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## Homework Statement

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

## Homework Equations

ΔEg1= -GmM/(Re+h) + GmM/Re

ΔEg1= GmMh/(Re*(Re+h))

ΔEg2= mgh

## 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.