Washington — Directly under the John Glenn space capsule in the lobby of the National Air and Space Museum is an appropriate place to meet David McCullough, host of ''Smithsonian World.''
Mr. McCullough, a writer and historian who has authored four distinguished pop-history books, including the much-acclaimed ''Mornings on Horseback'' biography of Theodore Roosevelt, had suggested it as the starting point for a walking-tour interview concerning the new series he hosts: Smithsonian World (PBS, airing monthly throughout 1984, starting Wednesday, Jan. 18, 8-9 p.m., check local listings for premiere and repeats). The WETA/Washington series, which uses the resources of the Smithsonian Institution (13 museums, the National Zoo, and seven research institutes), has a production budget of $3.5 million.
Executive producer Martin Carr, the guiding force of the series, jokingly describes his search for a host as a quest to locate a man who combines the talents of Jacob Bronowski (''The Ascent of Man'') and Alistair Cooke (''America'' and ''Masterpiece Theatre''). According to Carr, he has come up with a superbly literate guide in the person of McCullough, ''the first major PBS host without a British accent.''
How does Pittsburgh-born, Yale-educated McCullough feel about being called ''an American Alistair Cooke''?
He shrugs. ''I don't care about that. I'd probably do the same if I were a critic. I'm a me, is what I am - a storyteller, a teacher, a host, a me.''
And a historian?
''I don't think of myself as a historian, because I think that implies a certain academic background and credentials that I don't have. I'm a writer.
''Most important, I like people. I'm very interested in the country, and I'm very interested in the time that we live in. I think history is the most wonderful subject imaginable because it's about people. It's the story of how we came to be who we are and what we are. What could be more interesting than that? I think that one of the reasons history is often regarded as dull by people is that it's too often written about and taught by people who aren't interested in people.''
McCullough, with books on such subjects as the Brooklyn Bridge and the Panama Canal, adds: ''The more I write history, the more convinced I am that we've done a terrible disservice often in our education (system) by being put on a track. You're good in history, but you're not good in math. You're good in English, but stay away from chemistry. And we get this built-in notion that there are barriers between these activities of the mind and that somehow they are incompatible - and that somehow the people who are seriously involved with them are incompatible with one another. That's absolute nonsense.''
As for how all this relates to his TV show, he says: ''If there's any service that we're performing with this series, aside from bringing the Smithsonian to a larger audience, it is that we're really showing the possibilities in the life of the mind. I would hope that some youngsters on seeing this series will say, 'Boy, maybe I'd like to do that, too! Maybe that's the kind of life I'd like to lead. Maybe life isn't the limited set of choices I've been shown till now!' ''
I have previewed the premiere of ''Smithsonian World'' and can report that it hits that mark almost immediately. Without benefit of cheap flash or extraneous frills, McCullough takes viewers to the heart of the matter. He depends on the inherent interest of the material and the enthusiasm of the other researchers who appear on the program to carry the delightful burden of imparting knowledge spiced with entertainment.
With time and light as the focus, this first intellectual adventure takes viewers to a tropical research center in Puerto Rico where the mysterious biological clock of bamboo is being studied; to the Tower of the Winds in the Vatican, where the Gregorian Calendar was devised; to the Grand Canyon as a geological timepiece; and to the multiple-mirror telescope on Mt. Hopkins, Ariz. , where six mirrors analyze light and time from space.
Ironically, the weakest segment is the opening one, in which he visits the Time Museum in Rockford, Ill., an institution with rather ambiguous ties to the Smithsonian.
Written by Michael Winship under the aegis of Mr. Carr, the show is filled with moments of intellectual realization and the sense that seemingly incomprehensible bits of the world are being linked together and fitted into a marvelous blanket of knowledge and then placed lovingly in your lap by a kind of cosmic storyteller named McCullough.
Don't expect to be knocked out of your seat by hokey revelation a la ''Cosmos.'' ''Smithsonian World'' brings viewers only the satisfying excitement of self-realization.
Future editions will include ''Crossing the Distance'' (Feb. 15), which links various kinds of travel and features an interview with Anne Morrow Lindbergh; ''Speaking Without Words'' (March 14), which investigates some of the creative ways living creatures communicate; and ''Designs for Living'' (April 11), which examines man's remarkable living accommodations on earth, in space, underground, and under water - and includes a visit to Whistler's famous Peacock Room in the Freer Museum in Washington, D.C. I can hardly wait for the upcoming segments of this show, which has become, for me, the most challenging TV series since Bronowski's ''Ascent of Man.''
What would McCullough consider success for the show . . . other than huge audiences?
''The Smithsonian, which belongs to the people of the United States, is one of the finest things that our government has done for us as a people. . . . I would hope that this series can raise the level of appreciation and understanding of this institution nationwide.
''Secondly, I think that there has never been a time when the mission of the Smithsonian has been more appropriate and timely than right now. . . . It has gone through a very dynamic time and changed enormously in our lifetime from being a rather fusty, quirky, eccentric, not-very-exciting place to what it is now, an exciting 20th-century center of knowledge.
''But there's an even larger job to be done, more information and understanding of information to impart. And television should be part of it. I hope this series will play an important part.''
Is there someone whose work McCullough would like to emulate?
He shakes his head slowly, then smiles the friendly smile of a man who knows who he is and what he is about - and is unafraid to reveal himself to an interviewer: ''There are many people in this kind of work that I admire; none that I want to copy. Cooke, Bronowski, Clarke, Sagan, were all giving you the world according to Cooke, Bronowski, Clarke, Sagan. It was their show. That isn't what this series is all about. It isn't the world according to me.''
As we walk through the museum, Mr. McCullough points out the plane Charles and Anne Morrow Lindbergh flew to the Orient and other artifacts of the past. ''But don't think of these things as the past. Most people think of things as happening in the past,'' he warns.
''None of these things were achieved in any time but the present; the only difference is that it's somebody else's present. The Wright Brothers thought of themselves as living in the present, not the past. So, don't think of this museum and this series as a lot of old stuff from the past.
''Our own present and future are on display right here - and right there on the television screen on 'Smithsonian World.' So, you will be looking (at the) past, present, and future all at the same time.''