A Planets Mass

[igosaur]

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?

[timo]

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.

[swansont]

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.

[thedarkshade]

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!