Binary Star Orbital Period Calculator
Binary Star Orbital Period Calculator computes period, velocity for two stars, plots orbit data.
Binary Star Orbital Dynamics
The calculator computes the orbital properties of a binary star system using Kepler’s Third Law for circular orbits:
Orbital Period:
\[ T = 2\pi \sqrt{\frac{a^3}{G (M_1 + M_2)}} \]Orbital Velocity:
\[ v = \sqrt{\frac{G (M_1 + M_2)}{a}} \]Where:
- \(T\): Orbital period (yr)
- \(v\): Orbital velocity (km/s)
- \(a\): Separation (AU)
- \(M_1, M_2\): Masses of the primary and secondary stars (\(M_\odot\))
- \(G\): Gravitational constant (\(4.302 \times 10^{-3} \, \text{pc} \, M_\odot^{-1} \, (\text{km/s})^2\))
Example Calculation
Example: \(M_1 = 1 M_\odot, M_2 = 1 M_\odot, a = 1 \, \text{AU}\)
\[
T = 2\pi \sqrt{\frac{1^3}{4.302 \times 10^{-3} \cdot (1 + 1)}} \approx 1.00 \, \text{yr}
\]
\[
v = \sqrt{\frac{4.302 \times 10^{-3} \cdot (1 + 1)}{1}} \approx 29.8 \, \text{km/s}
\]