PEARCE AIR FORCE BASE, Australia — A British satellite company has solved one crucial aspect of the mystery surrounding the Malaysia Airlines flight that disappeared on March 8, using a complex mathematical process to determine that it ended its journey in the middle of the southern Indian Ocean.
Guided by a principle of physics called the Doppler effect, the company, Inmarsat, analyzed tiny shifts in the frequency of the plane’s signals to infer the plane’s flight path and likely final location. The method had never before been used to investigate an air disaster, officials said.
The first definitive news of the fate of the Boeing 777 jet brought heartbreak to the families of those on board as Malaysia’s prime minister, Najib Razak, announced on Monday that no one is believed to have survived the flight.
“This is a remote location, far from any possible landing sites,” a somber Mr. Razak said. “It is therefore with deep sadness and regret that I must inform you that, according to this new data, Flight MH370 ended in the southern Indian Ocean.”
Mr. Najib appeared eager to bring some finality to the families of the passengers, who had complained for more than two weeks about the incomplete and sometimes contradictory information they were getting. Two-thirds of the plane’s passengers were Chinese citizens, and the flight was bound for Beijing when it took off from Kuala Lumpur, Malaysia, after midnight on March 8.
But many furious Chinese relatives and friends of passengers refused to believe it, wailing with anguish and screaming that the Malaysians were lying and hiding what they knew.
“The Malaysian government is not telling the truth,” said one woman among the relatives of passengers who gathered at the Lido Hotel in Beijing to wait for news of the flight. “All governments are corrupt. The Malaysian government is hiding something.”
The announcement did little to solve the deeper mystery of the plane’s disappearance, shedding no light on why someone with detailed knowledge of the plane’s navigation and flight systems diverted it radically from its course. Investigators said they have looked into the backgrounds of the 239 people on board, including the two pilots and the crew, and have so far found no answers to that central question.
However long expected, the news that the jet was lost came as a body blow, dashing the hopes that many had clung to with increasing desperation that somehow the plane had been hijacked and taken to some obscure spot where the passengers could still be alive.
A few people in the hotel ballroom in Beijing collapsed and were put on wheeled stretchers and taken to the parking lot, which was full of police cars and ambulances. Inside the hotel, police officers in navy-blue uniforms stood guard every few feet and blocked scores of jostling journalists from entering the ballroom. Several women emerged sobbing so hard that knots of friends and family had to help them walk to the elevators.
“We demand the truth,” said a young woman in a red ski jacket. “The Chinese government should step up and find out the truth for us. Nobody cares about us. Nobody cares about the lives of our family.”
Li Chengpeng, a popular Chinese social critic, gave voice to the deep skepticism held by many Chinese of the official announcement. He posted a message for the seven million followers of his microblog, calling Mr. Najib’s news conference staged theater. “Just now, they were not actually publicizing the truth but were merely giving a show of publicizing the truth,” he wrote. “It looks like there are traces of rehearsal. Politicians are shameless! Keep investigating!”
The Malaysian prime minister based his announcement on a new analysis of satellite signal data that ruled out any chance that the plane had flown north, toward land, from its last known position on March 8. It had to have flown south, the analysis found, and by the time of the last recorded signal, it would have been nearly out of fuel over a rough, deep ocean, more than a thousand miles from anywhere it could have landed safely.
The search focused more tightly on that area on Monday after an Australian military search plane spotted several floating objects that could be debris from the plane, and ships raced to investigate. On Tuesday, officials said, search flights were called off because of bad weather.
One of the assumptions in the analysis was that for the final few hours of the plane’s flight at least, it was cruising at a fairly constant speed and direction, suggesting that it was being flown by the autopilot system. Experts said it was certainly possible for that to happen.
A former Boeing instructor pilot, who spoke on the condition that he not be identified, said, “ ‘Heading select mode’ is dumb,” referring to one way the plane’s autopilot could be set. “It doesn’t know anything except, ‘maintain this heading.’ ”
The instructor, who has trained Boeing pilots at airlines around the world, said that in that mode, the plane would probably fly on steadily until one engine’s fuel supply was exhausted, but that after that, the plane would probably soon become destabilized and crash without a skilled human pilot at the controls.
The plane took off with ample fuel to fly to Beijing, more than 2,500 miles from Kuala Lumpur, with a margin of safety. Based on that, Malaysian officials have estimated that it could have stayed in the air until about a half-hour after the last satellite signal was recorded.
The floating objects were spotted on Monday about 1,500 miles southwest of Perth, Australia, by the crew of a P-3 Orion surveillance plane from the Royal Australian Air Force. An Australian naval survey ship, the Success, was directed to try to find and recover the objects, the Australian authorities said. A Chinese military aircraft also reported a possible sighting of floating objects in the search area, but that sighting was at a different location and was much more tentative.
The search for the aircraft’s fuselage, and other bulky parts of the jet that probably sank to the bottom of the ocean, is likely to be focused within a limited distance from the suspected flight path. But the search for floating debris is likely to be widespread.
Erik van Sebille, an oceanographer at the University of New South Wales who studies and has conducted experiments on the flow of water around Australia, said the conditions of the southern Indian Ocean are “extremely hostile,” with large waves, swirling currents and winds that are among the strongest on the planet. Currents in the southern Indian Ocean could scatter floating debris, he said.
“The whole ocean down there is like a pinball machine,” Dr. van Sebille said. “It is difficult to track or predict where water goes, or do what is really important now, which is to backtrack where water came from.”
Finding the plane’s flight recorders, or black boxes, will be crucial to determining what may have caused the plane’s disappearance. The devices are designed to transmit signals to help searchers locate them, but searchers have only about two weeks left to find them before the devices’ batteries run out.
The United States Pacific Command said Monday that it would move a Towed Pinger Locator System, capable of locating a black box to a depth of 20,000 feet, into the region. “This movement is simply a prudent effort to pre-position equipment and trained personnel closer to the search area, so that if debris is found, we will be able to respond as quickly as possible, since the battery life of the black box’s pinger is limited,” Cmdr. Chris Budde, a Seventh Fleet operations officer, said in an email statement.