In Los Angeles, the flame that burned for the 1984 Olympics was relit for 24 hours. In Houston, motorists drove with their headlights on. In New York, St. Patrick's Cathedral was ablaze with candles. And in Evansville, Ind., a porch light vigil originally intended to celebrate the nation's first teacher in space became a memorial to her.

Across the country, these lights symbolized the nation's mourning for the seven-member crew of the space shuttle Challenger. One day after it roared into the skies and exploded in flames, shock and disbelief gave way to down-to-earth expressions of grief.

For families and friends, the grief was intensely personal -- the loss of an older brother, an only child, a father, a neighbor.

"It's worse today somehow than it was yesterday," said Patrick Smith of Beaufort, N.C., whose older brother, Michael, piloted the space shuttle for 74 seconds before its disastrous end.

For the communities that lost a local hero, it was a day to gather in church, to plan memorials, to pay tribute. Over the public address system at Auburn High in Washington state, two students played taps into hushed classrooms for Challenger commander Francis R. (Dick) Scobee, Class of '57.

For the nation at large, the public tragedy summoned memories of another time, more than two decades ago, when the nation and its schoolchildren unexpectedly learned at midday of a national catastrophe -- the assassination of President John F. Kennedy. A national memorial service for the shuttle crew is set Friday in Houston, site of the Lyndon B. Johnson Space Center and home to five of the astronauts who died.

"The whole space program has tremendous symbolic meaning," said Brian Flynn of the National Institute of Mental Health. "It involves some of the best talent, the best we can be as human beings. It represents the best of our technology. And it also captures and reconfirms the spirit that founded the country -- new explorations and taking risks to expand our horizons."

Flynn, a psychologist who specializes in working with disaster victims and the cycle of mourning, from shock to acceptance, said the tragedy "takes on an emotional meaning that is more than a comparable number of deaths on a commuter crash. It has much more meaning."

Its impact was magnified, he said, by crew member Christa McAuliffe, a Concord, N.H., high school teacher.

"A teacher on board provides an opportunity for people to identify tremendously with the victims . . . . In some ways, astronauts are seen as different from the rest of us, but here was one of us," Flynn said.

The rest of the crew was a cross-section of America -- a black physicist, a Jewish female engineer, an Asian American and two Vietnam veterans, one of them a small-town southerner. They were Ronald E. McNair, Ellison S. Onizuka, Gregory B. Jarvis and Judith A. Resnick.

While people sat transfixed before television sets Tuesday, watching the fiery spectacle over and over in excruciating slow motion, yesterday they began to cope with the event's reality and express their common sentiments in concrete ways.

"Life has to go on, and so does the space program," President Reagan told reporters in the Oval Office. Like many Americans, he went back to work, but he took time to phone relatives of the crew to express his condolences. Reagan will attend the Friday memorial services in Houston with his wife, Nancy.

Meanwhile, the usually boisterous New York Stock Exchange paused for a moment of silence. In Concord, the children who lived in McAuliffe's neighborhood gathered for a tearful prayer service. Flags everywhere flew at half-staff, and in Houston, as elsewhere, church bells tolled for seven minutes at the precise time of the Challenger's explosion, 11:39 a.m.

A commemorative plaque went up in the National Air and Space Museum, and wreaths of flowers appeared underneath the "Space Window" at Washington's National Cathedral -- a stained-glass expanse with an embedded piece of moon rock and dedicated to explorers of the unknown.

Many sought to pay tribute through special funds and scholarships. In Washington, attorney Delbert Smith organized a trust fund at American Security Bank for the 10 children of the Challenger crew.

The U.S. Space Foundation in Colorado Springs, Colo., also set up a special fund in memory of the astronauts, with proceeds going toward construction of a new space shuttle. The group has pledged $10,000. In Akron, Ohio, Mayor Tom Sawyer and school superintendent Conrad Ott proposed a scholarship fund in honor of native Judith Resnik for women interested in aeronautical engineering.

NASA spokesman Mary Fitzpatrick said many people had phoned the agency asking if they could contribute money to the crew's children or to build a shuttle.

The agency issued a statement saying that while the National Aeronautics and Space Administration can accept donations without strings attached, "there can be no promise made that the donated money will be used for a specific project, even if the gift is made expressly for that purpose. The unconditional donations go into a general fund to be used as NASA sees fit."

But while the disaster brought the country together, for some it also produced second thoughts. Marilyn Givens, who lives near Houston's space center, questioned the wisdom of sending a private citizen into space. "I just don't think they were ready for civilians yet. They should have waited," she said.

And Patrick Smith wondered why it took a tragedy to earn his brother the world's respect. "It's a shame for him, a shame for all seven of them, that they had to die before they got all this attention."

In Mike Smith's home town of Beaufort, N.C., about two dozen friends got together Wednesday to erect a memorial on U.S. 70 near Joe's Grocery.

It features seven large flags at half-sfaff -- six in a half circle and one, a little larger than the rest, in the middle for Smith. A two-foot-high sign reads:

"Mike Smith is a success. He has lived well, laughed often and loved everybody. He has accomplished his task and left the world a better place than he found it. He has earned the respect of others and looked always for the best in others and gave the best he had. He's our friend, and we love him."