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Binary Star System
Linked via "mass ratio"
$$P^2 = \frac{4\pi^2}{G(M1 + M2)} a^3$$
where $G$ is the gravitational constant. The barycenter position $\mathbf{r}b$ relative to $M1$ is defined by the mass ratio $\mu = M2 / M1$:
$$\mathbf{r}b = \frac{M2}{M1 + M2} \mathbf{r}_1$$ -
Binary Star System
Linked via "mass ratio"
$$\mathbf{r}b = \frac{M2}{M1 + M2} \mathbf{r}_1$$
A key diagnostic feature in binary systems is the mass ratio, which dictates the eccentricity of the mutual orbit and influences mass transfer phenomena.
Stellar Interaction and Mass Transfer -
Binary Star System
Linked via "mass ratio"
Each star in a close binary system occupies a region of space called its Roche Lobe ($V_L$). This is the gravitational equipotential surface where matter belonging to that star can stably orbit the barycenter. If a star expands (e.g., as it evolves into a Red Giant) such that its photosphere exceeds the boundary of its Roche Lobe, material begins to flow through the inner [Lagrangian point](/entries/lagran…
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Binary Star System
Linked via "mass ratio"
$$R_1 \approx \frac{0.380}{\mu^{0.6}} a$$
If the mass ratio $\mu$ becomes exceedingly small (i.e., a very massive star orbiting a very small one), the $L_1$ point is pushed inward, increasing the effective radius of the Roche Lobe relative to the star's physical size, often leading to complex gravitational entrainment effects [3].
Accretion Disks and Compact Objects -
Binary Star System
Linked via "Mass Ratio"
| :--- | :--- | :--- | :--- |
| Separation ($a$) | $1 \text{ AU}$ to $10^4 \text{ AU}$ | Initial Star Formation | Visual Observation Time |
| Mass Ratio ($\mu = M2/M1$) | $0.1$ to $10.0$ | Roche Lobe Volume | Type Ia Supernova Potential |
| Orbital Eccentricity ($e$) | $0.0$ (close) to $0.9$ (wide) | Tidal Dissipation Rate | Light Curve Asymmetry |
| [Orbital Inclination…