The space shuttle Challenger departed today on a scientific mission chartered entirely by the West German space agency, ferrying eight people and a room-sized research laboratory into a circular orbit 201 miles above Earth.

At noon, exactly on schedule after a routine countdown, the 2,250-ton orbiter and its disposable fuel tank roared away from the Kennedy Space Center here.

NASA officials said the smoothness of the countdown and launch, a contrast to several previous launches when equipment failures forced delays, proved that the space shuttle is achieving "maturity."

Aboard Challenger in addition to five American astronauts are two from West Germany and one from the Netherlands. The Europeans are scientists who will conduct a planned 76 experiments in the Spacelab module, an 18-foot-long capsule mounted in the shuttle's cargo bay.

The laboratory was designed, built and checked out in Europe before being flown to Florida and installed in the shuttle.

Mission control for the scientific operations during the planned seven-day flight will be at the West German space agency's center in Oberpfaffenhofen, near Munich. Ground control for flying the shuttle will be in Houston, as usual.

Shortly after launch, the crew, dispensing with the usual exclamations about being in space, went matter-of-factly to work. They opened a hatch at the back of the crew compartment and the two West German scientist-astronauts, Reinhard Furrer and Ernst Messerschmid and the Dutch scientist, Wubbo J. Ockels, floated into a tunnel leading to Spacelab. There they began throwing switches and assembling equipment to start the experiments.

One of the first to be performed was on causes of the motion sickness that has afflicted about half of those who have gone into space. In this experiment, which will be repeated throughout the flight, astronauts will be strapped into a sled that is pulled along rails on the laboratory floor. The idea is to see what kinds of motion produce abnormal reactions in the astronaut's balance-control mechanism, the so-called vestibular apparatus of the inner ear.

Only two problems, both said to be minor so far, have emerged. A temperature control valve on one of the spacecraft's three electricity-supplying fuel cells was malfunctioning, causing its temperature to fluctuate too much. Still, flight controllers said, the fuel cell was delivering its full output of electricity. If the problem becomes worse, it could force a cutback in the experiments to be performed.

A second problem involved another valve, one that keeps fuel flowing to attitude-control thrusters on the shuttle's right side. A backup valve took over the function, however, and was working properly.

West German space officials say Spacelab is a major step toward what they hope will be a larger laboratory module attached to a permanent American space station that NASA envisions for the 1990s.