Question #cb61c

1 Answer
Nov 22, 2016

Answer:

Start with #r = root(3)(GMT^2/(4pi^2))#

Explanation:

Reference Orbital period

#r = root(3)(GMT^2/(4pi^2))#

Where r is the radius of the orbit, measured from the center of the Earth.

The distance, d, above the Earth is #r - R_(earth)#

#d = root(3)(GMT^2/(4pi^2)) - R_(earth)#

where #R_(earth)# is the radius of the Earth.

Six hours converted to seconds:
#T = 21600 s#

Gravitational Constant
#G = 6.67 xx 10^-11 m^3kg^-1s^-2#

Earth's Mass
#M = 5.972xx10^24kg#

Earth's Radius
#R_(earth) = 6371000 m#

#d = root(3)((6.67 xx 10^-11 m^3kg^-1s^-2)(5.972xx10^24kg)(21600 s)^2/(4pi^2)) - 6371000 m#

#d = 10388631 m#