If you have an ideal spring with a mass m on it, and you measure a spring constant of 8 n/m, what do you expect to happen to the spring constant if you (be realistic):
a. take it to the moon -
b. take it to the sun
The spring constant of the system will not change. However, the force exerted on the mass will change because of the variations in gravity (the moon has less gravity, so force on mass will be smaller.)