Cosmological perturbations on local systems

We study the effect of cosmological expansion on orbits--galactic, planetary, or atomic--subject to an inverse-square force law. We obtain the laws of motion for gravitational or electrical interactions from general relativity--in particular, we find the gravitational field of a mass distribution in an expanding universe by applying perturbation theory to the Robertson-Walker metric. Cosmological expansion induces an ($\ddot a/a) \vec r$ force where $a(t)$ is the cosmological scale factor. In a locally Newtonian framework, we show that the $(\ddot a/a) \vec r$ term represents the effect of a continuous distribution of cosmological material in Hubble flow, and that the total force on an object, due to the cosmological material plus the matter perturbation, can be represented as the negative gradient of a gravitational potential whose source is the material actually present. We also consider the effect on local dynamics of the cosmological constant. We calculate the perihelion precession of elliptical orbits due to the cosmological constant induced force, and work out a generalized virial relation applicable to gravitationally bound clusters.Comment: 10 page

Starting a new business later in life

Self-employment in later life may be either a career option or a form of partial retirement. This paper adds knowledge about those individuals who start a business when they are older. A large longitudinal data set is utilized to examine the transitions of individuals aged 55–74 to self-employment in Finland. The significance of prior activity as well as personal, household, financial, and environmental characteristics is analyzed for the transitions. The results show that most of those entering self-employment in later life have prior self-employment experience, thus suggesting that entrepreneurship at later ages is often habitual. Habitual entrepreneurs deviate from novice entrepreneurs in many respects at older ages: they are less educated, more likely men, and live mostly in urban areas. An entrepreneurial spouse has a significant effect for both, but this effect is greater for novice entrepreneurs. In most cases, a large income increases the probability to start a business at older ages.peerReviewe