which factor mass or distant changes the result of the gravitational force the quickest? Why?

Answer 1

In general, distance changes will have the greater effect... and of course, if you only are allowed to either double, triple, etc... one of the masses, or double, triple, etc... the distance, then distance will have the greater effect.

Grav Force = G m M / [ dist ]^2

G = grav constant ; m, M are the masses of the two objects, and dist = distance between the two objects...

Notice the [ dist ]^2 term in the denominator... squaring a number will change the answer more than just multiplying one of the masses above by that number....

For example, if you double the the value M, the Force will be 2 times the orig force, but if you double the value of distance, it is then squared, and you will make the denominator larger by a factor of 4, which has the greater effect ....

note also that taken together, the Force in the above example would be 1/2 the original [ mult by 2, but divide by 4 ] ... and distance again has the greater effect...

Now, if you change one of the masses a lot, while only changing the distance very little, the mass can affect the Force by a greater amount ...

The distance squared in the denominator results in what scientists call an 'inverse square law', one of several you may come across in Physics...

Answer 2

Distance, since it's an inverse square relationship and mass is only a linear factor (and the universal gravitational constant is -damn- sure not gonna change ☺)

Doug