Which displacement value will produce the smallest restoring force if the same spring is used in each case?

The smaller the displacement, the smallest restoring force it will create. 

As seen from the figure given below, The spring system follows the equation,

F = -Kx
 where, x is the displacement
F is the restoring force
k is the spring constant
If , K is kept constant, then,

F is directly proportional to the displacement but it acts in opposite direction due to negative sign.

F = G 
1.37*10^7 = 6.67384* 10^-11 * mass * 5.98*10^24 / (569 000)^2

m = 1.11*10^4 kg

that's about 11.1 tones