Analytical expressions of the Earth's position and velocity for the calculation of apparent positions

In order to calculate the apparent places of stars, the barycentric and heliocentric positions of the Earth and the barycentric velocity of the Earth are required. It is shown that several tens of trigonometric terms for their expressions are sufficient for analyses of optical observations which have an observational accuracy of the order of 0.001. We also give the analytical expressions of the position and velocity of the Earth with higher precision so that we can use them in the analyses of precise astrometry such as VLBI observations.