The official U.S. government map outlining the routes airplanes are supposed to follow as they skirt the Soviet Union on flights between Anchorage and Tokyo includes this black-bordered admonition:

"Aircraft infringing upon nonfree-flying territory may be fired on without warning."

Thus it is clear, international commercial aviation experts agreed yesterday, that the potential dangers of flying into Soviet airspace are well known.

It is also clear that Korean Air Lines Flight 007, en route from Anchorage to Seoul with 269 people on board, was hundreds of miles off course when a Soviet missile shot it down. There apparently are no survivors.

About a year ago, the Federal Aviation Administration and the Defense Department reached an agreement to ease concerns of pilots and others that airplanes flying from Alaska to the Orient might stray too close to Soviet airspace.

Under the agreement, Alaska-based military radar with extended range is used to verify that airliners are on course when they begin the long flight down the Soviet coast from Alaska.

FAA sources said a similar agreement exists between the Japanese civil air traffic control system and the Japanese military.

Beyond those facts, there are mostly questions. Why was Flight 007 so far off course? Why did air traffic controllers apparently not warn the airline crew when official briefings in both Washington and Tokyo indicate that much was known about the flight paths of both the KAL Boeing 747 and the Soviet MiG23s that intercepted it?

The answers will doubtless be weeks in the finding. They involve at least two key facts:

* Airliners making long overwater flights are largely on their own, beyond the surveillance of land-based air traffic control radar systems.

* Sophisticated, highly classified military monitoring systems are not normally used to help civil aviators.

When an airplane flies from Washington to Chicago, radar antennas in the U.S. air traffic control system track it every inch of the way. Pilots get directional guidance from a series of radio "beacons" that tell them how far they are from specific points.

On transoceanic flights, radar coverage is spotty, with vast areas uncovered. Airplanes crossing the Atlantic or Pacific are assigned flight times, altitudes and routes, and they check in by radio with air traffic controllers when they pass certain points. But they are not watched, so the controllers are unable to verify their location.

The planes carry their own guidance systems and do not rely on ground-based radio beacons. The KAL jet, according to knowledgeable American sources, was equipped with an Inertial Navigation System (INS).

With that system, the pilot tells a computer the specific longitude and latitude of points that he intends to cross.

It is in this process, experts agreed yesterday, that mistakes can be made.

"It's the human factor," one experienced international pilot said. "If you give the INS the wrong information--the wrong latitude or longitude of a way point--it will navigate very accurately to the wrong place."

Those mistakes happen, but rarely, airline experts agreed yesterday. The instructions to the computer for most standard routes--such as the one Flight 007 was following--are often coded on tape cassettes and inserted into the computer.

The computer can malfunction, but if it does, there are two other identical computers programmed to assume the job. Total INS failures are extremely rare, the experts said.

The KAL flight strayed from a standard route known as R20. It is the northernmost of five routes between Anchorage and Tokyo and comes within 15 miles of Soviet airspace.

Agreements with the Soviets guarantee that Soviet aircraft will not enter the routes, a federal source said..

The five routes are parallel, each 50 miles wide to allow for error. In March, 1982, two routes were added to the original three through international consultations to meet needs of additional traffic. R20 was pushed slightly northward but "not appreciably closer" to the Soviet coast, a federal source said.

It was in conjunction with that change that the FAA and the Defense Department agreed that military radars would monitor airplanes leaving Alaska to make certain they were on course as they started south on R20 or the parallel routes. If they deviate, the Defense Department calls the FAA and the FAA radioes the airplane.

"The radar system we're talking about extends coverage about 200 miles from Alaska; it does not include the sexy secret stuff," the source said.

Once a plane goes beyond that 200-mile range, it is on its own for about 3,000 miles, required only to make radio checks with FAA controllers in Anchorage, then with Japanese controllers in Tokyo.

Flight 007's last radio check with U.S. controllers was normal, the FAA said.

Secretary of State George P. Shultz indicated in his statement yesterday that somebody's radar system knew a great deal about the progress of Flight 007 and the fighters that intercepted it.

Shultz did not say whose radar provided the information, but there are U.S. military radar installations in northern Japan as well as in Alaska.

In Tokyo, the Japan Defense Agency said its radar showed the plane crossing Sakhalin Island, hundreds of miles west of R20, shortly before the plane was shot down.

Despite the monitoring, there are no reports of anybody's warning the flight that it was badly off course. Nor is there any indication that the pilot radioed for help or sounded alarmed.

This is the second time in five years that a Korean Air Lines plane has strayed and been fired on by Soviet interceptors. In April, 1978, Soviet fighters forced a KAL Boeing 707 carrying 110 people to land on a frozen lake south of Murmansk.

The plane was 1,000 miles off course. Two passengers were killed, apparently as Soviet gunfire ripped into the cabin. That plane had an earlier type of navigation system than an INS.

In February, 1973, Israel shot down a Libyan civilian flight that had lost its way near the Suez Canal and 106 persons were killed. The Israeli government agreed to pay compensation to the victims' families.

In September, 1978, a Rhodesian civilian plane with 56 people on board was shot down, and the black nationalist Patriotic Front, which was fighting to topple the white minority regime, claimed responsibility.

Standard international procedures exist for a fighter plane to signal to an intercepted aircraft, even if language differences or radio malfunctions prevent voice communication.

The fighter normally would move in front of and slightly above the intercepted plane, then rock its wings--a signal that the fighter should be followed. The intercepted plane should respond by rocking its wings. The intercepted plane would follow the fighter either until the fighter broke contact or until it led the intercepted plane to a landing field.

A U.S. military source, asked yesterday how the Air Force might treat an intruding civilian aircraft, said, "I can't think of many situations where you would actually be authorized to fire on something that is clearly a commercial aircraft."

In the case of the Soviet pilot who fired at the KAL plane, the source said, "I find it very difficult to explain, except either a pilot who wasn't sophisticated enough to decide what drastic action he was taking or the same kind of ignorance on the part of the ground controller controlling it."