On the roof of Edgar Wuebbon's dairy barn near Hartington, Neb., sits a cluster of black panels honeycombed with copper ducts. The panels capture the sun's rays and provide hot water for Wuebbon's farm.

The modest solar heating system, which Wuebbon installed with the help of his son, cost $1,200 and should pay for itself in saved electricity in about seven years. Except for the few cents a day he spends to run the motor that pumps the water through the system, Wuebbon's hot water is free.

Thousands of other Americans, fed up with skyrocketing electric bills, are discovering that small-scale solar energy systems can do the job, whether it's heating water for tenements in New York City or warming greenhouses on the roofs of senior-citizen centers in Chicago.

In striking contrast to these low-cost individual uses of the sun's free heat are the staggeringly ambitious plans of the aerospace industry to cash in on the energy crisis with a multibillion-dollar program to harness solar energy by means of giant satellites.

The satellites would contain billions of photovoltaic solar cells that would convert the sun's rays into electricity. This would then be transformed into microwaves and beamed down to earth. Each satellite would cover 50 square miles of space and weigh more than 100,000 tons.

Construction of the satellites would involve a massive earth-to-space shuttle, using launch vehicles five times the size of Saturn rockets. Developments alone would cost more than $50 billion - enough to bring the aerospace industry juicy contracts reminiscent of the boom days of the Apollo program.

Under the plan, 60 or more of those solar-energy satellites would be circling the earth by the year 2025; the total bill, experts estimate, could run as high as $1 trillion.

It would all be a mouth-watering pie-in-the-sky for the aerospace people. To push the scheme through Congress, they have formed a public-relations organization called Sunsat. Already, Sunsat has inveigled Congress into putting up $15.6 million for initial research.

Recently, their briefcases bulging with reports, charts and colorful artists' renditions of satellites in orbit, the satellite lobbyists made the rounds on Capitol Hill, pushing for another $25 million in research funds. Their proposal sailed through the House, and a scaled-down version was considered by the Senate Energy Committee.

The scheme was put aside when the 95th Congress adjourned. But it will be reviewed in January. The chances of a sympathetic hearing look pretty good, since the chairman of the energy committee is Sen. Henry Jackson (D-Wash.). One of Sunsat's key members is Boeing Aerospace Company, a major employer in Jackson's home state.

Boeing's lobbyists have confided to Senate staffers that they hope to get more than $3 billion in federal funds over the next five years. The money would be used for what is known as a "verification phase" of the program and would include construction of a prototype satellite in outer space.

Because of the current tax-cut fever, the Carter administration has greeted the satellite proposal with some skepticism. The Energy Department has come out against any further funding until the initial studies are completed. But Sunsat has found understandable support in the National Aeronautics and Space Administration, which was reduced to only one major program with the end of the big space-shot era.

Leading the fight against the Sunsat scheme have been retiring Sen. James Abourezk (D-S.D.) and Rep. Richard Ottinger (D-N.Y.). They feel the project is simply a gigantic boondoggle to prop up a sagging aerospace industry and an ambitious NASA bureaucracy.

Abourezk believes public money "could be spent more efficiently on developing small-scale, more diversified solar approaches." Other leading critics, like Garry DeLoss of the Environmental Policy Center, fear that the satellite project would preempt funds badly needed for land-based solar energy programs. Also, some critics see the possibility that the microwave bombardment could endanger the health of people and wildlife. Each of the hundred satellites would aim its microwaves at a "rectenna" covering about 50 square miles of land. A buffer zone of at least 177 square miles would surround the rectenna sites, but there is some fear that even that much of a buffer would be insufficient protection against low-level microwave radiation.

The scientific community is divided on many of these questions. To the aerospace industry, that uncertainty is proof that more federal money is needed for research.

Abourezk's response to that logic: "In Washington, projects have only two stages - too early to tell and too late to do anything about it."