You can place the Planet(X,Y,Z,T,eccentricity) anywhere and then as the time variable changes you can adjust the coordinates.
If the orbits are not affected by other objects, then the orbit will always be constant. As such you can determine ALL possible intersection points ahead of time. This will greatly reduce your need to check for intersection/collisions. For each planet you will have a very limited number of points for possible intersections. Planet A might have an intersection with Planet C & Planet H. After you have adjusted all coordinates (for all the planets), check the distance between planet A & planet C ; then check the distance between A & H. If the distance exceeds the radius of the collision limit then there will not be a wonderful fireworks display.
It is really more fun to use the interaction that gravity plays with the entities.