NavList:

Sean, you wrote:
"For β Hyi, Simbad gives a proper motion of +2219.54 mas/yr in R.A. and +324.09 mas/yr in dec.
The FK5 catalogue gives +1003.785µ / +323.7µ."

Yes, those look good. The RA proper motions are in different units, but let's not worry about R.A. (can come back to it later). Declination rates of change are exactly what they appear to be and easily interpreted. Simple (non-precessional) rates of change of dec. Some older sources list the values in arcsec per year, occasionally arcsec per century. The modern style is mas (milliarcseconds) per year which is, of course, equivalent to arseconds in a thousand years. All recent sources for beta Hydri have just about +324 mas/yr for the proper motion in dec. Even going back to the 5th edition of the Yale Bright Star catalog released before Hipparcos in 1991, the listed value is 0.324 as/yr --exactly the same.

Stellarium lists two sets of proper motion values for this star: the net and the position angle of the motion which are given as 2648 mas/yr towards 76.9°, and also the individual components "by axes" which are given as "2579 and 599" mas/yr. The two sets are consistent. You could just draw those latter two numbers on graph paper in the x, y directions, connect them with a hypotenuse and even in that simple way you find that the net length and the angle are "just right". But what the hell?? 599 mas/yr for the proper motion in declination?! That's nearly double the best estimates that have been available in the past thirty years. Is it wildly wrong? Is it displayed in some incorrect units but "right on the inside"? Could it be that someone has listed rate of change of dec with precession included (that just occurred to me ...don't know if it makes any sense)? I should add that I mentioned beta Hydri to start because it was the first that I noticed in a sample of three or four stars. Since then I have found other oddities. I don't see a pattern in them yet.

Sean, you added:
"no matter which numbers you use, that is relatively fast."

Yes, it's zipping along! Beta Hydri is a nearby star, so its physical motion translates to larger angular motion. 

A challenge for brave coders: What is Stellarium doing? Well, it's open-source, so go grab the code, open it up, and find out! I leave this as an exercise for the reader. Ha ha ha. Actually, I tired this approach a couple of years ago on another puzzle and found it far too much trouble (easier to diagnose from behavior than from code), but it's really the best way to ensure the code is okay.

Frank Reed

PS: I'm aware that this is moving rapidly away from navigation, and we will move it back to navigation or shut it down soon.