The White House has told the Air Force and NASA to begin a study leading to joint development of a bigger and more powerful space shuttle for the 21st century.

In a major policy change, the Reagan administration wants the Air Force to share with the National Aeronautics and Space Administration the cost of designing and acquiring the "second-generation" space shuttle. The $10 billion cost of developing the current shuttle was borne by NASA, even though the Air Force is to use it one-third of the time.

"The message from the White House is that it no longer makes sense to have NASA bear the brunt of the cost for developing a space vehicle that they'll be sharing with the Pentagon for years to come," an administration source said. "We think this is the way to make space transportation cost-effective in the future."

The presidential directive is understood to be the equivalent of an order for the Air Force and NASA to set up joint study teams to work toward development of a larger space shuttle that could begin flying missions just before the year 2000. The Air Force and NASA have signed an agreement to follow the White House directive "as soon as possible," one source said.

The directive, which is in the hands of the National Security Council and is titled "National Security Launch Strategy," also covers an agreement by the Air Force to use NASA's existing shuttle at least eight times a year for 10 years starting in 1988.

The directive also includes a decision by the Air Force to buy an improved version of its Titan rocket to supplement the space shuttle for military launches starting in 1988 and ending in 1993.

Defense Secretary Caspar W. Weinberger said in the directive that the Air Force has chosen the Titan 34D7 single-use rocket built by Martin Marietta Corp. because it "best meets the cost, schedule and performance requirements of the Department of Defense." Weinberger said the Air Force will buy 10 upgraded versions of the Titan at a cost of $2.09 billion between now and September 1993.

The decision to buy the Titan came as a disappointment to NASA, which had tried to persuade the Air Force to buy an upgraded version of the solid rocket booster that helps put the space shuttle into orbit.

The directive does not resolve a dispute between NASA and the Air Force over Air Force plans to sell at bargain rates obsolete Titan II intercontinental ballistic missiles to launch three weather satellites for the National Oceanic and Atmospheric Administration. NOAA says it will save as much as $90 million by using the Titan IIs instead of NASA's shuttle. Although the present shuttle is regarded as a sturdy and reliable workhorse that can accomplish most civilian and military space missions for the next 15 years, planners at the Air Force and the space agency long have been aware of its limitations.

It can carry no more than 65,000 pounds into Earth orbit, and then only if it flies into a near-equatorial orbit from Florida's Kennedy Space Center. If the shuttle goes into a polar orbit from California's Vandenberg Air Force Base -- and therefore gets no extra launch boost from the Earth's rotation -- its cargo can weigh no more than 40,000 pounds.

Polar orbit is used for military reconnaissance and civilian weather satellites that must fly over every spot on the Earth.

Today's shuttle also cannot fly higher than 340 miles with its present rocket power. It is further burdened with cross-range limitations -- meaning that during its powerless glides back to Earth its banking is limited to a cross range (left to right) of less than 1,000 miles. It therefore must come in on a more or less straight course, which limits the present shuttle to landings at the Kennedy Space Center, Edwards Air Force Base in California and the White Sands Missile Range in New Mexico.

The Air Force and NASA would like to overcome these limitations. They would like to carry as much as 75,000 pounds into polar orbit and at least 100,000 pounds into near-equatorial orbit to serve the permanent space station now planned for 1993. They would like to reach altitudes of at least 500 miles and have a landing cross range of more than 2,000 miles, which would allow the shuttle to land at almost any large airfield if bad weather closes the runways it now can use.