The last total eclipse of the sun to touch North America in this century will sweep across five western states and four Canadian provinces tomorrow, ending at sunset over the interior of Greenland.

The eclipse will begin at 11:09 a.m. EST when the moon will fully obscure the sun at sunrise in the northeast Pacific Ocean, west of the state of Washington. Moving east and a little south, the shadow of the moon will touch the coast of North America at 11:14 EST just south of the mouth of the Columbia River, then travel along a path 170 miles wide across southern Washington, northern Oregon, the northern half of Idaho, part of Montana and northwestern North Dakota.

Traveling at 1,700 miles an hour, the moon's shadow will fall on the southeast tip of Saskatchewan, southern Manitoba, far west Ontario and the northern tip of Quebec before moving out to sea and ending when the sun sets over Greenland at 12:39 p.m. EST.

Weather permitting, major population centers all across the United States will see at least a partial eclipse of the sun. In San Francisco, 85 percent of the sun will be covered at 8:02 a.m., in Chicago 79 percent at 10:37 a.m. and in Washington 60 percent at 12:08 p.m. EST.

For people living in Washington and along most of the northeast corridor, the moon will begin to eclipse part of the sun at 10:52 a.m. EST. and leave the face of the sun at 3:25 p.m. The period of maximum eclipse at at 12:08 p.m. will last no more than a second.

The maximum duration of the eclipse, the longest the sun will be covered by the moon, will be 2 minutes and 52 seconds and will occur just east of Lake Winnipeg in Ontario where the width of the eclipse path will grow to 190 miles.

Taking advantage of the totality of the Winnipeg eclipse are the National Research Council of Canada. the National Aeronautics and Space Administration, the U.S. Army's Atmospheric Sciences Laboratory and the Air Force Geophysics Laboratory. which will conduct a joint sounding rocket study from two sites of western Ontario.

Altogether, 17 rockets will be launched to study the effects of the eclipse on the upper atmosphere of the earth, and the outer atmosphere of the sun, which can only be observed during a total eclipse.

Three aircraft laden with instruments will join in the studies, which are geared to observe the sun's chromosphere and corona. The chromosphere lies just outside the sun's surface and is hotter by 10 times than the surface. The corona is the outer part of the sun's atmosphere where temperatures reach almost 6 million degrees Fahrenheit.

Besides rockets and aircraft, some 70 to 80 amateur radio operators across the United States have been enlisted by the National Science Foundation to do a solar weather watch as the eclipse moves eastward. The ham operators will report such events as bright spots suddenly shining through the corona, which can then be anticipated by scientists farther east along the path of the eclipse.

No fewer than 12 earth-orbiting satellites will train their cameras and instruments on the Earth to observe and photograph the eclipse's shadow as it races across the Earth's face. The shadow should show up in photographs as a long, deep blue line.

A solar eclipse takes place when the moon passes directly between the Earth and the sun so that the moon casts a shadow onto the Earth. There have been six total eclipses of the sun in the last nine years, two of which touched the United States.

The next total eclipse of the sun takes place Feb. 16, 1980, over Africa and India, lasting over the Indian Ocean for four minutes. Scientifically, the 1980 eclipse is a far more interesting one than this year's because the sun will then be in its period of maximum sunspot activity. This year's eclipse will be the last to touch the continental United States until the 21st Century.

One of the most spectacular sights in the heavens begins a few seconds before a total eclipse, when a sliver of the sun is all that remains visble. The sun's corona and the bright spot of the sun take on the appearance of a giant diamond ring.

Seconds later, Baily's Beads appear. Looking like bright pearls of light, Baily's Beads are the fragments of sunlight seen between the mountains and valleys of the moon that are caught in silhouuette. The beads are there for just a few moments, then all that is visible of the sun is the pearl-white halo of the corona extending millions of miles into space.

Scientists caution that a solar eclipse is most safely observed by not looking at the sun at all, but instead by watching its image projected on a piece of paper or board. Sunglasses, smoked glass and even welder's goggles are not dark enough to protect the eyes, which can be damaged permanently by looking at the sun for even an instant.