April 30, 1985

Seven astronauts rocketed into orbit aboard the shuttle Challenger today to devote a week of scientific inquiry to the mysteries of both inner man and outer space. Late this afternoon, five hours after the 2,250-ton spaceplane blasted up through the Florida coastal haze, the astronauts successfully launched one satellite. But 15 minutes later they failed in their attempt to release a second one, a 150-pound Navy communications device. Its antennas apparently became stuck in its launching can. The can eventually was resealed, and the satellite will probably be returned to earth aboard the shuttle, although an attempt to deploy it Tuesday was not ruled out.

A QUIET revolution is going on in psychotherapy. As a result, by far the largest portion of the nation's therapy is now done by nonmedical professionals. Psychiatrists, who are medically trained, find themselves increasingly limited to the most severe mental disorders. ''Because of the plethora of nonmedical therapists, psychiatrists are increasingly being pushed into treating the more severely ill,'' Dr. Melvin Sabshin, medical director of the American Psychiatric Association, said. ''And the competition will continue to become more intense as time goes on.''

The abrupt retirement of the commander of all uniformed officers in the New York City Police Department will be announced today in a continuing shake-up stemming from charges that suspects were tortured at a station house, police officials said yesterday. They said that the retirement of three other officials, all commanders in Queens, where the purported torturing took place, would also be announced. The retirements were said to have been made voluntarily, but at the request of the Police Commissioner, Benjamin Ward. The departure of the Chief of Patrol, Hamilton Robinson, who holds the third-highest rank in the department and is the commander of its 17,000 uniformed officers, carries the shake-up begun by Commissioner Ward last week into the highest echelons of the force.

SINCE the turn of the century, students entering New York State high schools have found themselves face to face with daunting obstacles: the basic building blocks of math. Millions soldiered on, mastering geometry in 9th grade, algebra in 10th grade, and trigonometry in 11th grade. Millions more fell by the wayside, casualties of isosceles triangles, quadratic equations, and sine, cosine and tangent. This year, for the first time since the state's basic geometry textbook was written in 1947, a new math curriculum is being used in New York's high schools. In short order, the curriculum change has caused turmoil in the normally neatly ordered world of high school math.

Israel completed the second phase of its three-stage withdrawal from Lebanon today, pulling out of the southern port city of Tyre, the last major city under Israeli military occupation. As happened in previous pullouts by the Israelis, their departure from the predominantly Shiite Moslem area set off joyous celebrations, particularly in Shiite villages. Seven Shiite villages near the port had been raided by Israeli troops and armor during searches for guerrillas under Israel's ''Iron Fist'' policy, which began after guerrilla raids against the withdrawing troops increased sharply. The guerrilla attacks were frequent, and the region from Tyre to Nabatiye came to be known as the ''arc of resistance'' P.L.O. Guerrillas Blocked Within hours of the Israeli departure today, Shiite militiamen moved to block guerrillas of the Palestine Liberation Organization from returning to three Palestinian refugee camps near Tyre. [Page A13.] The leader of the mainstream Shiite militia known as Amal said the action was intended to prevent a repetition of what happened in Sidon, the port north of Tyre, where Palestinian guerrillas joined Christians in battles against Moslems that began after the Israeli withdrawal. The Christians are in the minority in southern Lebanon, and the Shiites are the predominant religious group.