13.11: Light-time Correction
Before going further, however, our current estimates of the geocentric distances are now sufficiently good that we should make the light-time corrections. The observed positions of the planet were not the positions that they occupied at the instants when they were observed. It actually occupied these observed positions at times \(t_1 − ∆_1 / c\), \(t_2 - ∆_2 /c\) and \(t_3 − ∆_3 / c\). Here, \(c\) is the speed of light, which, as everyone knows, is 10065.320 astronomical units per \(1/k\). The calculation up to this point can now be repeated with these new times. 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.