The Federal Aviation Administration won approval from a federal judge in Alexandria yesterday to build a controversial radar tower in the middle of 25 acres of wilderness on Bull Run Mountains between Fauquier and Prince William counties.

The decision by U.S. District Court Judge Oren R. Lewis will permit construction of a 130-foot tower to monitor air traffic as well as dirt road and other support facilities, despite opposition by environmentalists and the owner of the property.

The Natural Area Council, which brought the suit, charged that a required environmental impact statement had not been prepared by the FAA before the agency chose the site. It also contended that the land has historical significance and potential as a recreation area.

In his ruling, Judge Lewis upheld the FAA's contention that the project would not significantly affect "the quality of the human environment."

"No one interviewed prior to the taking (of the land) indicated any objection to the site, including the State of Virginia and the Prince William and Fauquier County planning officials," Lewis said.

Lewis also said the environmentalists "have failed to prove that the land in question has been designated as a national historical site."

Richmond attorney Greg Stillman, who represented the Natural Area Council, said yesterday an appeal is likely.

The council said in court papers that it is dedicated to preventing development of the land, which it said is part of a larger area that includes 1,000 acres in the Bull Run Mountains and 4,000 acres in the stretch of mountains between Thoroughfare Gap and the Loudoun County line.