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?

1 Answer


273000 m


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...