How the law of inertia got discovered?

Question

In the Feynman lectures, it is mentioned that [Vol 1; Gravitation]:

Galileo discovered a very remarkable fact about motion, which was essential for understanding these laws. That is the principle of inertia—if something is moving, with nothing touching it and completely undisturbed, it will go on forever, coasting at a uniform speed in a straight line. (Why does it keep on coasting? We do not know, but that is the way it is.)

How Gallileo discovered the law of inertia ? In those time, there were probably no frictionless area so that he could test his hypothesis. And uncontrolled "thought experiment" can lead you astray like Aristotle (who belived that continuous force is required to get a particle moving all the time).

Here, I do find Feynman's quotation (of Tycho Brahe's "idea" ) relevant, but I can't make the connection:

This [debates about the nature of the motions of the planets would best be resolved if the actual positions of the planets in the sky were measured sufficiently accurately] was a tremendous idea—that to find something out, it is better to perform some careful experiments than to carry on deep philosophical arguments.

A quote by Paul Dirac is also relevant here (not directly, the bold words are only relevant):

". For example, rough experiments about the relation between the pressure and volume of a gas at a fixed temperature give results fitting in with a law of inverse proportionality, but it would be wrong to infer that more accurate experiments would confirm this law with greater accuracy, as one is here dealing with a phenomenon which is not connected in any very direct way with the fundamental laws of motion.",

How you can be sure that the less friction you use, the more accurate it becomes ?

Update: Since most of the person are focusing on galileo did that (my ill written title misled them), I actually wanted to know how scientists get rid of their Aristotlian intuition and developed the idea (notion) of inertia.

Answer 1

Galileo' formulation of inertia is not "perfectly" newtonian.

See the discussion into his Dialogo (1632), page 128 of Th.Salusbury's English translation (1661):

[page 128 ] SALV. Now tell me, what would befall the same moveable upon a superficies that had neither acclivity nor declivity?

SIMPL. There being no declivity, there can be no natural incli­nation to motion: and there being no acclivity, there can be no resistance to being moved; so that there would arise an indifference between propension and resistance of motion; therefore, methinks it ought naturally to stand still. [...]

SALV. Well: but if there be no cause of retardation, much less ought there to be any cause of rest. How long therefore would you have the moveable to move?

SIMP. As long as that superficies, neither inclined nor decli­ned shall last.

SALV. Therefore if such a space were interminate, the motion upon the same would likewise have no termination, that is, would be perpetual.

SALV. That hath been already supposed, when it was said, that all external and accidental impediments were removed, and the brittlenesse of the moveable in this our case, is one of those impediments accidental. Tell me now, what do you think is the cause that that same Ball moveth spontaneously upon the inclining plane, and not without violence upon the erected?

SIMP. Because the inclination of grave bodies is to move to­wards the centre of the Earth, and onely by violence upwards to­wards the circumference; and the inclining superficies is that which acquireth vicinity to the centre, and the ascending one, remotenesse.

SALV. Therefore a superficies, which should be neither de­clining nor ascending, ought in all its parts to be equally di­stant from the centre. But is there any such superficies in the World?

SIMP. There is no want thereof: Such is our Terrestrial Globe, if it were more even, and not as it is rough and montai­nous; but you have that of the Water, at such time as it is calm and still.

SALV. Then a ship which moveth in a calm at Sea, is one of those moveables, which run along one of those superficies that are neither declining nor ascending, and therefore disposed, in case all obstacles external and accidental were removed, to move with the impulse once imparted incessantly and uniformly.

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The newtonian formulation is basically due to Descartes' Principia philosophiae (1644), art.XXXIX:

Altera lex naturae: quod omnis motus ex se ipso sit rectus; et ideo quae circulariter mouentur, tendere semper ut recedant a centro circuli quem describunt.

Answer 2

Galileo, Newton, or even the medieval physicist Jean Buridan (1295-1358), who developed the notion of impetus, were not the first to discover the law of inertia.

The first was John Philoponus ("The Grammarian"), who lived in the late 5^th and 2^nd ½ of 6^th century A.D.

From his Dictionary of Scientific Biography entry:

Philoponus’ main significance for the history of science lies in his being, at the close of antiquity, the first thinker to undertake a comprehensive and massive attack on the principal tenets of Aristotle’s physics and cosmology, an attack unequaled in thoroughness until Galileo.

From here, Philoponus

argued that the sun is fire and of terrestrial-like, corruptible matter. He devised a precursor to the notion of impetus which Buridan later developed, that which keeps moving bodies in motion even after the mover ceases being in contact with them; air does not keep projectiles in motion. He discovered that light rays travel the same both backwards and forwards. He invented functions of variables and their "courses" (what we'd call "first derivatives" in modern calculus). He discovered the law of inertia, that bodies in motion remain in motion unless something impedes their movement, literally a thousand years before Galileo, Newton, et al.!

He's certainly one of the "grands génies de l'Antiquité" ("great geniuses of Antiquity") and "principaux précurseurs de la Science moderne" ("principle precursers to modern Science"), as [the historian of medieval physics] Pierre Duhem wrote.

Answer 3

I don't have any references, but I recall reading that he used inclined planes and marbles. Since the speed of a rolling marble is far less than a free falling one, air drag is much less noticeable.

He then realized that if you let a marble go down a slope it will gain velocity, and if then it is forced to go up another slope, ir will stop at exactly the same height where it started, no matter the angles of the slopes.

A similar experiment can be made with a pendulum: no matter if you bend the thead, the top height of the pendulum at both sides of the oscillation is always the same.

Then Galileo reasoned: if the angle of the second up slide is very small, the distance needed to reach the original height will be very large. And if the angle is exactly 0, then the distance will be infinite and the marble will roll forever!

The failure in Galileo theory is that it only worked horizontally. You have to wait until Newton to get a really general law of conservation of movement.