Kepler's laws govern the mission to the comet

Kepler's laws govern the mission to the comet

I am sure that many, like me, followed the development of the company "wake up Rosette" with great interest, about how a small European rover was launched after 31 months of sleep. It is nice to see that after all this time, Rosetta returned to online mode, is in working condition and is ready for rapprochement with Comet 67P / Churyumov-Gerasimenko in November of this year. It would be great if my car was so reliable.

As I get to know the progress, I’m thinking how wonderful it really is that we can send a man-made object over many millions of kilometers to a small piece of rock and arrive at the right place at the right time - given that these goals often travel thousands of kilometers per hour. Navigating the solar system is not easy, but it became available with the “discovery” of the three laws that govern the planetary motion.

It was in the 1600s, Johann Kepler published his three laws of planetary motion, and they still remain relevant today, as well as more than 400 years ago. They not only regulate the motion of the planets around the Sun, they also regulate the motion of satellites around the planets and even exoplanets around distant stars. The laws are invaluable in understanding not only the movement of the planets in our solar system, but also helped us learn about the families of the new planets in the depths of our galaxy. The first of the laws says that all the planets in our solar system move in elliptical orbits with the sun at one of the focus points of the ellipse. This is not surprising, perhaps, since many of us know from childhood that the Earth's orbit and indeed the orbits of all the planets are elliptical.

An ellipse is essentially a drawn circle, and you can imagine how it can have two points of focus if you first visualized a circle with a point in the center. If you stretch the circle from top to bottom, the center point will be divided into two parts and both will move outwards. In the case of the planets of the solar system, the sun is at one of these points, and this is the point that defines the orbit.

Kepler’s second law states that the line connecting the sun to the planet, known as the radius vector, describes equal areas of space at equal intervals of time. In other words, the planets move faster when they are closer to the sun and slower when farther away. But this is the third and last law of Kepler, which was published only ten years after the first two, it describes the mathematical relationship between the time it takes for a planet to orbit and the distance from the Sun. According to Kepler, "... the square of the orbital period of the planet is directly proportional to the cube of its average distance from the Sun." This means that we can estimate how long an object orbits the sun from simple observations and know that we can calculate its average distance with some accuracy. Understanding these three laws gives us great knowledge about the movement of the planets around the solar system and using them in combination with other laws - for example, Newton's laws of motion and small corrections on Einstein's general theory of relativity - means that we can move around the solar system and make it is with high accuracy, thanks to which we know exactly where Comet Churyumov-Gerasimenko will be located 10 years after the launch of the Rosetta!

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