Gravitational Field from Irregular Object How does one calculate the gravitational field of an irregularly shaped object? I was thinking specifically of the gravitational field due to a human, and tried to see if modeling a human as an infinite wire would work, and of course it's a horrible approximation*. 
Is there anyway to do it without relying on a computer, or is numerical approximation the only option? And even with a computer, what process does it actually do to get an answer? I would assume that it uses superposition with $\vec{F}= \frac{GMm}{ \vec{r}^{2}} \hat{r}$, which would work for an irregularly body acting on a point particle, but how would you calculator the field of two irregularly shaped bodies acting on each other?  


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*I used Gauss's law for Gravitation, and ended up with a distance of 289 Å, which would make the acceleration equal to $g$, which sounds really wrong, considering that the distance between atoms is only on the order of a few Å. 

 A: Firstly, I tried to reproduce your thin wire calculation : if you assume a wire of mass 60kg with a length of 2 metres, then I reckon the magnitude radially symmetric field near the middle of the wire from your Gauss law technique at $\frac{2\,G\,M}{\ell\,r}$ with $m = 60\mathrm{kg}$ and $\ell = 2\mathrm{m}$, which works out for me to give $r = 4\times10^{-10}\mathrm{m}$ to get the same attraction as at the Earth's surface with $G = 6.7\times10^{-11}\mathrm{m}^3\mathrm{kg}^{-1}\mathrm{s}^{-2}$. Gravitation is $very$ weak in comparison with other everyday forces - think of the classic trick of picking a nail up with a magnet: the currents in the tiny magnet are overwhelming the gravitational attraction of the $whole\,Earth$. Your wire model will be more accurate than you might think (see a few paragraphs below).
Really, for irregular shapes, numerical methods are the only way. And, to calculate the gravitational field at any point, they work pretty much as you would think, either summing up the fields from finite element masses calculated individually with the $\frac{G\,\Delta M}{r} \hat{\mathbf{r}}$ formula, or by solving the Poisson equation $\nabla^2 \phi = 4\,\pi\,G\,\rho$, where $\rho$ is the mass density and $\phi$ the gravitational potential. There are highly developed numerical algorithms for the Poisson equation, and then one just works out $\nabla \phi$ to get the field.
To get the force between bodies is a little less straightforward, as you seem to realise in your question, because the field is the force on a small test particle ($i.e.$ one too small to disturb the outside field). What you need to do is sum up the forces on all the point masses making up one body exerted by the point masses exerted by the other body. You do $\mathbf{not}$ include the force exerted by points in the same body on the other points in the same body. Thin of it this way. Suppose we have a human (human 1)begetting a gravitational field: then we bring in the first piont mass making up the other human (human 2): we calculate the force on the test mass. Then we bring in the second point mass making up human 2. The total force on this one is of course that owing to the human 1 $plus$ that from the first test mass in human 2. However, this latter force is balanced somehow by an internal pressure force within human 2. Otherwise human 2 would gravitationally collapse! So the nett force on the second point mass considered as part of human 2 is just the sum of the forces arising from human 1.
I would approximate two humans as long cylinders, not wires. Your Gauss technique will work just as well for cylinders in isolation (inside a long cylinder the gravitational field rises linearly with distance from the centre, inversely with radius outside). Then calcalate the forces by an integration keeping in mind the last paragraph. You won't be far wrong.
Another, beautiful way to get a good working idea of solutions to Laplace's equation (which is what you are doing outside the body) if you don't want to use a computer is the graphical technique of curvillinear squares. See http://www.ie.itcr.ac.cr/acotoc/Maestria_en_Computacion/Sistemas_de_Comunicacion_II/Material/Biblio2/chapt06.pdf.
