orbital elements - How do I calculate the positions of objects in orbit?

I'm not sure how much this will help, but I can give you this passage from Wikipedia:

Under ideal conditions of a perfectly spherical central body, and zero perturbations, all orbital elements, with the exception of the Mean anomaly are constants, and Mean anomaly changes linearly with time[dubious – discuss], scaled by the Mean motion, $n=sqrt{frac{mu } {a^3}}$. Hence if at any instant $t_0$ the orbital parameters are $[e_0,a_0,i_0,Omega_0,omega_0,M_0]$, then the elements at time $t_0+delta t$ is given by $[e_0,a_0,i_0,Omega_0,omega_0,M_0+ndelta t]$.

In other words, most of the orbital elements (save $M_0$) are constant under very short intervals.