[Kstars-devel] Proper Motion Corrections - The Right Way

[James Bowlin]

On Wed July 9 2008, Akarsh Simha wrote:
> Is there some way of verifying the validity of these results?

I think there are two things we need to check:

  1) Is the new PM calculation correct?
  2) Are we calculating the trixels correctly?

I first checked the formula by comparing it with our old formula for 
small angles and the two different formulas gave the same results.  
Then when I increased the angles, the formulas started to deviate.  
This indicates that new formula is correct, at least for small angles.

Ideally, we could compare the positions of a few high PM stars at large 
time shifts with someone else's published results.  This will test the
formula (or at least test that someone is using the same formula).

I think a level 3 mesh only has 32 trixels around the equator (if the 
path has a very small but non-zero declination) so getting close to 32 
trixels for a given path may indicate a problem (or maybe not).  

One check would be to take smaller steps and use a hash to "or" the 
results (so you don't count the same trixel twice) but I don't suggest 
doing this right away because it is a lot of work for little payoff.

I'm very surprised to see such a large difference in the two scatter 
plots.  One way to go about checking this big difference is to use a 
much smaller time scale, maybe just +/- 100 years.  Then the angles 
will be much smaller and the scatter plots should be in much closer 
agreement.  You might have to remove or reduce the safety margin in
order to keep a reasonable number of points in the scatter plots.

For +/- 10,000 years, 1000 milliarcseconds/year corresponds to an
arc that is roughly 5.5 degrees long.  I'm surprised the scatter plots
differ so much down in this area.  I would have expected a deviation but 
not the factor of 2 or 3 (or more) that we seem to see.

BTW: I just saw your commit fixing the proper motion calculations.
Someday, we might want to store the magnitude of pm and the direction
in the data file (and in new StarObject fields) to slightly streamline
the PM calculation.

BTW2: Did you know what the percentage of duplication is when we use the 
new formula?  But maybe I should wait until we verify the formulas 
before getting my hopes up.


-- 
Peace, James