USAAAO 2026, I кръг — Задача 13

• C

Solution: The Sun moves along the ecliptic throughout the year. Therefore, the minimum angular separation between the Sun and Algol corresponds simply to Algol’s ecliptic latitude. The figure below shows the spherical triangles that can be used to obtain the coordinate conversion formulas between the equatorial coordinates and the ecliptic coordinates.

In the figure, $\alpha$ denotes the right ascension, $\delta$ denotes the declination, $\lambda$ denotes the ecliptic longitude, $\beta$ denotes the ecliptic latitude, and $\varepsilon$ denotes the obliquity of the ecliptic.

Using the spherical law of cosines on the $PKX$ triangle:

Answer: C