Monthly Notices of the Royal Astronomical Society, vol. 111(6): 107-116, 1951.
My outlook on computing has been rooted in my work in astronomy, in which I was engaged over a period of 16 years, starting when I was 14 years old. With such roots I have never been surprised about the difficulty of achieving correctness in computing: for centuries the astronomers have been responsible for producing correct figures in the almanacs on which the lives of the sailors depended, and have had to live with the daily drudgery of checking and double checking. This concern is also quite visible in the present sample of my astronomical work. As a help to the astronomically uninitiated reader it may be mentioned that the problem treated in the work is the basic one of computing the motion of a small body, such as a minor planet, through the Solar System, according to Newtonian mechanics. The forces are the gravitational attractions from the Sun and the seven major planets. It is thus a problem of a set of ordinary differential equations. Astronomers talk about perturbations because the attractions from the planets are small compared to that from the Sun and are often treated as a perturbation to the elliptical motion of the two-body situation involving only the minor planet and the Sun. The perturbations are called special when they are determined by a step-by-step numerical integration, and not by an analytical form of approximation. It may further be added that the present work is one out of a series of my works in this area, of which the others deal with applications to a particular planet, including determinations of its position by measurements on the night sky, thus spanning the complete range of empirical and theoretical astronomy.
The problem of special perturbations has been prepared for the electronic calculator EDSAC in Cambridge. The machine is made to perform a step-by-step integration of the equations of motion, taking the attractions of all the major planets into account, and its prints the date and the three Cartesian coordinates for each step. The various sources of errors are discussed and it is shown that the accuracy of the method applied to a minor planet is 10-9 astronomical units. The total time required when using this method is between 4 per cent and 10 per cent of that required when using an ordinary desk computing machine.