Understanding physics starts with performing experiments and performing observations. The chalenge is to improve the experiments and the observations to improve our understanding.
A different line of attack is to use a mathematical model i.e. a set of equations, of the physical process involved and to match the results of the calculations with the observations of the experiments. In many cases the parameters of the mathematical model are not all known, that means in the first phase these parameters have to be calculted based on observations.
A different problem arises if all the parameters are known, but still the results of the observations don't match with the calculated results. In that case it makes sense to repeat the same observations at different location and observe is there is any discrepancy. If there is more study is required to explain these different observations, because specific observational errors can be involved.
If by repeating the experiments and all the results are the same (within a certain margin) the only reason can be in the mathematical model which is a representation of a physical model. Both have to be adapted.
The major problem is the 'exact' definition of what is the difference between an experiment, a law, a model and a theory.
- In an experiment all the variables involved should be measured as part of the experiment. The result of the experiment is one of these variables, which should match the predicted value, defined as the result of calculation using all the other variables.
- In the case of Newtons law the result of the experiment is the observed forward movement of the angle of the planet Mercury. The calculated or predicted angle is based on Newton's Law and the observed positions of the planets. This predicted value is not in agreement with the observed value, that means Newton's Law is 'wrong', and has to be adapted.