The Number of Planets Around Stars
Based on the large number of elliptical planetary nebulae I argue that about 55 per cent of all progenitors of planetary nebulae have planets around them. The planets spin up the stars when the later evolve along the red giant branch or along the asymptotic giant branch. The arguments, which were presented in several of my earlier works, and are summarized in the paper, suggest that the presence of four gas-giant planets in the solar system is the generality rather than the exception. I here continue and: (1) examine the possibility of detecting signatures of surviving Saturn-like planets inside planetary nebulae, and, (2) propose a model by which the second parameter of the horizontal branch, which determines the distribution of horizontal branch stars in the HR diagram, is the presence of planets. A red giant branch star that interacts with a planet will lose a large fraction of its envelope and will become a blue horizontal branch star.