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Originally posted by apache:
Well, I looked up planet surface gravity, and all kinds of other stuff just to find out where you got your information. Yes, I did find plainly given stats that claimed the surface gravity compared to earth's surface gravity. Now, I calculated through the numbers using the universal law of gravitation, and the maximum radius of Jupiter. This gives the aforementioned statistics that Jupiter's surface gravity is approximately 2.5 times that of earth's. However, the fact is that the 'surface gravity' here is the gravity at Jupiter's outer atmosphere. We don't know where the surface of Jupiter actually lies, and as such, using such a statistic to calculate gravity at the 'surface' of jupiter is pretty ridiculous.
Well, if you want to be picky
, but remember that when you get all the way down to the center of Jupiter, gravity is zero because you have an equal amount of mass pulling in every direction. The pressure is pretty high though. The point, however, is that raynor and Barnacle Bill posted about how high gravity would be on a gas giant, but it isn't. It's similar to Earth's in many cases because of the low density of gas giants.
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If Jupiter had a solid core the size of earth, for example, the gravitational acceleration there would be about 3520 times that of Earth's.
I'll have to question your math here. Jupiter has 318 times the mass of Earth so if it were the same size as Earth, it would have 318 times the density and, consequently, 318 times the gravity.
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Oh, and I still have no idea where you found that gravity is some function of density, because its absolutely untrue. It is a function of mass and distance only. This is related by the equation, a=GM/(r^2) where M is the mass of the planet in kilograms, r is the distance from the center of that planet in meters, and G is the univerersal gravitational constant, 6.672*10^-11. This gives you the acceleration due to gravity.
Perhaps you weren't aware that mass is a function of density, namely density times volume, and that the volume of a sphere is a function of r^3 (4/3 pi r^3 IIRC). Therefore, the simplest form of the gravitational equation is a constant (4/3 pi G) times density times radius. So if you used this form of the equation, gravity would depend only on density and radius. In reality, the three variables (mass, density and radius) are interrelated, and the equation can be written using any two of the three. You can, however, have two planets with identical masses but different densities that have widely different surface gravity. In that case, gravity would vary with density to the 2/3 power.