Three passengers and two crew were on board the jet which was believed to have
been flying at 43,000ft.
It had taken off from Orlando, Florida, and contact was lost with those on
board at Gainesville.
US Air Force F-16 and F-15 fighters followed the jet and reported seeing no
activity on board.
British aviation expert David Learmount, of Flight International, said
depressurisation at that altitude would have resulted in the crew and passengers
becoming unconscious within seconds.
He told Sky News: "The F-16 fighter pilots have looked at the windows and
they have said that they appear to be frosted over which indicates a very, very
low temperature inside the aircraft and that might mean depressurisation at a
very high altitude.
"We understand the Learjet was at 43,000ft which is well above what most
airliners fly at.
"If the aircraft did depressurise at that height literally you wouldn't have
time to get an oxygen mask to your face before you passed out from lack of
The golfer's mother, Bee Stewart, she did not know if her son was on the plane
but confirmed he was a co-owner.
Gene Abdallah, of South Dakota Highway Patrol, confirmed that the plane had
crashed about two miles west of Mina, in the north-central part of the state.
There was no confirmation as to the identities of other people on the plane.
White House spokesman Joe Lockhart said US President Bill Clinton was informed
of the situation during a meeting with his economic advisers.
Two Federal Aviation Administration officials were dispatched to the scene of
the crash, as had a National Transportation Safety Board representative.
Planes that fly above 12,000ft are normally pressurised, because passengers
would have difficulty breathing the thin air above that altitude.
If there is a pressurisation problem, those aboard the aircraft could slowly
lose consciousness and, if not returned to a normal altitude, die.
Once reaching a cruise altitude, pilots often switch on the autopilot. If they
passed out, the plane would cruise until it ran out of fuel.
Father of two young children Stewart, 42, has been one of the most
recognisable players in golf because of his trademark plus fours and
He has won 18 tournaments around the world, including the three major
In June, Stewart won his second US Open over Phil Mickelson with a 15ft putt,
the longest putt to ever decide that championship on the final hole.