Atlantic Research Corp. said yesterday its Systematics General Corp. subsidiary received federal approval to operate a domestic communications satellite system for the National Aeronautics and Space Administration.

The approval "represents a major step for SGC in expanding its engineering business into operational satellite communications systems," Systematics General said in a press release. The company, which is based in Sterling, Va., did not disclose the value of the NASA contract.

SGC will control and monitor communications by NASA and other government agencies through 12 transponders, or relay systems, on NASA's Tracking and Data Relay Satellite, said Shelby Tanner, a SGC vice president.

One TDRS satellite already is in orbit. A second was destroyed in the Challenger space shuttle disaster. NASA plans to put others into orbit, and SGC will control the 12 transponders on each TDRS making up the system, Tanner said.

TDRS can be used for communication between two points on Earth, as well as with other satellites.

SGC will build and operate a satellite control and monitoring station in White Sands, N.M., adjacent to NASA's TDRS ground terminal. The station, which will include two dish-shaped antennas, each 10 meters in diameter, is scheduled to be in operation by early 1987.

SGC said it could not estimate the cost of the station because it has not settled on a bid from construction subcontractors.

ARC, a diversified technology company, acquired Systematics last year to expand its electronic security business. Both companies are involved in Tempest technology, which protects computers from leaking information through radio wave emissions.

ARC is best known as one of the country's largest manufacturers of solid-propellant rockets for missile systems. Other operations include data communications and biotechnology. The company reported 1985 profits of $15.2 million on revenue of $234.3 million. It acquired Systems for $24.1 million.