Proper Motion, Radial Velocity

[ckirmser]

Greetings, all.

I'm working on a real-time star map for a role-playing game where each star is located in its time-corrected 3d coordinates. With this, each star will be where it should be in a moment of time and not where it is observed to be.

To do this, I take the proper motion of the star in RA and Dec, and the Radial Velocity and use the current distance in light years plus the date from 2000 to determine the star's position.

Mathematically, this is a breeze. But, the problem comes in with the radial velocity.

My game is set in 2871. As a result, stars can move a long way.

This got me to thinking.

The way the motion of the stars is defined, they either spiral away from Sol or spiral in. Nothing travels tangentially. No stars will ever "pass" by Sol and, anything with a negative radial velocity will, sooner or later, collide.

I can see no other conclusion, given the way the data on stellar motion is provided.

Is this just something we're stuck with, or is there some step I'm missing that would allow tangential travel and not every star either spinning away or spinning into slap the Sun?

Thanx!

 

[Bandersnatch]

For the very small angles that constitute proper motion, it is equivalent to instantenous tangential velocity. Just multiply the angle in radians by distance.

It is used preferentially over actual tangential velocity, because it can be measured directly and with good precision. Tangential velocity in km/s can be only derived from proper motion and distance measurement, the latter being often burdened with high uncertainty.

Radial velocity, on the other hand, can be measured directly from doppler shift.

 

[Bandersnatch]

Just to make sure I got my point across, as I feel my answer was not exhaustive enough - stars most definitely do not spiral in or out from the Sun. They move in mostly straight lines.

In polar coordinate systems bodies moving in straight lines will have their radial and tangential velocites change all the time(unless moving exactly along the radius).

To predict the position of a star in the far future:
-calculate the transverse velocity vector(equal to instantenous tangential velocity at the moment of measurement);
-add the radial velocity vector;
-transfer the resultant velocity to a cartesian coordinate system;
-calculate future position(simple, since it's a constant velocity movement along a straight line)
-transfer back to the polar coordinate system to find out where the star would appear to be in the sky

By the way, Hayden Planetarium released a freeware planetarium software called "Digital Universe" that models motion of neighbouring stars. Perhaps it could be of some use to you. http://www.amnh.org/our-research/hayden-planetarium/digital-universe

 

[ckirmser]

How coincidental - the RPG for which I'm making this map is for my Ringworld campaign.

"Bandersnatch" - love it!

Anyway, thanks for the responses. I know that the stars don't all spiral in or out, but I didn't see any alternative, given the data at hand, so I thought that, perhaps, I was not understanding the motion parameters in general.

One thought I had was to take a star's coordinate for year X and for year X+1. Then, to create a vector from those two points to give a straight line path. But, even with this solution, if I was misunderstanding the basic data, I'd be getting bad results.

So, I see that I have the data down, and I'll see what I come up with. Of course, given the time frame and that I'm only interested in stars within 100 ly, my maximum displacement will be only about 1,000 years, so the positions probably won't change all that much.

Oh, and thanks for the link to the Hayden data, I'll give that a good going over.

 

[Bandersnatch]

Of course, given the time frame and that I'm only interested in stars within 100 ly, my maximum displacement will be only about 1,000 years, so the positions probably won't change all that much.

Actually, in the timeframe of ~1000 years, even the fastest moving of the neighbouring stars - Wolf 424, which moves at a whooping 550km/s, or roughly the galactic escape velocity - will only cover 1.7 light-years. On the celestial sphere it'd move by a less whooping 0.5 degrees, or the size of the Full Moon's face.

Barnard's Star, the second-closest star to the Sun, with its 140ish km/s of true speed, will move by about half a light-year of true displacement, which will be more noticeable due to its closeness. It'd move by roughly 3 degrees of arc, while getting closer - from 6ly to 5.7ly.

But then, both are red dwarfs, so you wouldn't see them anyway.

What I'm saying, is you could just as well forget about all but the closest of stars, and even with these if you were to simply use proper motion to shift them on the celestial sphere by a few degrees at best, you wouldn't lose too much accuracy.