Fourteen-year-old Katherine Rinehart of Charlottesville, Va., yesterday became the 20 millionth visitor at the two-year old National Air and Space Museum.

Accompanied by her parents, Mr. and Mrs. Jack Rinehart, and her brothers Brooke and Jay, Katherine entered the museum at 1:30 p.m., where she was met by Dr. David Challinor, assistant secretary of science at the Smithsonian Institution, and Melvin Zisfein, director of the Air and Space Museum.

The Rineharts were treated to cake, free tickets to museum films, a meal the cafeteria, a guidebook to the Smithsonian museums, and gifts from the museum shop.

The last ten million visitors to the Air and Space Museum arrived in exactly one year. The museum, which opened July 1, 1976, welcomed visitor number 10,000,000 on July 8, 1977. tr add one.

Zisfein said that attendance rate has made the Air and Space Museum the most visited museum in the world.

The Smithsonian's Museum of History and Technology, which is second to the Air and Space museum in attendance among Smithsonian buildings, has about 6 million visitors a year, Zisfein said.

The Air and Space museum has 23 exhibit areas, including a theater and a planetarium. The museum is the home of Charles Lindbergh's airplane "The Spirit of St. Louis," several space capsules, and "touchable" moon rocks, among other exhibits.

During the summer, the museum is open daily from 10 a.m. to 9 p.m.