To solve this problem it is necessary to apply the concepts related to gravitational potential energy.
The change in gravitational potential energy is given by,
[tex]\Delta PE = PE_f - PE_i[/tex]
Where,
[tex]PE = \frac{GMm}{R}[/tex]
Here,
G = Gravitational Universal Constant
M = Mass of Earth
m = Mass of Object
R = Radius
Replacing we have that
[tex]\Delta PE = \frac{GMm}{R+h} -\frac{GMm}{R}[/tex]
Note that h is the height for this object. Then replacing with our values we have,
[tex]\Delta PE = \frac{GMm}{R+h} -\frac{GMm}{R}[/tex]
[tex]\Delta PE = GMm(\frac{1}{R} -\frac{1}{R+h})[/tex]
[tex]\Delta PE = (6.65*10^{-11})(7.36*10^{22})(1170)(\frac{1}{1740*10^3} -\frac{1}{211*10^3+1740*10^3})[/tex]
[tex]\Delta PE = 57264.48*10^{11}(5.1255*10^{-7}-5.747*10^{-7})[/tex]
[tex]\Delta PE = 3.56*10^8J[/tex]
Therefore the gravitational potential is [tex]3.56*10^8J[/tex]
