordinate system rectangular, cylindrical, or spherical?
* Is the Sun stationary in that co-ordinate system, or is it moving
as well?
* If the Sun is moving in that co-ordinate system, what is its velocity
vector?
--
Please reply to:
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Date: 23 Sep 2007 15:04:55
From: Brian Tung
Subject: Re: Stellar velocity question: Can anyone help?
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Paul Ciszek wrote:
> A friend sent me this question:
>
> >Paul,
> >
> >How's your celestial mechanics? I'm having trouble understanding
> >astronomerspeak. Epsilon Indi ("Home" in Niven's Known Space) is 11.83
> >ly from earth and has a radial velocity of -40.4 km/s (meaning, I think,
> >that the redshift indicates that it's headed toward us at that speed).
> >But I'm trying to figure out where it will be, distancewise, in 50,000
> >years, which should require all three relative motions. Wikipedia lists
> >these as "U=-77, V=-38, W=+4". I don't know what the three letters stand
> >for, and I don't understand why none of them correspond with the radial
> >velocity (unless the V is a slightly different value for the same
> >thing). Any ideas?
>
> I posted this in rec.arts.sf.science, and there seems to be some
> confusion as to whether the velocity is given in a co-ordinate system
> in which the Sun is stationary or moving. So I thought I would start
> from scratch in this newsgroup. I would be grateful if anyone could
> tell me:
>
> * What units go with the numbers?
The UVW are in km/s.
> * Is the co-ordinate system rectangular, cylindrical, or spherical?
The UVW are cylindrical.
> * Is the Sun stationary in that co-ordinate system, or is it moving
> as well?
The Sun has UVW motions.
> * If the Sun is moving in that co-ordinate system, what is its velocity
> vector?
I don't recall, unfortunately. I think you could probably look that up,
though.
Your friend has given us motions in two different reference frames. The
UVW velocities are referenced to the galaxy: they refer to motion around
the galactic axis, toward the axis, and parallel to the axis.
Radial velocity, on the other hand, is referenced toward the Sun. In
addition to its distance of 11.83 light-years and radial velocity of
-40.4 km/s, it has a proper motion of 4.7 arcseconds per year, which at
its distance translates to a linear transverse motion of about 81 km/s,
if I haven't made a mistake in my calculations. Assuming that to be so,
in 50,000 years, it will have moved 6.7 light-years radially, and about
13.4 light-years transversely. It will therefore be about 14
light-years away, but in a completely different part of the sky--about
70 degrees away.
--
Brian Tung <brian@isi.edu >
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html
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Date: 23 Sep 2007 16:19:52
From: Brian Tung
Subject: Re: Stellar velocity question: Can anyone help?
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I (Brian Tung) wrote:
> Your friend has given us motions in two different reference frames. The
> UVW velocities are referenced to the galaxy: they refer to motion around
> the galactic axis, toward the axis, and parallel to the axis.
Sorry--a couple of caveats. First of all, I switched U and V. U is
positive toward the axis, and V is positive clockwise around the axis
(as seen from the north galactic pole).
Secondly, UVW, though they are reckoned with respect to the galactic
axis, are generally computed heliocentrically--something I had forgotten
when I wrote my first post. As a result, the UVW space velocities
usually factor out the motion of the Sun--the Sun has, in this system,
no UVW velocities, despite the fact that its orbit is not precisely
circular and does not remain precisely within the galactic plane.
Nonetheless, in order to determine where epsilon Indi will be, relative
to the Sun, it's easiest in my opinion to deal with parallax (or
distance), proper motion, and radial motion.
--
Brian Tung <brian@isi.edu >
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html
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