## Speed of Aircraft at the Edge of Space

The Karman Line is the supposed edge of space. It is set so that the speed at which an aircraft must fly to maintain the flow of air over its wing, so control of the aircraft can be maintained, is equal to the speed the aircraft would have were it in orbit.The Karman line is 60 miles (96540 m) above the Earth's surface. The Earth is a sphere of 6370000 m. To find the speed of an aircraft at the Karman line equate the centripetal force to the gravitational force.

\[\frac{m_{Aircraft}v^2}{r} = \frac{GM_{Earth}m_{Aircraft}}{r}\]

Cancel

\[m_{Aircraft}\]

\[\frac{v^2}{r} = \frac{GM_{Earth}}{r^2}\]

Multiply by

\[r\]

and square root.\[v=\sqrt{\frac{GM_{Earth}}{r}} = \sqrt{\frac{6.67 \times 10^{-11} \times 5.98 \times 10^{24}}{6370000 + 96540}} = 7853 m/s\]

This is about 24 times the speed of sound at sea level.