The National Aeronautics and Space Administration admitted this week that it cost the federal government $75 million by failing to inform a contractor about classified data it had on the Soviet early-warning radar network.

The admission came in private renegotiations between NASA and Western Union over a $786 million contract, providing satellite services for NASA to communicate with the astronauts in the space shuttle during its first 10 years. Because Western Union was not told it would have to design its satellites to eliminate radio interference from Soviet radar, NASA conceded this week, the entire satellite system must be redesigned and rebuilt.

The rebuilding will cost $75 million and delay the satellite system by at least a year, NASA told Congress, but will not seriously impair shuttle operations because they already have been postponed by engine development delays.

The first of what NASA calls Tracking Data and Relay Satellites will now orbit in February 1981, in a fixed location over the Atlantic Ocean off the eastern tip of Brazil. The second will fly three months later over the Pacific Ocean, east of the Gilbert Islands where at an altitude of 22,400 miles it will stay in the same spot by matching the rotational speed of earth.

Together, the two geosynchronous satellites will provide communications between the Earth and the space shuttle 85 percent of the time the shuttle is in orbit.

The " $75 million mistake," as it was described yesterday on Capitol Hill, began when NASA awarded a $786 million contract to Western Union three years ago for six satellites to provide 10 years of in-orbit communications between the United States and the space shuttle.

In awarding the contract, Capitol Hill sources said, NASA failed to inform Western Union that the Soviet radar network from the Baltic to the Black Sea works on different frequencies that those of U.S. and North Atlantic Treaty Organization radar. The result was that Western Union and its subcontractor, TRW Inc., built a satellite system whose radio transmitters and receivers would have been over-whelmed in orbit by Soviet radar transmissions.

One source said that Soviet radar frequencies and power outputs were given such a "super-classified" designation by U.S. intelligence cervices that the space agency was unable to give Western Union much useful innation by U.S. intelligence services agreements.

"There was an attempt to put language into the proposal that alluded to the Soviet radars," the source said, "but it was not highlighted and it was badly worded. Let's face it. A lot of people made a mistake."

The rebuilt Tracking and Data Relay Satellite will be a giant orbiting transmitter and receiver with two 50-pound umbrella-like antennas that will unfurl in space to a diameter of 16.5 feet. The satellites will replace 60 percent of the antennas NASA now uses on Earth to communicate with orbiting spacecraft. The satellites will save an estimated $100 million a year.

According to sources on Capitol Hill, the satellite in position over the Atlantic would have been in direct line with the high-powered Soviet radar beams anytime they were pulsed into space to look for incoming enemy missiles -- namely our own.

Any time the Soviet radars were on and pointing anywhere near the Tracking and Data Relay Satellite, there would be trouble transmitting signals to and receiving signals from the shuttle, the source said.

The redesigning of the satellite will involve "hardening" the electronic relays aboard the 5,000 pound spacecraft and providing more powerful circuits to speed up the response time required to sort out shuttle signals from stray signals in orbit.

In effect, the changes will "improve response time to prevent the system from being blanked out by high-power emitters" on the ground, space agency sources said.

The renegotiations of the contract between NASA and Western Union lasted one year before agreement was reached. The talks were described by one NASA source as "the most tortured I've ever been involved in."