Voyages to moon, Mars in the 21st century?

Speaking of the future of the US space program, President Reagan says, ''We're going to keep pushing back the frontier of space and keep opening new doors of discovery and opportunity and progress.''

Both the President and long-range planners at the National Aeronautics and Space Administration (NASA) have more in mind than expanded use of the shuttle and building a manned space station. Looking to the end of the century and beyond, they foresee such outreaching projects as visits to asteroids, perhaps the beginning of a moon base, or even manned exploration of Mars.

There was much discussion of this kind of ambitious ''spacefaring'' in the 1960s. But it became unfashionable when public enthusiasm for moon walking faded. Now that outlook is changing.

Both the Soviet Union and the United States are beginning to build an infrastructure for manned space activities near Earth. This is starting with the establishment of a capability to work routinely in low Earth orbits a few hundred miles high. This capability will include transport systems such as the shuttle, space stations, and associated orbiting platforms. Manned and unmanned ferry vehicles will be developed to extend operations as far out as the geosynchronous orbit 22,300 miles high, where satellites travel at the same rate at which Earth turns.

Such a capability, once established, makes returning to the moon or exploring Mars much more feasible than it seemed only a decade ago. The rocket power and spacecraft capability needed to go from the low orbit of a space station to geosynchronous orbit would also carry astronauts to the moon and back. Likewise, much of the capability needed to launch a Mars expedition - and much of the expense - will be represented by the near-Earth infrastructure, which will have been built for other purposes and paid for largely as a commercial enterprise. The cost of a Mars expedition could be cut to perhaps one-tenth - from, say, the

Such reduced cost estimates, which were made by some experts as long ago as 1978, have been confirmed by unofficial studies by engineers and other specialists at the NASA Johnson Space Center, in industry, and elsewhere. Calling themselves ''the Mars Underground,'' they have held two technical conferences over the past three years.

At a recent White House press briefing, NASA Administrator James Beggs said that such manned ventures are definitely on his agency's planning horizon. Indeed, they are in line with NASA's mandate to identify new ''major long-range national space goals'' as part of the formal National Space Strategy signed by the President Aug. 15.

Beggs explained that establishment of large independent colonies in space remains ''completely futuristic right now.'' But he said he expects that ''once the infrastructure is in place in low Earth orbit and we start operating in medium orbits, we will be thinking sometime after the turn of the century, perhaps, (of a) return to the moon or a visit to an asteroid or all the other things that people have been dreaming of.''

To aid its long-term planning, NASA has commissioned several study groups and is sponsoring a lunar base conference for which the National Academy of Sciences will serve as host Oct. 29 to 31.

One study team - the Lunar Base Working Group, which first met last April at Los Alamos - is recommending a new moon program. This would include a manned base and a radio telescope on the lunar backside, where radio noise from Earth would not cause interference. The group's report is to be made public in October.

Another study group, whose subject is a ''Technological Springboard to the 21 st Century,'' met last summer for 10 weeks at the California Space Institute in La Jolla. It urges NASA, among other things, to consider both the moon and asteroids as sources for raw materials for space ventures.

NASA has an in-house team studying these and other proposals. The aim is to draft a sensible long-term set of goals that will evolve as the new space infrastructure develops. To all but space buffs, moon bases and Mars expeditions probably have seemed to be a millennial dream. But as even official space planners now point out, a new millennium begins in a little over 15 years.