A planet moves round the Sun in an ellipse of eccentricity $0.50$, with a period of $12$ years. B and B' are the two ends of the minor axis, and P is the point nearest the Sun, as shown in the figure. How long does the planet take to go from B to B' through P?

Fig. 1: An elliptical orbit of eccentricity 0.5 with centre C and the Sun at the right focus F. The dashed minor axis has ends B at the top and B' at the bottom, P is the perihelion at the right end of the major axis, and an arrow shows counterclockwise motion.