Quick question that has been bugging me for a while.

 

I was looking into the recent discovery of a new 'Earth like' world, Gliese 581 c, which has a mass 5 times that of the Earth.

 

However, its gravity would only be twice that of our planet.

 

Question: Why is the gravity not 5 times as much if the mass is?

How do you quantify gravity? My guess would be that "twice of our planet" means that the acceleration due to gravity at the surface is twice that of earth. The 5-times mass can then be countered by a larger radius, i.e. you are comparing values at different distances from the respective centers.

or, to quantify that,

 

a = GM/r^2

 

mass grows with r^3 if you have the same density. a should be 5^(2/3) = ~3 times larger , so one can conclude a slightly smaller density than earth.

Question: Why is the gravity not 5 times as much if the mass is?

It is because of density! Swans above has given the equation why it is that way!