Why is that? Are you saying that universal function approximators can't invent higher level models? Isn't that what happens in the hidden layers when an neural network is trying to predict things that require those higher level models?
you'd need to measure the force between planets, the distance between them, etc. no such direct measurements have taken place to my knowledge, certainly not at newton's time
All "universal fn approximator" means is that given any dataset which is sampled from a function, you can recover that function with enough data points. It does not mean, eg., that given a 2D dataset you can derive a 3D function -- you cannot, this is impossible.
So you need to be sampling from F=GMm/r^2 to find that function. So you need to know the answer before you begin. Fn approximators are only useful for empirical refinements to existing knowledge.
In order to construct such datasets you need to do science; hence experiments, etc.
The issue is that to prepare the dataset from which that formula is learnt requires already knowing it. This is the triviality of applications of universal function approximators to science -- empirical data modelling isnt new, and neural networks are just one example of it; not all that special.
All observational data on the solar system, at any point in time, would not yield this formula via empirical function approximation. there really isnt "observational data" to collect, in this sense
This is what I mean about rigging -- there is no 'bare dataset' which tells you what the world is like. to construct experiments which yield data that 'presents' scientific laws as if statistical patterns requires millenia of theory-building science
science uncovers the necessary causal relations between objects and their properties, as determined by extremely controlled experiments which take millenia of engineering and theory-building to even conceive, let alone execute
stats is the dumb 'accounting' of this data -- by the time you actually have it all the science (and indeed, all the intelligence) is done
what can be automated at this point is 'stamp collecting' as rutherford said