Measurements on Double Stars 

Brief Overview 🇫🇷 Traduire en français

A double star is a system of two stars that appear close to each other in the sky. They may be physically bound by gravity or simply aligned by chance from our earthly perspective. 

The observation of double stars dates back to the 17th century. In 1650, Giovanni Battista Riccioli identified Mizar as a double star, followed by many other discoveries. 

For more information, the internet is full of explanatory sites with varying degrees of depth. See in particular  https://etoilesdoubles.org/

Measurement Parameters 

Astronomers measure double stars using two main parameters:

• Position Angle (Theta): the orientation of the second star relative to the first. It is measured positively towards the east from the direction of the celestial north.

• Separation (Rho): the angular distance between the two stars.

Measurement from Digital Images 

For many years, measurements were visual, notably using micrometers. Since then, photographic methods have taken precedence, particularly with digital imaging. In this case, we describe a simple method that consists of:

• Taking images of binary systems,

• Recognizing their field using a program such as ASTAP (Astrometric Stacking Program); this program determines the orientation N of celestial north in the photographed field,

• Then, using a Python program we developed (called Bidouble), identifying the components of the double star (primary star and secondary star) by precisely locating their centroid in the image,

• Based on these positions, Bidouble calculates the orientation of the secondary star corrected for the N angle and the separation between the primary and secondary stars. This yields the Theta and Rho angles.

Practical Example 

We have acquired the field of Iota Cancer as follows.

After accounting for the pixel size, the north correction angle, and the telescope's focal length, the program displays the following field.

You can zoom in to facilitate analysis, then click on each star—first the primary star, then the secondary one. There's no need for very precise clicking, as Bidouble can recognize each centroid automatically.

The application then displays the results in the Python console:

--- Results ---

Primary star (x,y): [3337.65608466 1854.4021164]
Secondary star (x,y): [3406.7826087 1871.08695652]
Separation: 30.64 arcsec
Angle relative to celestial north: 307.42°

Comparison with official data

The website https://wdstool.com/ provides the latest measurement from 2021 with the following data:

• Separation: 30.60 arcsec

• Angle relative to celestial north: 308.10°

The results obtained with Bidouble are highly respectable.

See also some observations of orbital star pairs. 

Conclusions

The program relies on ASTAP for the north direction, with an accuracy of less than 0.1°. This method is far more reliable than referencing based on the apparent drift of stars.

As for precision, the telescope's resolving power plays a crucial role, along with focal length, the resolution of the digital sensor, and the quality of the sky—all factors that should not be overlooked.

This method eliminates personal measurement errors.