Aball with weight of 1000 pounds is held 1000 above the earth. what is the ball's potential energy in kip-feet? one-kip=1000 pounds

I assume the ball weighs 10000 pounds force at that altitude. ? 

Can't use PE = mgh as the value of g changes with altitude. At that heigh, it is significantly lower. 

First we need the mass. 
10000 lb force = 44452 newtons 
1000 miles = 1.61e6 m 
g value at that altitude is 

g = Gm/r² 
g is acceleration from mass attraction in m/s² 
m is mass of earth or other body generating the a 
r is radius of body in meters. 
G = 6.67e-11 m³/kgs² 
earth radius6,371 km = 6.37e6 meters 
earth mass M 5.974e24 kg 
earth GM = 3.987e14 
g = (3.987e14) / (6.37e6+ 1.61e6)² = 6.26 m/s² 

mass = 44452/6.26 = 7098 kg 

Gravitational potential energy (to surface) 
from height h 
E = [GmM/(R+h)] – [GmM/R] 
E = GmM[(1/(R+h)) – (1/R)] 

E = (3.987e14)(7098)[(1/(6.37e6+ 1.61e6)) – (1/6.37e6)] 

you can do the rest. 

edit: 
E = (3.987e14)(7098)[(1/(6.37e6+ 1.61e6)) – (1/6.37e6)] 
E = (3.987e14)(7098)[(3.17e-8] = 8.97e10 J 

for curiosity, use E =mgh so see the difference. 
E = (4336)(9.8)(1.61e6) = 7.16e10 J (false

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