In the past, when discussing the role of chaos in climate models, I’ve been known to argue that the complexity of multi-body dynamical systems means that we could probably not run a model of the formation of our Solar System that would actually produce a result entirely consistent with what we see today. That doesn’t mean, however, that we can’t use such models to understand how our Solar System formed and evolved. Similarly, that climate models are inherently chaotic does not mean that we cannot use them to understand how our climate might respond to changes in anthropogenic forcings. The response I would typically get is that gravity is verified/validated (or whatever other term the person chooses to use) but climate science is not (ignoring that much of the underlying physics is about as well understood as gravity).
Ignoring the complications of General Relativity, the gravitational force between two bodies of mass and a distance apart is
where is the gravitational constant. If you look up the value of you’ll find that it is something like m3 kg-1 s-2. However, John Mashey has pointed out in a comment that it may not be quite as well known as one might think (I’ve since found another article that discusses this). It turns out that the experiments that are trying to measure the gravitational constant disagree quite markedly. In fact, if you look at the figure below, they not even disagree with each other, some are actually quite discrepant with respect to the currently accepted value. Given that we know the value of some constants to many more significant figures than we do , this is somewhat surprising.
So, we don’t know the value of nearly as precisely as we do other constants, and independent experiments don’t even agree particularly well. Is this some kind of controversy and does it really matter? Firstly, I’m not even sure how many people are actually aware of this issue. Also, the gravitational force is extremely small compared to the other forces, so it is maybe not surprising that it is extremely difficult to make a precise measurement. None of this, however, suggests that it isn’t a constant. Given that, not knowing the precise value is not really a particularly big deal.
One way we use gravity is to estimate the masses of astrophysical bodies (by observing the orbits of other bodies and then using Kepler’s laws). However, we don’t understand the internal structure of these bodies well enough to independently estimate their masses with more accuracy than we can get using gravity, even if isn’t precisely known. Therefore, a possible error of a fraction of a percent is not that significant. Also, most gravitational calculations/simulations are scale free; they assume . In this case, mass ratios might be important, but if all the masses have been estimated using a consistent value for , then this will be fine. You can then convert from scale-free to real values by assuming a value for . Therefore, even though we don’t have a precise value for doesn’t mean that we can’t trust simulations of the dynamical evolution of our Solar system, simulations studying the future paths of Earth-crossing asteroids, or even those that investigate the evolution of our universe. It doesn’t really matter.
So, since John pointed this out, I thought I might write a brief post. It’s certainly interesting in its own right, but also shows how people can recognise that even if we can’t measure something precisely, we can still do lots of interesting research as long as we understand the situation and as long as we’re consistent. Noone’s shouting that we can’t do any dynamical N-body calculations until we’ve estimated to 8 decimal places, because everyone recognises that it doesn’t really matter.