What affects the solubility of CaSO4 in different solvents?

[chmmr]

Say I've got a solid lump of CaSO4 that I put into water.
When I first learned about Solubility Constants, Ksp was defined as [Ca][SO4], meaning how much Calcium and Sulfate ions dissolved. But now I found out when I look up a Ksp value it is [Ca][SO4]\gamma_Ca\gamma_SO4. I understand the concept of activity, that those new constants take into account the activity of the water on the ions. So does this number just mean how much of the CaSO4 would dissolve in a nonpolar solvent?

 

[Borek]

It is not about activity of the water, it is about electrostatic interactions between ions. In nonpolar solvents (with low dielectric constant) interactions between ions are much higher, so the activity coefficients will change much faster with concentration.

I don't think it makes much sense to try to assign a special meaning to the equation without activity coefficients (or more precise - with activity coefficients equal 1). The closest thing I can think of is a border case of infinitely diluted solution.