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This assert cannot be proved empirically, because no one can observe forever the body moving.

The idea, empirically, is that for a body to alter his movement is necessary to act upon it something external to he body. This cannot be proved neither empirically.

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You are correct. Following the philosophy of science developed by Popper, we can never confirm anything to be 100% true, but must instead consider statements which simply have not yet been falsified. So far the statement that a body will keep moving at a constant speed if nothing acts upon it has not yet been falsified, as all observable predictions of this statement have indeed been observed empirically.

You can also consider the second statement justified through indirect observations: A planet orbits a star because of gravitational attraction. By measuring the movement of the planet, it can be shown that all acceleration / change in movement is accounted for by the influence of gravity (to a basically infintely good approximation). Thus, if one were to remove the gravity, one would also remove the only source of acceleration. Under the assumption that the behaviour of the system does not change over time, it will then continue with constant speed forever (or until it meets a new source of acceleration).

This example uncovers one of the basic assumptions of physics: That the basic laws of physics are the same at all times and in all points of space. If I conduct an experiment in Alpha Centauri, it should give the same result as here. If I conduct an experiment a million years into the future, it should give the same result as now. This is of course impossible to prove, but has not yet been falsified, and stands as an axiomatic assumption behind all physics.

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Newton set out his "Rules of Reasoning in Philosophy" in Book III of Principia and they are still the basis for science.

Rule 1: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

Rule 2: Therefore to the same natural effects we must, as far as possible, assign the same causes.

Rule 3: The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

Rule 4: In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, not withstanding any contrary hypothesis that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

They are still a pretty good basis for "doing science". Of course you can choose to ignore them, but the result of doing that is likely to be something different from the mainstream notion of "science".

Of course, following these principles doesn't make any conclusion "true". In fact Newton inadvertently gave an excellent example of that in his discussion of the principles in Principia itself, when he used the illustration that a coal fire on earth produces heat, and therefore following Rule 2 one should assume the heat of the sun is produced in the same way!

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