To calculate weight we use formula:
[tex]F=m*g=882N[/tex]
When we have two bodies we use general gravity formula:
[tex]F=G* \frac{ M_{p}*M_{E} }{ r^{2} } [/tex]
Where:
G = gravity constant = [tex]6.67* 10^{-11} m^{3} kg^{-1} s^{-2} [/tex]
Mp = mass of person = 882 / 9.81= 89.9kg
ME = mass of Earth = [tex]5.97* 10^{24} kg[/tex]
r = distance between Earth and person
From these two equations we find that left sides are equal so the right sides must be equal too.
[tex]m*g=G* \frac{ M_{p}*M_{E} }{ r^{2} }[/tex]
We solve this for r:
[tex]r= \sqrt{G* \frac{ M_{p}*M_{E}}{M_{p}*g} [/tex]
r=6371116m = 6371.116km
This is distance from center of Earth. Radius of Earth is 6370km and height above surface is 6371.116 - 6370 = 1.116km or 1116m.
