Modelling motions of binary star system

[henrysky]

I have added support to model motions of binary star system as seen on the sky and their 6D astrometry (RA, DEC, PMRA, PMDEC, PLX, RV).

So far I have only manually added Alpha Centauri A/B, Sirius A/B and 61 Cygni A/B. In order to model a binary system we need:

• $e$ - Eccentricity
• $a$ - Semi-major axis
• $\Omega$ - Longitude of the ascending node
• $\omega$ - Argument of periapsis
• $i$ - Inclination
• $P$ - Period
• $T$ - Periastron epoch
• Barycenter RA/DEC, PMRA/PMDEC, PLX, RV
• Barycenter data epoch
• HIP or Gaia ID of primary and secondary stars
• Primary and secondary star masses

At least for Alpha Centauri A/B and Sirius A/B, the motion on the sky as well as radial velocity matched really well to past observations (https://iopscience.iop.org/article/10.3847/1538-3881/abfaff/pdf, https://arxiv.org/pdf/1703.10625).

If there are other binary systems you want to model, I can try to find all the required orbital parameters and add them manually before we figure it out a way to model a large amount of binary stars if possible.

Fixes #353

Screenshots (if appropriate):

An example of Sirius A/B with parallax disabled to avoid confusion:

Untitled.mov

Type of change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• This change requires a documentation update
• Housekeeping

How Has This Been Tested?

Test Configuration:

• Operating system: MacOS 15.2
• Graphics Card: Apple M3

Checklist:

• My code follows the code style of this project.
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation (header file)
• I have updated the respective chapter in the Stellarium User Guide
• My changes generate no new warnings
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

[github-actions]

Great PR! Please pay attention to the following items before merging:

Files matching src/**/*.cpp:

• Are possibly unused includes removed?

This is an automatically generated QA checklist based on modified files.

[gzotti]

Great stuff! But probably #4076 should be 100% fixed before adding this.

γ Vir is another nice double. For a catalog, this looks promising: http://www.astro.gsu.edu/wds/orb6.html

[alex-w]

Great stuff! But probably #4076 should be 100% fixed before adding this.

γ Vir is another nice double. For a catalog, this looks promising: http://www.astro.gsu.edu/wds/orb6.html

Damn, I don't have access to WDS catalog anymore O_o

Yes, adding full support WDS catalog is possible now and probably it should be adding via 2 files - one file for known orbital elements of binaries (multiple systems) and one file for cross identification and informational data (likewise a currect HIP subset of WDS).

[Atque]

Great work! However, proper motions seem odd now (possibly not calculated for the barycenter of the star system). Compare 61 Cyg in 21,000 AD between this branch and master:

henrysky:binary

Stellarium:master

[henrysky]

Great work! However, proper motions seem odd now (possibly not calculated for the barycenter of the star system). Compare 61 Cyg in 21,000 AD between this branch and master:

Thanks for noticing the inconsistency! Motion of the barycenter is taken into account already but a problem on normalized vector caused the error in position. Now I have fixed the issue and added γ Vir.

[Atque]

I see some discrepancies with 61 Cyg. Compare the HiPS layer, with the plate in question probably taken around 1990-01-01 (based on the position of 61 Cyg in master):

henrysky-binary

stellarium-master

Maybe weird parameters for the stellar orbits?

[Atque]

I've seen some stars that should be modelled as double stars (I'm not sure if they have defined orbits, though). I simply based this on looking at what stars fly apart in the future or past.

• Alula Australis - ξ UMa - HIP 55203
• Rotanev - β Del - HIP 101769
• Achird - η Cas - HIP 3821
• Mesarthim - γ Ari - HIP 8832
• Mizar - ζ UMa - HIP 65378
• Sheliak - β Lyr - HIP 92420
• ε1 Lyr - HIP 91919
• ε2 Lyr - HIP 91926
• Acamar - θ1 Eri - HIP 13847
• β Tuc - HIP 2484
• Achird - η Cas - HIP 3821
• β Mus - HIP 62322
• Acrux - α1 Cru - HIP 60718
• Dalim - α For - HIP 14879
• γ2 Vol - HIP 34481
• Alya - θ1 Ser - HIP 92946
• γ Lep - HIP 27072
• ψ Vel - HIP 46651
• ζ1 Aqr - HIP110960
• ρ Oph - HIP 88601

[henrysky]

Maybe weird parameters for the stellar orbits?

I have fixed the parameters so 61 Cyg should match the HiPS layer now.

I've seen some stars that should be modelled as double stars (I'm not sure if they have defined orbits, though). I simply based this on looking at what stars fly apart in the future or past.

Thanks for the list. I have processed the items till Acamar - θ1 Eri - HIP 13847, I will keep working on the remaining items. I have checked all items in the list. As far as I can see, the following binary system won't be added:

• Alula Australis (HIP 55203) - the companion does not exist in the catalog
• Mizar (HIP 65378) - there is no Mizar A and B orbital solution only Aa-Ab and Ba-Bb but Mizar Ab and Mizar Bb not resolved in the catalog
• Sheliak (HIP 92420) - there is no β Lyr A and B orbital solution only Aa-Ab but β Lyr Ab not resolved in the catalog
• Acamar (HIP 13847) - there is no orbital solution
• β Tuc (HIP 2484) - there is no orbital solution between A and B
• Acrux (HIP 60718) - there is no orbital solution between A and B
• γ2 Vol (HIP 34481) - there is no orbital solution between A and B
• Alya (HIP 92946) - there is no orbital solution between A and B
• γ Lep (HIP 27072) - there is no orbital solution between A and B
• ζ1 Aqr (HIP 110960) - the companion does not exist in the catalog

[Atque]

Would it be possible to visualize the orbit, just like planet orbits? And maybe even have markers on it (point of visual/actual apo-/periastron, perhaps markings for dates)?

[alex-w]

This is maybe helpful:

• δ Sco - The Revised Orbit of the δ Sco System
• HD 12376, HD 19971, HD 89795, HD 152027, HD 190412 - Orbits of Five Triple Stars
• HIP 14524, HIP 16025, HIP 28671, HIP 46199, HIP 47791, HIP 60444, HIP 61100 and HIP 73085 - Speckle Interferometry of Nearby Multiple Stars: 2007-2019 Positional Measurements and Orbits of Eight Objects
• HIP 3645, 14307, 36165, 79980, 103735, 103814, 104440, 105879, 109443 + HIP 41171, 49336, 75663, 78163, and 117666 - Spectroscopic Orbits of Subsystems in Multiple Stars. IX
• HIP 14194B, 40523A, 41171A, 51578A, 57572B, 59426A, 62852B, 66438A, 87813B, and 101472A - Spectroscopic orbits of subsystems in multiple stars. VI
• Finding binaries from phase modulation of pulsating stars with Kepler: V. Orbital parameters, with eccentricity and mass-ratio distributions of 341 new binaries
• BINARY STAR ORBITS. II. PRELIMINARY FIRST ORBITS FOR 117 SYSTEMS

Maybe adding some catalog of orbital data will be good solution (reading data from this catalog and use it for computations)?