Question

Question #cb61c

Answer 1

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`