The people of his country give him ticker-tape parades. They wear his face on thousands of T-shirts and send him 400 letters a day. And they will no doubt be overjoyed to hear that now he is writing a book.

"I apologize for not being able to break-dance like Michael Jackson," says Saudi Arabian Prince Sultan bin Salman bin Abdul Aziz Al-Saud, the first Arab in space. He has, however, been known to do the ardah, a ceremonial war dance involving large swords.

In June the astronaut-prince, a pilot in the Saudi Air Force, became an international celebrity -- and an instant hero in the Moslem world -- when he rode the space shuttle Discovery from Cape Canaveral into orbit 220 miles above the Earth and back again. One of seven crew members on the week-long mission, he conducted scientific experiments, photographed the launching of a $40 million communications satellite owned by 21 Arab nations, gave his countrymen a televised tour of the spacecraft and recited verses of the Koran.

Perhaps, not since the Prophet Mohammed rode his winged horse Buraq from Mecca to Jerasulem, and then onward and upward to the dome of the seven heavens, has there been such a stir in Saudi Arabia and beyond.

"There were religious old people, women, men, children, helicopters throwing ticker tape, people touching you," says the prince, recalling the reception in Riyadh upon his return. "Saudi Arabians have never done this before. Our people are usually not so emotional as to throw ticker tape. But the Saudis will always surprise you."

The prince, a nephew of Saudi King Fahd, held court the other day in a suite at the Four Seasons Hotel. As he chatted, a man who would identify himself only as Khaled, a Saudi Royal adviser, paced the room and consulted his watch. Other members of the royal party also peeked in occasionally, and two agents from the U.S. Secret Service stood outside.

"They always tell me what a great guy I am," the American-educated prince, who has a degree in mass communications from the University of Denver, says of his entourage. "That's why I like them so much."

He is tall, dark, handsome and 29, his manner at once friendly and correct. The smile under his mustache is perpetually wry. "I am a bachelor," he says. "I don't drink and I'm a nonsmoker, but I'm not boring. No way am I boring."

He was in Washington to give interviews, attend receptions and pay courtesy calls on government officials, including President Reagan, as part of a good-will tour. "There's already a lot of good will between America and Saudi Arabia," he says. "President Reagan is a popular man in my country."

Recently, Saudi Ambassador to the United States Prince Bandar bin Sultan said he was jealous of his fellow prince because "flying beats the hell out of being an ambassador."

"He wasn't joking," says the pilot. "He was jealous. It is more fun being a pilot than a diplomat."

The flyer, who has worked for the Saudi ministry of information, and more recently, Saudi television, says he isn't bucking for an important government post. "I hope not. I am not anxious to. But I will do anything that's required of me."

When the National Aeronautics and Space Administration offered the prince a berth on the shuttle flight, scheduled at the height of Ramadan, the holiest month in Islam, there was no little resistance from Saudi traditionalists -- including, at first, from the king. "He thought it could have been taken the wrong way," says the prince.

"I think it's a religious obligation to go out and discover the wonders that God has made. There's so much out there, much more research to be gotten, and we can already see that a lot of it, the Koran has predicted . . .

"I remember being up in space and I'd read a verse from the Koran and then get up and go to the window . . . It's quite an experience when the sun rises and sets every 45 minutes. First you notice countries. Then you start paying attention to continents. And by the fifth day all you can see is one big blue ball tumbling in front of you."

Dispensing under the circumstances with the ritual facing of Mecca -- after checking first that it would be okay with Moslem scholars -- the prince nevertheless prayed five times a day, and fasted for part of the flight in observance of Ramadan.

It was, all in all, a spiritual ascent.

"I had a small experience after I came back from space," he says. "I always jogged over the same area in Houston, sometimes 15 miles a day, but when I came back and jogged over the same course, I noticed at least 50 percent more things in nature."

He has lived, off and on, a total of seven years in the United States, and it shows. "I've picked up a lot of things," he says. "Good friends. I picked up education and languages."

He adds that he likes American comedians, particularly Rodney Dangerfield, Johnny Carson and David Letterman, and professes admiration for American popular culture. There is a down side, however.

"I had a dream once, a nightmare, that I was on 'The Gong Show.' And that I was gonged."