What would happen if the force of the gravity was increasing with the distance?

All that you have studied one day little physics you will not have problem too much in remembering the called law of the universal gravitation, enunciated by Isaac Newton any more than 300 years ago and published in 1687 in his famous ones It "Begins", perhaps the most influential scientific work of the history of the humanity. The legend that he accompanies to this law (certainly, that for only a few days is already not a legend, since there is written steadfastness of which it happened really) tells that it occurred to Newton while he was listening to the noise of an apple after there rushed to the soil from a branch of his tree mother (one notice the party indexes to "Incarnation"). He wondered what could be the force that could explain the fall of the apple and the movement of the Moon about the Earth. And it found it. A simple, beautiful law. Expressed briefly he was coming to affirm that between two any bodies of the universe an attractive force existed, an action over a distance that it was increasing proportionally with the values of the masses of both bodies but that, on the other hand, was diminishing in inverse reason with the square of the distance that was separating them.

This force had the same nature, already out between the apple and the Earth or between this one and the Moon. All the bodies of the universe were moving following orbits determined by the law of the universal gravitation. It was proper Newton who deduced how there would be the geometric forms of the orbits or trajectories that should describe the planets, asteroids and comets about the Sun or also an apple dropped close to the terrestrial surface, as well as if it was thrown by different impulses from the top of a mountain. The above mentioned trajectories could be only three classes: parables and hyperbolas (open curves) and ellipses (closed curves). The above mentioned, that is to say, that the orbits were elliptical in case of the planets and the Sun had been already discovered by Johannes Kepler in 1609, when it enunciated the first two laws of the planetary movement that take his name, basing for his deduction on the precise remarks carried out by the Danish astronomer Tycho Brahe. In the first one of them, Kepler was establishing that all the planets of the solar system were moving about the Sun following ways with elliptical form, being always the Sun placed in one of two foci of the above-mentioned curve. The circumference was a particular case of the ellipse, that one in which both foci were coinciding with the same point (the center of the circumference). Nine years later, in 1618, Kepler would complete his work with the statement of a third law. This one establishes that the time that uses every planet in giving a finished return about the Sun depends on the mutual distance between them. More exactly: the square of the period of rotation is straight proportional to the bucket of the biggest semiaxis of the orbit. This way, the duration of the years in other planets more removed from the Sun than the Earth is every time major as his distance increases our star. On the other hand, Mercury (88 days) and Venus (225 days) they have years shorter than the terrestrial ones.

Like already handyman, Johannes Kepler discovered his laws of empirical form, based on extraordinarily precise astronomical remarks on that epoch. Nevertheless, it had not even idea of which age the deep reason in which they were resting his discoveries, that is to say, did not know the mathematical form that had to have the interaction force between the Sun and the planets. So in the year 1684 he decided to come to Newton, who informed him almost immediately that the mysterious force for that Kepler was looking was verifying the famous law of the inverse one of the square. It was doing years that Newton was supporting a series of sour discussions and philosophical battles with Robert Hooke. Apparently, the last one had proposed to him to Newton the idea of the change of the force with the inverse one of the square of the distance and had suggested him the resolution of the mathematical problem. Newton never recognized the value and the ideas of Hooke.

Although I do not know and (still) I have not managed to find the original sources, it seems that the first ideas of Hooke on the concrete form of the law of the gravitational force supposed that this one was similar to the exercised one by a wharf on a body subject to him for an end. This way, he was imagining the Earth joined by a gigantic wharf to the Sun. In 1660, Hooke had thought that the above mentioned flexible force was proportional to the stretching of the wharf. How in case of a planet and the Sun was the stretching of the wharf major major all that was turning out to be the distance between two stars, the gravity was increasing with the distance instead of diminishing with the square of this one, as we know nowadays.

But perhaps you are wondering how it is possible that there could occur to someone similar idea, an idea seemingly frenzied and arisen from the boldest history of science fiction, worthy of the most creative movie of the genre in the last years (separate, clear Roland Emmerich). If you have been attentive to the dates, you will have noticed that from 1609, date of the first two laws of Kepler, already it was known too that the planetary orbits were elliptical. How then was anybody daring to propose a law of the gravitation so different from the newtoniana (still not known for then)? Since the reason was very simple. The flexible gravitational force suggested by Hooke was predicting also elliptical orbits for the planets. In effect, since well you will have learned also in the books of basic physics, when a body is subject to a force of flexible type like the given one by the law of Hooke, and whenever the movement is in only one dimension, the trajectory continued by the above mentioned body will be a straight line and the movement receives the name of harmonic simply. On the other hand, if the trajectory that continues the body is contained in a plane, as it is the case of the Earth or any other planet about the Sun, then what is had is a superposition of two simple harmonic movements, perpendicular both between themselves. When these two simple harmonic movements get together there arises an ellipse as trajectory (other well-known different combinations exist as curved of Lissajous, but they do not come to story now). Do you consider now Hooke a senseless one? No, truth? Well, since perhaps with what I am going to tell you next your opinion change.

The truth is that the law of gravitation suggested originally by Hooke (I have already told you that later he would rectify himself and would suggest to Newton an inverse law with the square of the distance) is not coherent with the Kepler laws any more than in the elliptical character of the orbits. Why? For several reasons. The first one is that when the movement equations are solved the first contradiction arises and this one is not different that, in contrast to what Kepler was affirming, now the Sun is already not in one of the foci of the ellipse, but in the center of the same one. The second one, and more serious if it fits, has to do with the third Kepler law. Really, if one day you have deduced this law supposing an approach of circular orbit and using the law of universal gravitation together with the expression of the centripetal force, you have only to carry out a calculation exactly equally but replacing the law of force of Newton with that of Hooke. You will verify immediately that now the time that takes the planet in describing a return about the Sun it is always the same one, independently of the distance that it separates from the star. All the planets would have years of equal duration.

And this way, this way so elegant and effective the science works. A phenomenon is observed, it is experienced (if one can), there is prepared a theoretical - mathematical model who explains the remarks and potentially observable new phenomena are predicted. If these phenomena are not explained by the proposed theoretical model, this one gives in and one looks for one that does it. Hooke was a scientist of volume and loin. He proposed his theory. It saw that this one was fitting to some of the remarks but, on the other hand, it was contradicting others already verified by other means (the Kepler laws, in this case). This way, then, it directed his efforts towards another more guessed right model and, consistently, more next to the truth. Some voluntary pseudoscience that makes it better?

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