Methods are compared for computing the gravity vector outside the earth. The gravity vector is conveniently split up into a normal part, the vector of normal gravity, and an anomalous part, the vector of gravity disturbance. The theoretical foundations and a practical method are given first for the computation of the vectors of normal gravity and gravitation. The method is adapted for electronic computation. A numerical example is given. Accuracy studies are made next in order to determine the best practical procedure for the computation of the gravity disturbances.