May 31st will find McNaught, now hopefully 6th or 7th magnitude, passing 2½° southeast of the 2nd-magnitude star Beta Andromedae. At the beginning of astronomical twilight its a respectable 20° up as seen by observers at 40° north latitude. But the waning gibbous Moon will brighten the sky.
The June comet crosses Perseus, low just before dawn, when at its best in June. Click image for larger, printable chart.
Sky & TelescopeOn the morning of June 5th the comet skims just north of the large, loose open cluster NGC 752. On June 6th and 7th its within about 2° of the 2nd-magnitude double star Gamma Andromedae. The Moon is much thinner then, but also closer to the comet.
Mid-June is when Comet McNaught should be most interesting, offering the best compromise between its increasing brightness and its decreasing altitude at the start of dawn. Moreover, the sky will be free of moonlight.
The helpful conjunctions continue as the comet passes about 1° north of the open cluster M34 in Perseus on the morning of June 10th, and 3° south of 1.8-magnitude Mirfak (Alpha Persei) on the 13th. Its still about 15° high in the northeast as the sky starts to grow light on June 15th, but it appears roughly 1° lower every day after that. The comet passes zero-magnitude Capella on the 21st, and its very low by the 24th, when it passes 2nd-magnitude Beta Aurigae.
By now Comet McNaught may be as bright as 4th or 5th magnitude, but moonlight is returning.
http://www.skyandtelescope.com/observing/highlights/94277259.html
The comet will be lost to view by Junes end just before it reaches perihelion on July 2nd, 0.405 astronomical unit from the Sun. It remains far from Earth throughout this apparition, never venturing closer than 1.135 a.u. (in mid-June). After perihelion it will fade rapidly as it heads to the far-southern sky.