09_একাদশ শ্রেণী_পদার্থবিদ্যা_মহাকর্ষ - কেপলারের সূত্রাবলী
09_একাদশ শ্রেণী_পদার্থবিদ্যা_মহাকর্ষ - কেপলারের সূত্রাবলী
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00:00In the Greek philosopher Aristotle, in 300 BC, he proposed a geocentric system of planets.
00:16According to his theory, the Sun, Moon and other planets are the centers of the Earth.
00:25If we knew this today, we would have completely forgotten this theory.
00:30The post-Greek philosopher Ptolemy supported this theory and added some more terms.
00:37He said that the universe and all its elements, i.e. planets, stars, planets,
00:44represent the Earth in a very spherical shape.
00:48The Greeks believed that the shape of the Earth is the largest form of God.
00:55Since this universe is the creation of God, the origin of the planets is the Earth.
01:01This theory was valid for about 1,500 years.
01:05That is, no mathematical proof can deny this theory.
01:11The work of the Polish scientist Nikolaus Copernicus on the evolution of planetary systems
01:16is published in a book titled Death.
01:19In this book, he proves that the Sun is the center of our universe
01:25and that the Earth, Moon and other planets represent the Sun in a spherical shape.
01:31The scientist Galileo was also a propagandist of this theory.
01:35At that time, it was possible to accept this new theory for the Catholic society.
01:40Most people on Earth believed in the previous geocentric model.
01:46So no one gave any importance to this new heliocentric model.
01:51During Galileo's time, the Danish scientist Tycho Brahe
01:55had been studying the evolution of planetary systems for many years.
02:00During this period, he also did some modernization of the Sextant machine.
02:06He came up with a lot of theories.
02:10But he did not want his theory to be published.
02:13Because he was afraid that other scientists would use this theory to investigate further.
02:20So, to solve his mathematical problems, he appointed a German mathematician Johann Kepler.
02:28Yes, he watched our video.
02:31The funny thing is that Brahe did not even talk to Kepler about his theory.
02:38After Brahe's death, Kepler came up with Brahe's collective theory.
02:44He worked on Brahe's theory with his mathematical skills.
02:49After that, he was convinced by this theory
02:52that the Earth or other planets do not orbit the Sun in the upward direction.
02:59In fact, this planet is in the upward direction.
03:03This fact has not been published by any scientist before.
03:07And this is the first theorem of Kepler.
03:10According to its first theorem,
03:12planets orbit the Sun in the upward direction.
03:16The Sun is located in a focus of this upward direction.
03:21Do you know what is the upward direction?
03:24In simple words, if you squeeze the Earth from either side,
03:28you will get the upward direction.
03:31Like the Earth, there are two centers.
03:37The big eye of the upward direction is called the big eye and the small eye is called the opposite eye.
03:44Let's go back to Kepler's theorem.
03:47The first theorem says that the Sun is located in a center of the upward direction of the planets.
03:54That is, the distance from the Sun to any planet is not equal.
03:59That is, this distance is different in different places of the upward direction.
04:04Kepler further states that the distance of the planets is not equal.
04:09That is, when they are close to the Sun,
04:12the distance from the Sun to any planet is equal to the distance from the Sun to any planet.
04:21Kepler's second theorem states that
04:33This is also called the Law of Aerial Velocity.
04:37Aerial Velocity is denoted by dA by dt.
04:41dA by dt is equal to L by 2m is constant.
04:47Let's look at this through a diagram.
04:50In the picture, we can see the orbit of a planet.
04:54When the Sun is close to the Sun at any point in time,
04:58the planet orbits the path AB and the Sun at the same time.
05:05Kepler's second theorem states that
05:13We can think of this as a pizza slice.
05:16Like the orbit of a planet,
05:18when a pizza is divided equally among its friends,
05:21a large portion will be equal to a large portion.
05:26However, in the case of our solar system,
05:29the distance between the centers of the planets is very small.
05:34This causes a lot of mathematical problems.
05:36The orbit of the planet is also very small.
05:39So, in many places on the orbit of the planet,
05:41the distance between the planets is very small.
05:44Kepler tries to understand the various parameters of the planet
05:49when the distance and position of the planets vary over a long period of time.
05:54At this time, he examines the position of the planets,
05:57that is, the time when they orbit their entire orbit,
06:02and finds a miraculous relationship between the distance between the planets and the Sun.
06:08He calculates that the distance between the planets and the Sun is very small.
06:17That is, if the planet and the Earth orbit the Sun once at T1 and T2,
06:25and the distance between the planets and the Earth is as large as R1 and R2,
06:31then T1 square by R1 cube is equal to T2 square by R2 cube,
06:38from which T2 is proportional to R3.
06:44And from this relationship, he writes his second principle.
06:48The distance between the planets and the Sun is equal to the magnitude of the distance between the planets and the Sun.
06:56Even if he can prove the truth of this relationship through his mathematical proof,
07:02he cannot explain the reason for it.
07:05A few years after the death of Kepler,
07:08his mathematical proof of this third principle was discovered by Sir Isaac Newton.
07:13Let's see how he proved it.
07:16If a planet of this size is orbiting at a distance of R2 from the Sun of capital M,
07:25the magnitude of this planet and the Sun will be F1 is equal to capital G into capital M by R square.
07:34We know that this magnitude of the planet is equal to the magnitude of the orbit of that planet.
07:40If the planet is orbiting at a distance of small v,
07:45then its magnitude will be F2 is equal to mv square by R.
07:51Let's see the equation.
07:53If the planet is orbiting at a distance of small v,
07:56then its magnitude will be F2 is equal to mv square by R square.
08:02If the planet is orbiting at a distance of small v,
08:05then its magnitude will be F2 is equal to mv square by R square.
08:08If the planet is orbiting at a distance of small v,
08:11then its magnitude will be F2 is equal to 4m pi square R square by R T square.
08:18Or 4m pi square R by T square.
08:23As I said earlier, the magnitude of the planet and the orbit of that planet will be equal.
08:28That is, F1 is equal to F2.
08:31Then we got G into capital M by R square is equal to 4m pi square R by T square.
08:40To simplify this relationship,
08:44T square by R cube is equal to 4 pi square by gm.
08:504 pi square by gm is a derivative.
08:53So, T square is proportional to R cube.
08:58Surprisingly, even after 500 years,
09:01the truth of the Kepler's theorem is still unknown.
09:04Its role in modern astrophysics is unknown.
09:08Newton himself proved the validity of his theorem based on this fact.
09:13Because if Newton's Mahakosha theorem could not prove the Kepler's theorem,
09:18it would not have been accepted in the scientific world.
09:21There is another important point in the next video.
09:25The answer to many mysteries of Mahakosha is still to be found.
09:28Keep watching.