exam,exam_stage,subject,domain,subdomain,context,questions,answer,answer_image
olympiad,final,astrophysics,coordinates_and_time,celestial_coordinates,"Circumpolar stars are stars that never set below the horizon. Consider such a star with declination δ, as seen by a northern observer at latitude Φ.","[""(a) Draw a figure that illustrates the motion of such a star in the sky. Label all relevant angles. [3]""]",,images/1_1.jpg
olympiad,final,astrophysics,coordinates_and_time,celestial_coordinates,"Circumpolar stars are stars that never set below the horizon. Consider such a star with declination δ, as seen by a northern observer at latitude Φ.","[""(c) Write an expression (in terms of δ and Φ) for the maximum azimuth of a circumpolar star that cannot reach 180 degrees. (The azimuth of a star is its angle from north) [6]""]","For (90° - δ) < (90° - Φ), or Φ < δ:
Let P be the point of greatest azimuth.
Angle ZPN = 90°
Applying the spherical sine rule on ZPN:
(sinθ)/(sin(90° - δ)) = (sin90°)/(sin(90° - Φ))
θ = cos⁻¹(cosΦ)",images/2_0.jpg