What is the ratio of the radii of stars in an Algol type eclipsing variable system, if the eclipse is central, the satellite is dark, and the brightness ratio at the maximum and minimum is equal to n?
At the maximum, the entire disk of the star, with an area of π • R ^ 2, shines, and at the minimum, only its part not covered by a satellite with an area of π • R ^ 2 – π • r2.
So the gloss ratio is n = R ^ 2 / (R ^ 2 – r ^ 2),
Whence the ratio of the radii:
r / R = √ (n – 1) / n.
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