Stellar velocity question: Can anyone help?

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: | "One of the hardest parts of my job is to
pciszek at panix dot com | connect Iraq to the War on Terror."
Autoreply is disabled | -- G. W. Bush, 9/7/2006

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
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

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
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

Brian Tung wrote:

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.

I agree. A step-by-step guide to doing this kind of calculation is
given here,

http://astronexus.com/node/40

Note that the right ascension and declination you get at the end of this
calculation are expressed in the epoch of the original position, usually
J2000. If you want to know where it will appear in the sky for a given
observer in the future, you also have to precess those coordinates to
the observer's time.

- Ernie http://home.comcast.net/~erniew