Johannes Kepler – The Laws of Planetary Motion
Johannes Kepler’s interest in astronomy started in his early age. As a boy, he has witnessed several astronomical events, such as the Great Comet in 1577 and a lunar eclipse in 1580. Unfortunately, his love for it came to halt when he suffered from a disease in his childhood years, which left his hand crippled and his eyesight weak.
Yet a great mind cannot be hindered. During his university days, he proved to be a great mathematician and astrologer, and was recommended to teach in the University of Graz after his studies. It was during this time that he made his first astronomical work, the Mysterium Cosmographicum. In this book, Kepler described the structure of the universe with the use of five regular polyhedra and believed this to be God’s design of the universe. Although this theory was in error, further studies in astronomy owes a lot to Kepler’s first manuscript since it pointed to the sun as earth-orbit’s center, which was a mere assumption during those times.
The publishing of Mysterium Cosmographicum became Johannes Kepler’s ticket to associating with famous astronomers, like Reimarus Ursus and Tycho Brahe. Eventually, he became Tycho’s assistant. Their working relationship was not ideal at first, as Tycho guarded his data due to fears of Kepler taking his place as the premier astronomer, but this improved later on when Tycho continued to be impressed by Kepler’s ideas. Johannes studies prior to this were mostly based on chronology and the numerological relationships between mathematics, music, and the universe. Given the chance to work in Tycho’s observatory was of great importance to him so he can gather accurate data.
In 1601, Tycho met his untimely death, which brought Kepler to replace him as imperial mathematician to Emperor Rudolph II. His main responsibility was to give astrological advices to the emperor, which includes giving horoscopes and solutions on political matters based on the stars. Along with this, Kepler also took over finishing all of Tycho’s unfinished projects and the privilege of taking hold of all of Tycho’s data. With the help of these data and his own theories, Kepler was able to develop the Laws of Planetary Motion, which is an accurate description of the planets’ orbit motion.
Laws of Planetary Motion
First Law (The Law of Ellipses): The planets rotate the sun in an elliptical shape, with the sun located at one of focus of the ellipse.
To better understand this, you must first know that an ellipse has two foci. These points are located inside the ellipse. When you take the sum of the distance of both foci from a single point on the perimeter of the ellipse, it will always be a constant. A focus is not located in the midpoint of the ellipse and since the sun is located at one focus, therefore it is not in the midpoint of the planet’s orbit. As the planet moves along its orbit, its distance from the sun will vary too.
Second Law (The Law of Equal Areas): The line connecting the planet to the sun will sweep out equal areas at equal times travelled.
Since the planets orbit at varying distances from the sun, so will its speed. A planet travels faster when near the sun and slower when it is the farthest from the sun. Now, imagine connecting a line from the sun to the planet and take that line as day one. After 30 days of travel, form another line and calculate the triangular area travelled. This area will be equal at any point you start along the ellipse for equal period travelled, whether the planet is closest or farthest from the sun.
Third Law (The Law of Harmonies): The ratio of the squares of the revolutionary period of any two planets is equal to the ratio of the cubes of their semi-major axes.
This shows how planets are harmoniously related among each of them. If the former two laws are focused on a single planet’s motion and distance from the sun, the third one correlates any two planets. According to this correlation, the ratio of the square value of the total orbital time-period of a particular planet over the cube value of its semi-major axis is the same to all planets. As a clear presentation, this value is equal to 1.01 for Venus, 1.0 for Neptune, 1.0 for Earth, and 0.99 for Jupiter. This ratio also holds true between the movements of satellites around a planet.
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