Astronauts Thomas K. Mattingly and Henry W. Hartsfield spent their busiest day in space today, working for more than 14 hours on tasks ranging from aiming their secret Air Force telescopes at the Earth's horizon to endless exercises of the robot arm on the space shuttle Columbia.

Except for brief breaks to eat, Mattingly and Hartsfield were up and working from 5 a.m. to 7 p.m. at the direction of civilian mission controllers in Houston and Air Force controllers in Sunnyvale, Calif.

The two sets of controllers had the astronauts repositioning instruments, running a small pharmaceutical factory, checking out a new spacecraft refrigerator, measuring the contamination that clouds up the cargo bay whenever a rocket engine is fired, photographing lightning storms over South America and learning to use Columbia's towering tail to block out the sun so they can examine the cargo bay in daylight.

"Today is absolutely the busiest day in the whole seven-day flight plan," flight director Harold Draughon said at the Johnson Space Center.

So busy was the crew that flight directors still had not told them that their reusable solid rocket engines sank in 3,500 feet of water in the Atlantic Ocean after liftoff. "They've got more important things on their minds right now," Draughon said.

That mishap will cost the National Aeronautics and Space Administration $36 million. Unimportant as it might be to the astronauts, the lost boosters were very much on the minds of shuttle engineers, who still don't understand why they sank in a "very benign sea" 150 miles east of Cape Canaveral.

"Both boosters are on the bottom," said George Hardy, solid rocket booster project manager. "The only conclusion we can draw is that the main parachutes on both boosters were non-functional."

If each booster's three giant (115 feet across) chutes failed to open, as now believed, the 95-ton rocket motors would have hit the water at 340 mph. Hardy said that a C130 search aircraft saw one booster lying flat in what he called the "log mode," and the other standing straight up in the water like a pencil in the "spar mode" before they sank.

"The fact that the boosters sank implies they suffered structural damage at their motor joints," Hardy said. "If those joints aren't damaged, air is trapped in there and they float. Instead, water may have gotten in there and they sank."

Hardy said the Navy will lower television cameras mounted on searchlights into the sea so that engineers can examine the sunken boosters to see if they contain clues about what caused them to sink. Debris found on the surface also will be looked over for clues to their sinking.

"We will review the accident in excruciating detail," Hardy said. "We're proceeding on the assumption that we'll figure out the problem and fix it so we can launch the next shuttle right on schedule."

Above the ocean, 160 miles up, Mattingly and Hartsfield were hard at work for the Air Force, aiming and re-aiming the infrared and ultraviolet telescopes that look at the Earth's horizon to let one scope (infrared) track the exhausts of aircraft and missiles and the other (ultraviolet) navigate through space without being directed from the ground.

If anything, their mission for the Air Force had become even more of a secret than it was Sunday, when they started out.

Only once today did Mattingly talk over the public link with the Air Force in Sunnyvale. All other times he spoke into a tape recorder whose messages were relayed to Sunnyvale over a private link. The Air Force responded by sending its messages to Columbia on a teleprinter.

Mattingly rarely talks anyway. A taciturn man who didn't tell his fellow astronauts after his wife got pregnant or when he was getting divorced, Mattingly is at the same time one of the most methodical astronauts in the shuttle office. He is carrying a small computer he has programmed with all his tasks, and it beeps to remind him when a new task is coming up.

"That's just T.K.'s nature," flight director Draughon said. "He doesn't talk much because he's very disciplined and very regimented compared to almost everybody else I know."

The crew was so busy all through the day that they did not even attempt to fix an experiment in the cargo bay called the "getaway special." This is a 200-pound canister that carries 10 experiments devised by students at Utah State University. It was purchased for them for $10,000 by a wealthy Utah engineer, Gilbert Moore.

For some unexplained reason the astronauts have been unable to supply electricity to the canister to begin any of the 10 experiments since the Sunday launch. The earliest they can even attempt a fix is on Wednesday, when the shuttle flight plan is a little less crowded.

Thoroughly puzzled by why the "getaway special" canister is not working, flight directors say they do not believe that any fix the astronauts try in space will get it to work.

If the canister is never turned on, NASA has told getaway special users that they can refly their experiments at no extra charge on some future mission if the users can prove that their experiment failed through no fault of their own. The Utah State canister gets a reflight opportunity in November, when the next shuttle flight is scheduled.