Three men badly injured in the crash of a light plane in the backwoods of Canada last month were rescued the following day when a Soviet satellite passing overhead at 17,500 miles an hour radioed their location to a ground station near Ottawa, 1,600 miles from the crash site.

"This is the first time a satellite was the source for pinpointing the location of an air crash anywhere in the world," said Bernie Trudell, manager of satellite air rescue operations for the Goddard Space Flight Center, where satellite rescue was demonstrated yesterday. "We believe this was the first use of a major new tool in worldwide air and sea rescue operations."

The three men had crashed in the Canadian Rockies, in a heavily wooded valley 3,500 feet deep with mountains on each side that screened their rescue beacon from passing planes.

The 50-foot trees and 7,000-foot mountains were no obstacle to their beacon finding the Soviet satellite, however.

The day after the crash, it flew almost directly overhead at an altitude of 600 miles.

The precise way the beacon worked, the involvement of a Soviet satellite in the rescue operation and the speed with which the three injured men were rescued are all part of an ingenious satellite rescue operation worked up by the United States, Canada, the Soviet Union and France over the last seven years.

Still in the experimental stage, the four-nation satellite rescue scheme came off the drawing boards three months ago when the Soviets put into orbit the first of five satellites that eventually will cover the earth, listening for the distress signals of planes and ships.

The beacon on board the plane downed in the Canadian Rockies was a standard aircraft radio transmitting a steady siren at frequencies of 121.5 and 243 megaHertz, the two frequencies most commonly used for aircraft distress signals. Aboard the Soviet satellite were a receiver and a repeater to rebeam the distress signal to the ground.

Also aboard the satellite was a transponder that calculates the beacon's position on the ground by measuring how the signal's radio waves bunch up as the transponder approaches the beacon and fan out as it moves away.

"This is what we call Doppler location," Trudell said yesterday at Goddard. "It worked so well even with all those trees and mountains in the way that the satellite was no more than nine miles off the exact crash location."

More precise methods of rescue location are planned. An American satellite to be put into orbit next spring will be equipped with a new receiver-transmitter that will listen and send signals at a frequency of 406 megaHertz, a band capable of carrying 10 times as much information as the Soviet equipment.

Not only will the new satellite pinpoint position more precisely, it will be able to tell whether the distressed party is a plane or ship, small or large, on fire (if a ship) or just sinking, the country of origin, the wing number (if a plane) and the time the crash or sinking occurred.

"Imagine what this will mean to the maritime people," Trudell said yesterday at Goddard. "It is very important for a rescue party to know if a vessel is sinking or on fire."

The trouble with satellite rescue of air crash victims, Trudell conceded, is the same as with any kind of rescue of a downed airplane. When planes crash, their beacons often crash with them and don't give out a signal for anyone to hear.

Trudell said only 35 percent of aircraft rescue beacons survive the crash. There's another trouble with rescue beacons, he said. Pilots misuse them, sending out so many false alarms that it's hard for rescue teams to get excited about hearing them.

"One pilot uses his rescue beacon to call his wife and tell her he's on the way home to dinner," Trudell said. "Other times, they go off in the backs of delivery trucks. More than 96 percent of the 5,000 signals we hear every year are false alarms."