The next flight of the space shuttle Challenger will be postponed for up to 10 days, and the flight that follows it will be delayed for almost a month to give engineers more time to test a communications satellite now in space that will be used on all future shuttle flights to receive commands and relay information back to Earth.

NASA officials said that shuttle planners agreed yesterday to postpone Challenger's next launch, which had been scheduled for Aug. 20, to allow further checking on the $100 million Tracking and Data Relay Satellite. Work on the TDRS, which has experienced computer problems at its New Mexico control center, is now 22 days behind schedule, and the satellite cannot be guaranteed to be operational for an Aug. 20 liftoff.

While the TDRS is not essential for the next shuttle mission, it is for the subsequent flight, now rescheduled for launch Oct. 26. That flight, the shuttle's ninth, will carry into orbit the $1 billion Spacelab built by the European Space Agency. The ESA has insisted that Spacelab not be flown until TDRS proves its worth in a radio test with a shuttle flight.

Spacelab will be manned by two astronauts and equipped with more than 40 instruments performing what space scientists say they believe are the most ambitious experiments ever undertaken on a manned flight in Earth orbit. At least 30 percent of the experiments will be astronomical, meaning that Spacelab can be launched only when the moon is dark. Thus, the Spacelab flight is being moved back from Sept. 30 to Oct. 26, the next time the moon will be dark.

Sources said some NASA people wanted to delay the eighth shuttle flight until September to allow more time to check out the TDRS satellite, but they were overruled because the prime customer on the next flight is the government of India, which wants its Insat communications satellite in orbit in August.