Just imagine you are launching from earth to the moon and one of your calcs should have "Floored" a value but you did not. So a bad scenario is that your trajectory is out by 16%. Will have to burn a lot of fuel to correct the error.
That made me smile. Unfortunately, I only discovered this thread very late, I currently have a small problem with one red bar too many on the test strip...
I can reassure you Johan, this error would have been noticed earlier. At the latest with the orbit calculations for the orbit of the moon itself. As you may remember, I had exactly the same problem when implementing the orbit calculations for the Earth's satellite in my compass app, where I really wanted to map the moon and the sun to the corresponding position on the compass rose. I encountered the same problem there. Extreme deviations in the calculations due to minimal rounding differences in the floating point arithmetic. Well, at some point I solved the problem after weeks by reading a lot about orbital position calculations and then somehow got a usable result. I can't even say whether everything is 100% correct. But somehow it works for my purposes.
And one way or another, you always stumble across things like this. Have any of you ever tried to accurately calculate the movable Christian holidays and transfer them to our modern calendar system? It just gives you a headache at some point.
I had all the more respect for a mathematician who solved this problem for us centuries ago: C.F. Gauss. I still haven't completely understood his "Easter formula", but it works.
Back to the moon for a moment: please take a look at the film "HIDDEN FIGURES". A great film for several reasons. I still don't understand how the Americans managed (and dared) to fly to the moon and back again with an on-board computer that was not much more than a "pocket calculator" of our days. My respect for that. At the same time, it is all the more shocking to see how this was compatible with the racial ideology of the time, which is also beautifully and lovingly portrayed in this film. Take a look at this film. And well, I'm also a little proud of the first NASA "supercomputer" shown in the film, an IBM 7090, because I worked many years for IBM. A great time.