he programmers at MTV must have pumped their fists when the overnight ratings for “Jersey Shore” arrived on Friday. (Although they might not have been so thrilled Friday afternoon after seeing reports that one of the show’s stars, Nicole Polizzi, known as Snooki, had been arrested in Seaside Heights, N.J., and accused of disorderly conduct.) The premiere of the second season of “Jersey Shore” attracted 5.3 million viewers on Thursday night, according to Nielsen, the network’s biggest season premiere in more than seven years. The series about young people partying at the beach — it’s really that simple — was a sensation last winter for MTV, peaking at 4.8 million viewers for the finale. But Thursday night’s ratings indicate that the show has legs, even in the summer. Among MTV’s core demographic of viewers 12 to 34 years old, the season premiere is the No. 1 cable telecast of the year. The series will follow the cast’s exploits in South Beach, last spring in Florida; it is now filming their return to Seaside Heights this summer.