Determining Spring Constants in Different Gravity Environments

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To determine the spring constant, k, in a static experiment (i.e. suspending weights from a spring) we use the following expression;

k = (mass x gravity) / extension

But what if I was on the Moon (where gravity is 1/6 that of Earth) or in part of space where there is zero gravity? The spring is no less stiff when an Astronaut attempts to push or pull it, yet k has a much lower value.

Is it true that only the value of k derived from a horizontal experiment with mechanical loading gives us the true spring constant?

Thanks for your help
 
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The way to determine the spring constant is to apply a known amount of force (N) to the spring and see how far extends. You can do this by hanging a known mass near a planet with known gravitational pull or any other way that would let you know how much force you are applying to the spring. There're many ways to do this.
 
Silly me. K remains constant because it is a function of the intermolecular or atomic forces in the steel. Only the amount of displacement changes!

Not quite sure about the period of the oscillations, though. Think it remains the same but with a smaller distance covered?