Question

The International space station has a mass of 419,600 kg and GPE of 1,049,000,000,000 J. How high above the Earth is it?

Answer 1

273000 m

Explanation:

gravitational Energy is `E_w =mgh`
but you have only the mass and two unknown datas, h ang g, in fact you can't use for g 9,8m/s^2 because you are far from earth surface. so let us write g in function of h and you must use the relation `g= g°(1-2 h/R ) = 9.8 m/s^2 (1-2h/(6,38 xx 10^6 m))` where R is the radius of the earth so you have the relation
#E_w = m h g°(1-(2 h)/R ) = 419,600 kg xx h xx 9.8 m//s^2 (1-2h/(6,38 xx 10^6 m))#

solving in function of h you have the second degree equation `2h^2/(6,38 xx 10^6 m)-h+1,049,000,000,000J/(419,600kg xx 9.8 m//s^2)=0` whose result is h= 273000 m, not far from 250000 m that you wopuld have gotten if you had considered `10m//s^2` for the gravity acceleration...