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tarheel91 on 21 December 2009
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famousringo said:
tarheel91 said:
famousringo said:

Can somebody explain to me how this planet could have six times the Earth's mass and yet less gravity? Is it a matter of density and how far into the atmosphere you have to travel before you reach the surface?

Edit: Maybe they're figuring in displacement as if you didn't have to visit the planet inside a sturdy pressure hull?

The accleration you experience caused by an object equals GM/r^2 where G is a constant, M is the objects mass, and r is the distance between you and it.  When you put in Earth's mass and radius, you get 9.81 m/s^2 (or 1g).  When you put in 6.55 times the mass of the earth and 2.678 times the radius of the earth, you get 8.96 m/s^2 (or .913 g).  You can try it yourself.

More plainly, distance (radius) plays a larger role in the gravity than mass because it's squared, as opposed to just being to the first power like mass.

 

Edit: So, even though mass is 6.55 times bigger and the radius is only 2.678 times as big, the increased radius has a larger effect because it's squared in the equation (2.678 squared is 7.17).

Great explanation. Thanks for the formula and everything. That square explains the really counter-intuitive part. I'm just so used to thinking of planets as either dense rocks or enormous gas giants.

No problem, haha, Physics 205 saves the day.  I wasn't sure how complicated to get.  The formula can be confusing to someone who isn't the math type.