Binary Star : Mean Proper Motions and True Motions

Source: https://sourceforge.net/p/stellarium/discussion/278769/thread/e5092e67/

One of this continuing issues that I find with Stellarium is that moving into the distant future or sitant past shows the proper motions and true of binary stars, like Alpha Centauri, through space.

[Other examples are; Acrux, Gamma Centauri, Mu Verorum, Delta Velorum, y Centauri [not letter Gamma] or Beta Muscae. Northern examples, Delta Cygni, Alpha Piscium, Epsilion Hydra, The worst example is 61 Cygni, which at cuurrent date has the stars already too far ap.art

Here, in case of Alpha Centauri, A and B stars have different proper motions, using the HIP data, and these are displayed as two different diverging stars, flying apart, which simply get wider and wider as separate stars. (All these stars above do too!)

Alpha Centauri is the principle example, as it is the nearest star with very high proper motions. Using Stellarium as a planetarium for the past or future sky shows very poor educational value if the stars are not behaving as they should.

Exampled, for Alpha Cen A (HIP 71683) have individual proper motions pmRA= −3679.25 and pmDec.=+473.67 mas per year and Alpha Centauri B (HIP 71681) as −3614.39 and +802.98 mas per year.

The mean of these motions should adopted as a first approximation, I.e. When combined as −3646.82 and +638.25 mas per year. Hence, the proper motions for both stars would be better expressed as this value.

Usually, there are inherent problems with the companions proper motions, as their individual deviations in the directions they are travelling are not constant due to the binary system's orbital motion. Nominally, the true measure of the proper motion should be when both stars are travelling together (a line perpendicular to position angle of the direction the system is moving. The quoted proper motions here are not under this condition. [There are serious doubts on the given proper motion in declination for the B-star, and it could be easily argued that the A star motion should apply to both. Reasoning to explain this is not easy to say in a few words - at least in this expression of a problem.]

There are more serious issues than proper motions here, as the differing radial velocities of both stars. This changes over the 79.9 year orbital period, whose velocity varies by the orbital eccentricity / true distance the stars are apart. It is the mean or average radial velocity that is important here, being 25.1+/-0.3 km per second.

The other issue is that Stellarium data does not have radial velocity information, which is required to show not only the proper motion changes, but the real changes in distances by their true individual motions in space. Hence, the parallax and proper motions are actually variables not constants over time, where knowing the radial velocity means you can simply calculate these true motions.

If Stellarium had this too, when you advance or return in time, for example, the star magnitudes would change as they move towards or move away from the Sun. Like Aplha Centauri, the system is moving towards us, decreasing in distance but increasing in brightness. From current data, the maximum will be reached in 29,240+/-1,370 AD when the parallax will be +1098 mas. and Alpha Centauri shines at −1.05 than −0.27 magnitude today.

At present, the motions of stars into the future and past just stay the same in magnitude only taking into account a constant proper motion across the sky. [The only other addition is precession, which is nothing to do with true stellar motions.]

Suggested Reading to solve this is something like;

Matthews, R.A.J., "The Close Approach of Stars in the Solar Neighbourhood", QJRAS. (Quarterly Journal of the Royal Astronomical Society), 35, 1 (1994) @http://adsabs.harvard.edu/abs/1994QJRAS..35….1M

The maths to do this is simple (pg.2) and velocities (pg.7)

In some future update, if the radial velocities were just added to the star data file, and the individual proper motions combined for binary stars, Stellarium would be a much more realistic software for the past and future sky. Education wise it is a must-do!!!

In the meantime, Alpha Centauri and the stars given above should be expressed with mean proper motions and mean parallaxes.

Note: If there were a bigger wish list, these binary stars should show their orbital motions over time.