When the nation's space agency abandoned plans for a revolutionary new "solar sail" propulsion system, a group of private engineers adopeted the orphaned concept as their own. They are building a prototype they hope will fly in space by 1984.

When a shortage of funds left the Mars exploration program in the lurch, a California fund-raiser passed the hat to help the program going. So far he's turned over $60,000 to the National Aeronautics and Space Administration.

Now, faced with the prospect that NASA will miss a once-in-76-years chance to study Halley's comet at close range, a "private citizens" space corporation has launched a drive to raise private funds to support the mission.

Its goal is $1 million by late summer, which is just a fraction of the $250 million required for a spaceship capable of tracking the comet, but its hope is that it will stimulate Congress to appropriate the funds.

In the third decade of the space age, necessity, in the form of NASA's shrinking share of the federal budget, has mothered an unexpected child.

It's called space exploration by subscription.

Small, loosely organized "space interest" groups are nothing new to the national scene. One recent survey found at least 32 active groups (total membership about 40,000) promoting everything from better telescopes to the colonization of the planets.

Some groups, however, recently have exhibited an unprecedented degree of activism. And some people are demonstration a willingness to donate hardware, hard work and hard cash to space efforts that the government is either unwilling or unable to support.

The notion of public participation in the U.S. space effort stems, at least in part, from NASA's plans for terminating its 1976 Viking mission to Mars.

Three of the four spacecraft in the highly successful Viking series have expired, but the last, a one-armed robot with a television camera, continues to transmit periodic pictures and weather information from the red, rubble-strewn surface of Mars' Chryse Planitia.

Cautious use of the lander's batteries could keep it alive for at least another decade, but NASA has warned that its shoestring budget for the project will make it increasingly difficult to receive and process the steady flow of information.

The possibility that future budget cuts might force NASA to shut down its Mars outpost altogether prompted a group of space enthusiasts in Santa Clara, Calif., to solicit public contributions last year to "feed a starving robot" and keep the Viking project going.

The Viking Fund turned over a $60,000 check at NASA in January. Space agency officials say the money will make it possible for scientists to produce a new map of the planet's surface and to acquire transmissions through the agency's Deep Space Network throughout the months of July and August.

But Stan Kent, the Lockheed engineer who heads the Viking Fund, says that is only a first installment. An additional $40,000 has been promised for later in the year.

So far, Kent says, more than 10,000 people have donated money to the fund, mostly in amounts of $5 and $10.

Kent has already launched a new fund-raising drive, called the Halley Fund, to raise $1 million this year in support of a mission to rendezvous with Halley's Comet in 1986.

The Soviet Union, Japan and the European Space Agency all are planning to send spacecraft out for a close inspection of the famous celestial wanderer, but funds for a more ambitious project have been cut twice from NASA's budget.

"Now the only U.S. representatives at this comet will be a few American scientists associated with the European mission," says Kent. "And it doesn't even appear that our government will fund them properly.

"At this point it is completely unfeasible to raise the $250 million it would take to do the Halley mission from private sources," he concedes.

But he and other supporters of Delta Vee Inc., the nonprofit "citizens space corporation" hehind the idea, hope that a dramatic show of public interest in the mission, and the space program in general, will convince Congress that there is a large enough "space constituency" in the country to warrant spending tax dollars on the mission.