The innocent astronomical jokes of last week have resulted in an authentic avalanche commentary (more than eighty) already brave philosophical disquisitions. It was not my intention, but they are welcome, it never hurts to reflect on the big questions. Said which, we go with some small answers:
In purity, the planets and the sun revolve around the mass center of the solar system. But as the mass of the sun represents 98.8% of the total, that center is inside; Although not always: obviously, its position varies depending on the movement of the planets, and there are times when the baricenter of the solar system leaves slightly from our mother star. Made this exception, we can continue to say quietly that the earth and the other planets revolve around the sun.
Although it is not enough to reflect on the very concept of revolving around something (and they do so some of the comments of the previous delivery). In one of the classic recreational mathematics books of Yacov Perelman (not to confuse with Grigori, the eccentric genius that resolved the conjecture of Poincaré), the situation of a man who revolves around a tree in which there is a squirrel that, suspicious, never turns his back on the curious walker is described. Can we say that man has turned around the squirrel?
If by gas planet we understand a planet similar to Jupiter, obviously Jupiter is, by definition and antonomasia, a gaseous planet. But, tautologies apart, it is not: it has a rocky nucleus, surrounded by a huge mass of liquid metallic hydrogen, in turn wrapped by a layer of non -metallic liquid hydrogen, and the gaseous part, also basically composed of hydrogen, even being gigantic, is less than solid and liquid; But as is the part we observe, for us Jupiter is a gaseous giant.
The speed of light in a vacuum, usually represented with letter C, is insurmountable, but not in other propagation media. In the water, it is about 225,000 kilometers per second, significantly lower than in the void and in the air (where it is almost the same as in a vacuum), and that is why a ray of light that, from the air, penetrates obliquely in the water it deviates – is refracted – according to a refractive index that is the ratio between the speed of the light in the air and its speed in the water: approximately 1.33 (300,000/225000).
And in a medium in which the speed of light is lower AC, there may be particles with electric charge (such as electrons or protons) faster than the light in that medium, which produces a shock wave – symbil, mutatis mutandis, to the rupture of the sound barrier – that results in a characteristic bluish brightness known as Cherenkov radiation (but that is another article).
Notable points
When speaking of Baricentro in a section of mathematics like this, it is obliged to point out the curious case of a physical concept, related to the mass, which has sneaked into the Intangible Olympus of geometry.
As it is well known, in every triangle there are four “notable points”: incenter, circumcentro, Ortocenter and Baricentro. The incentive is the point of intersection of the bisectors of the three angles, and is the center of the circle inscribed in the triangle. Circumcentro is the point of intersection of the mediatrices of the three sides, and is the center of the circumscribed circle. The orthocenter is the intersection point of the three heights of the triangle (we can consider any of the sides as the base). And the baricenter, also called Centroid, is the point of intersection of the medians, and this is where physics sneaks into geometry, because if the triangle were a sheet of a homogeneous material, the baricenter – hence its name – would be its center of gravity. Can you think of a physical way of determining the medians of that matric triangle?
And put to convert the polygons into sheets, how would you determine the baricenter of a metal plate with an irregular pentagon shape?
OTHER: Without giving your school books, can you show that bisectors, mediatrices and medium -sized a triangle are cut at one point?
I leave the orthocenter for the end because, once the previous demonstrations have been made, it can be demonstrated in a simple and elegant way, from one of them, that the three heights are also cut at one point, and this was done by Euclid himself. As?
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