The observed positions of the planet were not the positions that they occupied at the instants when they were observed. This may seem tedious, but of course with a computer, all one needs is a single ...The observed positions of the planet were not the positions that they occupied at the instants when they were observed. This may seem tedious, but of course with a computer, all one needs is a single statement telling the computer to go to the beginning of the program and to do it again. I am not going to do it with our particular numerical example, since the “observations” that we are using are in fact predicted positions from a Minor Planet Center ephemeris.