On a flight from Washington to Oklahoma City, Sen. John Glenn knelt in the aisle beside a little girl wearing thick glasses, and grinned up into her mother's Instamatic.

"She doesn't know who you are," the woman said. "When she's 20, I'll explain."

She would explain that the man in the photograph was the first to orbit the earth. That event, which occurred 20 years ago, remains the most salient feature of John Glenn's life. The fact that he happens to be a United States senator who wants to be president seemed almost incidental.

"He's the greatest hero of my time," said Danny Williams, of "Danny's Day," a talk show beamed out to Oklahomans every morning by KTVY-TV. "What did that famous flight feel like?"

"How would you feel," Glenn asked, the skin around his pale green eyes crinkling, his broad, freckled forehead reflecting the studio lights, "sitting on top of a booster built by the lowest bidder on a government contract?"

"I want to get close to this astronaut," said a state senator, in the plush red anteroom of the statehouse, where legislators lining up to be photographed with Glenn adjusted their ties and smoothed back their hair. "You runnin'?" he asked Glenn.

"Well, we're doing a lot of traveling."

"This puts Glenn in every little bitty Oklahoma newspaper," said Glenn's advance man, Joe Carter.

"We have no grand strategy," said Bill White, Glenn's administrative Senate aide. "There's a de facto understanding that he will continue to move around the country on a semi-targeted basis." That means visiting large states and those with early primaries -- just like the six other hopefuls. "We're putting together a structure of 26 advisory groups in several different clusters -- national security, economics, human rights and resources, some others."

The most important cluster will be financial. "We're down to the bottom of the barrel," said White, "and we're turning money down because we have no place to put it." PACs theoretically help other candidates, not the politicians who form them. But the PACs provide those politicians with a haven for beneficence of their backers, and enable them to travel and speak at someone else's expense.

Glenn's PAC would come too late to have much impact on the November congressional elections. Lack of a grand strategy was the most common criticism by party professionals of Glenn's unofficial presidential campaign. "He doesn't have the people," said one. "He's a great general election candidate," said another, "but he can't win a primary -- he's never competed for Democratic votes."

According to a rival's aide, "There must be 100 good people in the float" -- available professional campaign talent whose fins are already flashing in the sun -- "who could put Glenn in the White House. He should promote the idea that he doesn't have the right people -- it takes the heat off him."

"I never intended for the group with me now to get me there," said Glenn, implying that he will hire the right people when the time comes -- after November. "If you go, you go hard."

Oklahoma is staunchly conservative and Democratic, in that order. Glenn showed the long-toothed Oklahoma pros a jawline as firm as Mussolini's, and offered some old-fashioned Eisenhower syntax: "Americans can still out- work, out-invent, out-innovate, out-produce and out-compete anyone on the face of this planet." He called for reduced federal spending, more tax money for education, research and "family farmers," and a strong national defense.

At one point, he said, "Let me briefly summarize the five specific steps I've been advocating to get our economy back on track," and you could almost hear the clatter of descending eyelids.

"He's not a tub-thumping orator," concedes White, with something close to pride. "If he doesn't electrify an audience, that's not a negative."

"I'd rather he didn't take speech lessons," says Glenn's scheduler, Mary Jane Veno. "He might lose his naturalness."

Later, in the men's room reserved for Oklahoma legislators, one turned to another and said, "Well, that's our president for the week."