# 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?

Oct 2, 2017

gravitational Energy is ${E}_{w} = m g h$
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 $2 {h}^{2} / \left(6 , 38 \times {10}^{6} m\right) - h + 1 , 049 , 000 , 000 , 000 \frac{J}{419 , 600 k g \times 9.8 m / {s}^{2}} = 0$ whose result is h= 273000 m, not far from 250000 m that you wopuld have gotten if you had considered $10 m / {s}^{2}$ for the gravity acceleration...