Assuming the expansion of the universe as a given fact, how does it influence orbits i.e. of the earth around the sun or other planets in the solar system? Is it also usually included into the calculation of trajectories of space crafts (i.e. Pioneer, especially with regard to the Pioneer anomaly)? Due to the universal expansion, the radius of the earth around the sun must be affected by it as well. The influence of the expansion on the earth orbit is very small but should still amount to approximately 0.5 meters every year. Is it the gravitational force of the sun which keeps the earth "on track" so the radius does not change at all?