Gravitational mass is determined by the strength of the gravitational field. Mass will always be static and constant, but gravitational mass will vary with the strength of the gravitational field.

@markjo, I think you are confusing weight and gravitational mass there. Here is what I learned from physics textbooks in grad school:

Let m

_{g} be the gravitational mass of object 1, M

_{g} be the gravitational mass of object 2, G be the gravitational constant, and r be the separation between the masses. Then the gravitational force on object 1 is F

_{g} = Gm

_{g}M

_{g}/r

^{2}. So, the gravitational mass determines the strength of the gravitational force on an object. The strength of the gravitational field created by object 2 at location r is g = GM

_{g}/r

^{2}. Then the force is F

_{g} = m

_{g}g. (Although many people do it, I think it is confusing to call g the "acceleration of gravity".) The force F

_{g} is called the "weight" of object 1. According to this treatment (which is the standard treatment taught in university physics classes), the gravitational mass of an object does not depend on the gravitational field, but the weight does. Note also that the gravitational mass of object 1 does not depend on object 2 at all. For example an object's gravitational mass is the same on Earth and on Jupiter, but the weights on Earth and Jupiter are very different because Earth and Jupiter create different gravitational fields.

Let m

_{i} be the inertial mass of object 1. When a force F acts on object 1 its acceleration will be a = F/m

_{i}. The inertial mass determines the relationship between any force (whatever its cause) and object 1's acceleration.

Experiments showing that m

_{g} = m

_{i} are routinely done in introductory physics laboratory classes.

**In my opinion the coincidence that m**_{g} = m_{i} is very surprising!!! For all other types of forces (for example electrical forces) there are other "charges" that determine the strength of the force, but in this way gravity is special. The theory of general relativity is built in such a way that m

_{g} = m

_{i} from the foundation of the theory, but it still does not

**really** tell us why gravity has this property that other forces don't have. This coincidence of m

_{g} = m

_{i} is the main problem of uniting gravity and quantum theory -- the biggest current problem of fundamental physics.

I have seen these quotes from sources like

*Encyclopedia Britannica*, which says "Gravitational mass is determined by the strength of the gravitational force experienced by the body when in the gravitational field g.", but I think they are confusing because of their use of passive voice. What they mean is that you can determine an object's gravitational mass by putting it in a gravitational field g and measuring the force F

_{g}. If you know g and F

_{g}, then you can calculate m

_{g}=F

_{g}/g. Given the way that the

*Encyclopedia Britannica* article discusses weight vs mass earlier in the article, it would not make sense to interpret this sentence in any other way. The authors assume that the reader has already understood that "mass" always refers to an object's own properties not related to its location or other surrounding objects.