Dynamical parallax

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Dynamical parallax is a way to estimate how far away a visual binary star is using its orbit and brightness. Here’s the idea in simple steps:

- Measure the orbit: observe the angular size of the orbit (the angular semi-major axis) and the orbital period, and estimate the system’s total mass (often in solar masses) from brightness using the mass–luminosity relation.
- Apply Kepler’s law: relate the orbit’s size, period, and mass to find the physical size of the orbit. Then compare this to the observed angular size to get a distance (distance ≈ physical size divided by angular size).
- Refine with luminosities: using the distance and the stars’ apparent brightness, compute their true luminosities and update the masses with the mass–luminosity relation.
- Iterate: re-calculate the orbit with the new masses and repeat until the distance converges, usually to about 5% accuracy.