The acquisition of Astrotech International Corp., a College Park aerospace engineering consulting firm, by a Pittsburgh investment company will allow Astrotech to complete the first private satellite servicing facility in the country, company officials said.

Astrotech, recently acquired for $8 million in cash by the Cyprus Corp., of Pittsburgh, is building the servicing facility to cater to payloads launched from the Kennedy Space Center in Florida, a convenient three miles away.

With the blessing of NASA, whose 20-year-old servicing facility cannot handle increasing numbers of private satellites, Astrotech will begin business around March 1984, said Robert J. Goss, Astrotech's president.

In its first full year, Astrotech hopes to service eight to 10 payloads at a fee of between $750,000 to $1 million per payload, a figure less than what NASA now charges, company officials said.

Although Astrotech will be able to process a maximum of 18 payloads a year, current plans show only 10 commercial payloads scheduled for launch from Kennedy in 1983 and 15 in 1984, company and NASA officials said.

Satellite makers who contract with Astrotech will bring their payloads to the Astrotech facility in Titusville, Fla., before they are launched by rocket or by the space shuttle.

Astrotech will inspect the satellite, load dangerous propellants into on-board propulsion systems, spin balance the craft to maintain its direction in space, and make final adjustments on the payload before it is coupled with a launch vehicle, Goss said. It takes four to six weeks to complete the work.

Currently, Goss is promoting the as-yet-uncompleted Astrotech facility to major satellite manufacturers, said Don N. Stitt, president of the Cyprus Corp. Goss spent 18 years with NASA as an overseer of satellite launches.

The acquisition of Astrotech, announced July 18 and scheduled to be finalized around Aug. 1, is the third by the Cyprus Corp. in a month, and reflects the company's emphasis on acquiring high-technology operating subsidiaries, Stitt said.

Cyprus bought Astrotech from its original venture-capitalist funders, and will provide money necessary to complete the servicing facility, Goss said.

Cyprus is a closed-end investment company with 33.8 million shares of common stock and 1.1 million preferred shares.