1. The problem statement, all variables and given/known data There are two equations from which change in gravitaton potential energy of a system can be calculated. ΔEg = mgh and the other Eg = GmM/R The first equation is only correct if the gravitational force is constant over a change in height h. The second is always correct. Consider the change in Eg of the mass m when it is moved away from the earth's surface to a height h using both equations, and find the value of h for which the equation ΔEg=mgh is in error by 1%. Express this value of h as a fraction of the earths radius and obtain the numerical value. m = mass of object M = mass of earth Re = 6.38x10^6meters 2. Relevant equations ΔEg1= -GmM/(Re+h) + GmM/Re ΔEg1= GmMh/(Re*(Re+h)) ΔEg2= mgh 3. The attempt at a solution So Fg = GmM/(Re+h)^2 mg = GmM/(Re+h)^2 g = GM/(Re+h)^2 ΔEg2 = mGMH/(Re+h)^2 So i have to find the the relationship between these equations so i say I)ΔEg1/ΔEg2 = 100/101 II)ΔEg1/ΔEg2 = 100/99 where 100 represents the one which does not have the fraction of error percent and 101 and 99 represent the one with the fraction of error percent I) When i solve I my answer is h = -Re/101 h= -63168.32 which yields a negative number so this is not the answer. II) When i solve for this h = Re/99 h= 64444.44 m When i double check these answers with my teacher she doesn't seem to have the same numbers so i'm just curious what i'm doing wrong? I know there are 2 other cases i didn't check III)ΔEg1/ΔEg2 = 99/100 IV)ΔEg1/ΔEg2 = 101/100 where III) yields h = Re/100 h= 63800 IV) h = -Re/100 h = -63800 But i know III) and IV) are not the case because that would mean that Eg = -GmM/Re is the equation off by a fraction of a percent. Anyways any help is appreciated.