User:Stestagg/Elevator

= Space Elevator =

Gravitational force
$$ F = \frac{mMG}{r^2}$$

Where m and M are the masses of 2 objects and r is distance between their centres of mass.

Centripetal force
$$ F = \frac{mv^2}{r} = m r \omega^2 $$

Where w is the angular velocity in radians/second. So, given that the earth rotates once(2π) per day (86400 s), we can specialize for geostationary orbit:

$$ w = \frac{2 \times \pi}{86400}$$

$$ v = \frac{\pi}{43200}$$