I'm trying to figure out what the mass or the average density of the Earth would be if it were made of the same material, but more of it, to the point that its radius were 4 times larger. My ultimate goal is to use this information to predict the surface gravity (relative to that of our current Earth) that one would encounter if the Earth were 4 times as wide, according to the equation Surface Gravity = (Mass (4r Earth) / Mass (1r Earth)) / (4^2). However I've run into a complication. I understand that as things (planets) increase in size, they compress under their own weight, meaning that the Earth would have a lower average density if it were smaller and less massive, and would have a higher average density if it were larger and more massive. As such, I would expect that it's mass would not increase linearly in relation to a change in radius. I understand that Density = Mass / Volume, and that M = D * V. However, according to this equation, one always needs either mass or density in order to calculate the other. While figuring out the Volume of "4r Earth" is easy, I have neither density nor mass, and am not sure how to determine either, independently. What I need is a way to calculate either mass or average density based on the radius alone, by predicting the extent to which the planet would compress under its own weight as the radius increased. Is there some kind of equation that can describe the compression of a planet as it increases in size, so that one can determine the true mass or average density that would result from an increase in its radius? We can assume that the planet is a perfect sphere. I know that there are different layers within the Earth, with different elemental compositions. I'm not sure to what extent this would play a factor, but I would expect that different substances compress to different extents, as pressure increases. If need be, perhaps we can assume a uniform composition throughout. Any help or advice is welcome. I honestly don't have a clue what to do. Feel free to let me know if we need more info and I'll do what I can to hunt it down. Thanks!