The space shuttle Challenger, now in its second day in orbit on a scientific mission chartered by the West German government, today launched a small American satellite designed for military research.

The satellite, an experimental device intended to find and relay signals from automated sensors on the ground and in the ocean, was built by Defense Systems Inc., of McLean, Va., a contractor with the Defense Department.

Launch of the satellite from a shuttle flight chartered by West Germany for civilian scientific purposes has reportedly brought protests from that country's political opposition party, the Social Democrats.

The 150-pound satellite, called the Global Low Orbiting Message Relay Satellite, was launched as part of the National Aeronautics and Space Administration's "Getaway Special" program.

Under this arrangement NASA will launch, for a fee, almost any object into orbit as long as it can fit into a standard, small container mounted in the shuttle's cargo bay.

The satellite, which was pushed out of the container by a spring, was launched for $10,000. By contrast, West Germany paid NASA $64 million to carry its astronauts and scientific equipment into space.

Getaway Specials are available on the shuttle on a space-available basis.

Although the satellite is intended as a forerunner of a type that could be used to relay data from undersea sensors that track Soviet submarines, Defense Systems officials said the one launched today will not be used for that purpose.

While launch of the satellite required only the press of a button, Challenger's eight-member crew, including two West German scientists and one from the Netherlands, worked in shifts round the clock on the shuttle's primary scientific mission.

All of the work is being done inside Spacelab, a European-built laboratory mounted in the shuttle's cargo bay and crammed with equipment that will carry out 76 experiments. A tunnel connects Spacelab with Challenger's crew compartment.

Many of today's experiments dealt with the problem of space sickness, which has afflicted many astronauts with nausea. It is believed that this sickness is caused by conflicting messages that reach the brain from the eyes and the body's balance control mechanism in the inner ear.

On the ground, information from these sensory organs agrees, making it easy to sense "up" and "down" and to judge the body's motion relative to fixed surroundings.

Under the effects of gravity, the inner ear senses these directions because the weight of tiny stones in the ear's vestibular apparatus presses down on nerve endings. Without gravity the inner ear can no longer supply information to the brain and, scientists speculate, the eyes become the chief source of information on body position.

This was confirmed today when Ernst Messerschmid, a German astronaut, placed his head inside a small dome whose inner surface, painted with dots, revolved slowly. Messerschmid said that when he did this, he had the feeling that his whole body, rather than the dome, was rotating.

Among the other biological experiments being performed are studies of how plant seedlings and animal embryos develop in the absence of gravity. It is believed that gravity's effects help developing organisms establish an orientation that guides their growth.

Results of most of the experiments will not be known until Challenger returns to Earth and the specimens are returned to various scientists, most of them in Europe, for analysis.

Challenger, which has experienced no major problems in flight, is expected to land Nov. 6 at Edwards Air Force Base in California.