Where does space begin, and where exactly does the Earth’s atmosphere end?
Strictly speaking, there is no such thing as an end to the Earth's atmosphere: An atmosphere does not technically end at any given height, but becomes progressively thinner with altitude.
However, the normally accepted boundary between the Earth's atmosphere and outer space is what is called the Kármán line, which is an imaginary line that lies at an altitude of 100 km (62.1 miles) above the Earth's surface. This definition is accepted by the Fédération Aéronautique Internationale (FAI), which is an international standard setting and record-keeping body for aeronautics and astronautics.
The line was named after Theodore von Kármán, a Hungarian-American engineer and physicist who was active primarily in the fields of aeronautics. He first calculated that around this altitude the Earth's atmosphere becomes too thin for aeronautic purposes. Also, there is an abrupt increase in atmospheric temperature and interaction with solar radiation. Though the calculated altitude was not exactly 100 km, Karman proposed that 100 km be the designated boundary to space as the round number is more memorable and the calculated altitude varies minutely as certain parameters are varied. An international committee recommended the 100 km line to the FAI, and upon adoption it became the internationally accepted boundary to space.
The U.S definition
The United States does not officially define a "boundary of space". However, its definition of an astronaut does not lie easily with the Karman line definition of where space begins.
The United States defines an astronaut as one who has flown above 50 miles (80.5 km) above mean sea level. This is approximately the line between the mesosphere and the thermosphere, and is 19.5 km or 12.1 miles below the Karman line.