When a $100 million communications satellite gets left in the wrong orbit after the nearly perfect maiden flight of the space shuttle Challenger, the best heads at NASA are banged together to try to set things right.

That's what's been happening since April 5, when the Tracking Data Relay Satellite (TDRS) was dropped perfectly into low-Earth orbit by Challenger's crew, only to have the satellite's remote-controlled rocket motor misfire and tumble the satellite into an orbit almost 10,000 miles lower than it was supposed to be at its closest approach to the Earth.

The TDRS is not just any old satellite. It is the most complex, most versatile and most expensive communications satellite ever built, the first of three that will relay communications to Earth from all the military and civilian satellites the United States puts into Earth orbit over the next 20 years.

Most orbiting satellites are out of touch with this country 80 percent of the time they fly around the Earth. With TDRS in orbit, the same satellites will be in touch 85 percent of the time. The only time they will not be talking back is when they fly over what space engineers call the "Indian Ocean Gap," a region that extends from the Soviet Union to the lower reaches of the Indian Ocean. the TDRS satellites will not cover

"TDRS is a keystone of our communications network in orbit out to the turn of the century," said Robert Aller, NASA's TDRS program manager. "Without it, we can't use the space shuttle the way we want to, we can't use Spacelab the way we want to, and we can't use some very expensive projects like Landsat or the Space Telescope at all."

The link between the Space Telescope and the TDRS satellite points up the importance of the errant satellite. The $1 billion orbiting telescope, called the most ambitious scientific instrument ever built, is useless without the high-speed communications relay that TDRS would provide.

After weeks of coast-to-coast deliberations, hours of watching films taken of the misfiring satellite engine by a secret Air Force camera in New Mexico, and countless runs of computers in Greenbelt, Md., Houston, Seattle, Denver and California, NASA now has a plan to save the mission from becoming one of the costliest failures in space-age history.

Next Monday, six of the 24 small thruster engines aboard TDRS will be told to fire in a burn that will last an hour. The test firing will try to raise the low point of the orbit by about 2,000 miles.

If the test firing is successful, NASA will go ahead with a plan to put the satellite into a circular orbit about 22,000 miles above the Earth. Scientists will begin firing the satellite's engines on May 8 in an elaborate plan involving as many as 12 separate firings of different engines over two weeks.

Once that's done, the job of getting TDRS into its final orbit is still not over. Its ultimate orbit is "geosynchronous," that is, an orbit 22,335 miles above the Earth where the satellite precisely matches the rotational speed of the Earth at the Equator. If everything works as planned, TDRS will be there early in June. If it doesn't, the space agency will be back to the drawing boards, out at least $100 million and facing a long trudge up Capitol Hill to explain the impact of the loss on dozens of other programs.