## Speed of Aircraft at the Edge of Space

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.