That was more interesting than the dry title would've suggested. I was motivated by mild curiosity because in the distant past I've written simple orbital mechanics simulators, and I wanted to see if anything's changed. A lot has changed, but what struck me as most significant was a conceptual milestone: IntegratedRelativity™.

Seems that, up to now in astronomical models, relativity's been applied as an ad hoc error-correction at edge cases. The models have been basically highly-refined Newtonian mechanics characterized by brute-force number-crunching, like integration of simple gravitational vectors to simplify the three-body problem. Looks like the new models, though, have relativity built-in. It must make the models much more complex, but that's what we have computers for. In most cases relativistic factors would disappear into the noise, but if they're relevant, they're included automatically, making the models inherently more robust and reliable and accurate. Nice.

The new Einsteinian models have a consequence that kind of spun my around at first: The new models have almost no fundamental constants. (Well no, being relativistic, they wouldn't, but still, that's a paradigm shift that took me a minute to digest.)

This circular does not contain a list of adopted fundamental astronomical constants, because the IAU is no longer maintaining such a list. The last set of officially adopted constant values was the IAU (1976) System of Astronomical Constants. That list is almost entirely obsolete. ... It can be argued that a list of fundamental astronomical constants is no longer possible, given the complexity of the models now used and the many free parameters that must be adjusted in each model to fit observations. That is, there are more constants now to consider, and their values are theory dependent. In many cases, it would be incorrect to attempt to use a constant value, obtained from the fit of one theory to observations, with another theory.

We are left with three defining constants with IAU-sanctioned values that are intended to be
fixed:

(Wow, that last underlined bit struck me as the Theory of Relative Theories. See what happens when you let Einstein get his nose in the tent?)

What are the three remaining certainties in our universe?

1. The Gaussian gravitational constant: k = 0.01720209895. The dimensions of k2 are
AU3M
·−1d−2 where AU is the astronomical unit, M
· is the solar mass, and d is the day of 86400 seconds.

2. The speed of light: c = 299 792 458 ms−1.

3. The fractional difference in rate between the time scales TT and TCG: LG = 6.969290134×10−10.
Specifically, the derivative dTT/dTCG = 1 − LG.

It's comforting to know that I can still count on gravity and the speed of light. I'll get back to you when I figure out why it helps to know the difference between times scales TT and TCG....