On 12/5/23 01:26, Darryl Gregorash wrote:
I rather doubt one needs that much precision for astronomical calculations, especially when working with an object that a) has an angular diameter of approximately 0.5 degrees, and b) is an oblate spheroid whose oblateness isn't really known to very much precision. I used LHC and LIGO as examples, because those are two examples where high precision is really needed. In the case of LIGO, for example, the delay is very, very small between receiving a true wave signal at each detector (gravitational waves travel at the speed of light). With the LHC, the time windows are even more critical, given a) the huge numbers of decay products that happen between the original collision and detection of the final decay products, and b) the relatively small sizes of the detectors. Besides, that equation you give looks to me like a perturbation expansion, unlikely anything close to single precision, and only taken out to 3 terms.
All depends on the number of coordinate system transformations involved before and after where precision bleed hurts. The transendentals and angular conversions (especially for angles near 0 and Pi). LHC and LIGO are both good examples. Monitoring for 10 billion year old gravity-waves is serious business :) -- David C. Rankin, J.D.,P.E.