The cosmological constant. A small addition with a great effect

The consequences of a cosmological constant Lambda to cosmological models on the one hand and to Newton's gravitational law in the weak field expansion on the other hand are discussed. In case of a negative Lambda with \Lambda\ less than or similar to 10(-56) cm(-2) our universe is open but does not expand forever. Furthermore, its age is compatible with the age of the oldest globular clusters. On the other baud, Newton's gravitational law is modified by an additional attractive force term linearly increasing with the distance. This term acts only over wry large distances. If one assumes a value Lambda similar or equal to 10(-56) cm(-2) the additional term acts for stars over a characteristic scale of about 120 pc and for galaxies over a characteristic scale of about 0.8 Mpc. A positive cosmological constant Lambda similar or equal to 10(-56) cm(-2) leads to an additional repulsive force which would have prevented the existence of galaxy clusters.