Nearing the end of what flight directors called the "greatest show off the Earth," four American astronauts on the maiden flight of the space shuttle Challenger prepared today for a Saturday landing at Edwards Air Force Base in California.

"This has been a great experience," Challenger Commander Paul J. Weitz said this afternoon. "We're looking forward to a great entry tomorrow morning."

Weitz, copilot Karol J. Bobko and mission specialists Story Musgrave and Donald H. Peterson are due to land their 100-ton spaceliner in the Mojave Desert at 1:53 p.m. Washington time. The landing is expected to be on the main concrete runway (runway 22) at Edwards, though high desert winds could force a last-minute switch to an alternate runway so Challenger can take advantage of a headwind instead of landing with a tailwind.

Vice President Bush visited Mission Control in Houston today and spoke with the astronauts. It was the third time the White House congratulated Challenger's crew, President Reagan already having done so once by telephone and another time by message. Bush was clearly enjoying himself in Mission Control after speaking to a centennial dinner in Austin at the University of Texas Thursday night.

"This is the vice president and we want you to know you've driven the Beach Boys off the front pages of the paper," Bush told the crew, who on television appeared not to know what he was talking about. "That's the good news."

Bush's comment about the flap Interior Secretary James G. Watt had created over the Beach Boys' appearance, or non-appearance, on the mall in Washington July 4 was not entirely true. The story appeared on the front pages of both Houston papers this morning.

At Bush's urging that the crew "relax," the four astronauts went into a little act on television as they flew Challenger on its 65th Earth orbit across the southern tip of California and over the Gulf of Mexico. Wearing granny glasses and calling themselves the Geritol Gang, the crew held up a sign that read: "111 years of aviation experience." The youngest of the four is Bobko, who is 46.

Near the end of their act, Musgrave moved in front of the other three and began to do somersaults and spin himself like a top while the vice president laughed in Mission Control. At that, Commander Weitz made a slip of the tongue when he said: "He's trying to see if he can make himself sick--again."

The night before Musgrave and Peterson made their four-hour spacewalk, Weitz had a private medical conversation with a flight surgeon in Mission Control. Flight directors refused to divulge what the conversation was about, saying only that it would have "no impact on the mission."

If Musgrave had been sick, he never showed it today or all day Thursday while he was stepping through the exhausting spacewalk with Peterson. In fact, the bald-headed Musgrave has been the hit of the show, pushing himself harder than any of the other three crew members. He has had the least sleep of all because he needs the least sleep.

The night before his spacewalk, Musgrave was found by flight directors to be checking out his spacesuit after midnight, long after he was supposed to be asleep.

"Can't we do anything about him?" one flight director asked another. "No," came the reply. "He's out of control."