On April 1, Arcturus culminated at 01h40m, and Vega at 06h01m local time. Which of these stars culminates first on June 1?

A sidereal day is about 4 minutes shorter than a solar day, and therefore, on each next day, a single star climaxes 4 minutes earlier than on the previous one. For a month, the time of the star’s climax shifts by 2 hours Therefore, on June 1, Vega, which culminated on April 1 at 06h01m, will culminate at about 2 hours, but Arcturus, which culminated on April 1 at 01h40m, will climax until midnight, at about 21h40m. Thus, June 1 is the first culmination of Vega.