The value of 'g' depends on the distance from the Earth's center, and
it decreases at the same rate as (the distance squared) increases.
If you're floating (double the Earth's radius) above the surface,
then you're (3 x radius) from the Earth's center.
Somehow, you moved from (1 radius) to (3 radii) from the center.
Your distance from the center increased by (3 times) so you
weight, and the value of 'g', changed by the factor of (1/3²) = 1/9 .
'g' is 9.8 m/s² at the surface, so up there, it's about 1.089 m/s² .
