According to a book I am currently reading, space rockets and ballistic rockets fly along an elliptic path. However they differ in where the focus of the ellips describing their path lays. For space rockets on of the foci is placed at the center of the sun (for ballistic rockets it is the center of the earth). Could someone explain, why the center of the sun?
I think you have a misleading picture here.
Earth orbit bounds rockets have the earth as the centre of their ellipse.
However; for interplanetary travel, or anything that goes beyond the earth sphere of influence, your rocket will orbit the sun, hence an elliptic sun centred trajectory.
The first part of the trajectory will however, always be earth centred (that is, until you escape the earth system).