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Rather than leave these as comments, I guess I should answer it since this has come up before. A 2D simulation does not mean there is no third dimension. Rather, it means we are saying there is no variation in the third dimension such that $\frac{\partial}{\partial z} = 0$. But that depth direction still exists and we typically just call it a "unit depth" ...

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For two bodies this is relatively easy as the equations of motion describe a conic (an ellipse for a closed orbit, a hyperbola for an "open" orbit). You can use the vis viva equation to get the parameters of the orbit (semi major axis etc) from the given initial conditions, and the rest follows. For an ellipse, you can also express the position as a ...

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Molecular simulation is certainly used in the field of astrobiology. For example, here's a quote from a NASA technical report specifically on Molecular Simulations in Astrobiology: We use computer simulations to address the following, questions about these proteins: (1) How do small proteins (peptides) organize themselves into ordered structures at ...

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It sounds like you're trying to solve the Langevin Equation. This is a model of Brownian motion where the particle experiences stochastic kicks at discrete time intervals. Your force, in this case, is a random variable you draw from a distribution each time step (instead of being given by an explicit formula). For the simplest case, the "kicks" are ...

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The simplest way to look at this is to consider separately the horizontal and vertical velocity/position. For a projectile launched at angle $\theta$ and velocity $v$, the components are: Horizontal velocity $$v_h = v\cos\theta$$ Vertical velocity $$v_v = v\sin\theta$$ The position at time $t$ is then given by (x, y) = (v_h\cdot t, v_v \cdot t - ...

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I am assuming that you do want a simulation of the whole universe and not just a theory of everything. Your question should be decomposed into two questions. The first is really a mathematical question: Can a part (the simulator) simulate the whole ? Given a positive answer to the first question, the second is whether the mathematical structures thus ...

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