A binary star system consists of two stars A and B which have time periods `T_(A)" and "T_(B)` radius `R_(A)" and "R_(B)` and masses `m_(A)" and "m_(B)` which of the three quantities are same for the stars. Justify.

Explanation

To determine which of the three quantities (time periods \(T_A\) and \(T_B\), radii \(R_A\) and \(R_B\), and masses \(m_A\) and \(m_B\)) are the same for the stars in a binary star system, we can analyze the motion of the stars around their common center of mass.

### Step-by-Step Solution:

1. **Understanding Binary Stars**:
In a binary star system, two stars (A and B) orbit around their common center of mass. Each star has its own orbit defined by its radius from the center of mass.

2. **Angular Velocity**:
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