Keplerian orbits
In the two-body problem, a bound orbit is a conic section — an ellipse for closed orbits. The Sun sits at one focus. The shape is set by six orbital elements: semi-major axis, eccentricity, inclination, longitude of ascending node, argument of perihelion and mean anomaly at epoch.
Real solar system
Planets mutually perturb one another; orbits are not fixed ellipses but slowly evolving curves. High-precision ephemerides integrate the n-body equations, as in Jean Meeus' Astronomical Algorithms.
