Kepler's laws

For years it was believed, in the Middle Ages and the Renaissance, that the true model that governed the Solar System (then considered as the whole universe) was the Ptolemaic Aristotelian system, which was a geocentric system, i.e. a system that placed the Earth at the center of the universe and the other planets and the Sun that revolved around us. Starting from the seventeenth century, however, with the Scientific Revolution (which counts scientists such as Galileo Galilei, Isaac Newton, Niccolò Copernico and our protagonist of today, or Giovanni Kepler) the theory began to be made that the universe was larger than the Solar System alone. , and that the geocentric theory, and therefore the Ptolemaic Aristotelian system, were wrong. Some scientists then began (with the opposition of the Catholic Church, which supported the geocentric system as it appeared in the Bible) to theorize that in the Solar System (and in general in the systems of planets and stars) there was a heliocentric model, that is, that the Sun (or the star, more generally) in the center and the planets (including the Earth, in the case of the Solar System) revolving around it.

With the progress of scientific research, it was established that there were laws that governed the motions of the planets around the Sun, and to understand which ones. Thus, starting from 1609, the German astronomer Johannes Kepler (Italianized name in Giovanni Kepler), began to establish laws that explained in a logical, mathematical and rigorous way how a planet revolved around a star, and therefore how the Earth revolved around the sun.

There are 3 laws in total, and they are called Kepler's Laws.

The first law, dated 1609, states that "the orbit described by a planet is an ellipse, of which the Sun occupies one of the two foci". In a very simplified way, the law states that the motion of a planet (in this case we take for example a planet of the Solar System) has the shape of an ellipse (ie a figure similar to a circumference, but with two "centers", said foci) and that in this ellipse one of the two foci is occupied by the Sun itself. This is due to the reciprocal gravitational attraction that the Sun and the planet exert on each other.

The second law, also from 1609, states that "the segment that joins the center of the Sun with the center of the planet describes equal areas in equal times". This means that, in the elliptical motion (in the shape of an ellipse) of a planet around the Sun (or a star), the segment (the distance) between the center of the sun and the center of the planet covers, in equal times, the same number of square kilometers. From this we understand that the speed that the planet has along the orbit is inversely proportional to how long the distance between the center of the planet and the center of the Sun is (the more the distance increases the more the speed of the planet along the orbit decreases, the more the speed of the planet along the orbit increases the more the distance decreases).

The third and last law, a little more recent, dates back to 1619, and is perhaps the most "mathematical" of the three, since it states the following: "The squares of the times that the planets take to travel their orbits are proportional to cube of their average distances from the Sun ". This can be summed up with the formula

T² = k • a³

formula where T is the period of the orbit (i.e. the time it takes the planet to circle around the Sun), a is the semi-major axis of the orbit, which we can define as the average distance of the planet from the Sun (average because we remember that there is not always the same distance between the planet and the Sun during motion, but there are different ones, since the orbit carried out by the planet is not a circumference, and therefore has no distance from the center always the same), and k it is a constant that is the same for all planets, and is sometimes called Kepler's constant, in honor of the scientist who hypothesized it. The law can therefore be summarized with the phrase "the more the cube of the average distance between the planet and the Sun increases, the more the square of the time it takes the planet to complete its orbit around the Sun increases".

The three Laws of Kepler are applicable to all planets that revolve around a star and, more generally, to all bodies that revolve around another body (such as satellites around our planet) and allow us to make some simplifications (we can neglect the mass of the planet with respect to that of the star and the same for their interactions with other bodies, for example those with any moons, or satellites, and it is also possible to consider the planet and the star as point-like, i.e. without dimensions, therefore without length, width and height).

These laws are fundamental to understand how a planet rotates around a star or how a body rotates around another body and have, together with other discoveries of the period of the Scientific Revolution, changed our way of seeing the Solar System and the whole universe, allowing us to understand them much better.

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