Hi. I'm writing a simulation of (an approximation of) the solar system. So far I've been able to translate the Wikipedia article on Kepler's laws to a function that uses a description of an elliptical orbit (eccentricity, periapsis, known position in time) to return a position when passed an arbitrary time. My issue is with generating the ellipse when given only a position and a velocity; my analytical geometry-fu is too weak for conics. I can't find much info on this, beyond references to offloading the calculation to software suites (e.g. HORIZONS and SPICE), which is of no use to me. Can anyone give me a nudge in the right direction? Thanks.