Johannes Kepler
Born in the 16th century, Johannes Kepler was in a constant battle against the ways of his time, particularly within the theology realm. Destined to even study theology at university, merely by luck he was persuaded toward astronomy by a math tutor and went on to later devote his life to the science. His life works and discoveries in astronomy would go on to change the way the world saw the stars, despite religious demand to keep a geocentric universe (Boantza, 2019).
Contributions to Orbital Mechanics
Before Kepler, the problems of kinematics and dynamics were separate issues to be dealt with as such. However, throughout his life he was able to join the two together and the result was the three laws that were named after him.
Kepler’s First Law
Kepler’s first discovery, and the resulting first law, was developed from Tycho Brahe’s challenge to Kepler to do a detailed calculation of the orbit of Mars. While going through Brahe’s research, Kepler calculated that Mars didn’t have a circular orbit, but instead had an elliptical orbit. The result was Kepler’s First Law, “orbits of planets are ellipses with the sun at one focus” (Sellers, 2014).
Kepler’s Second Law
Kepler later went on to measure individual segments of Mars’ orbit to realize that the closer the planet was to the sun, the faster it moved through its orbit. This would create a sector between the Sun, the planets starting spot (in this instance, Mars) and the planets ending spot after a certain period. The assumption is that the resulting sector would have a smaller area when it was closer to the Sun and larger when it was further away, not realizing that the speed of a planet accelerates closer to the Sun. However, Kepler soon realized that a planet moved faster when it was closer to the Sun and the two sectors’ areas were equal. This is what brought about Kepler’s Second Law, “The line joining a planet to the Sun sweeps out equal areas in equal times” (Sellers, 2014).
Kepler’s Second Law would later be revamped into Newton’s Law of Universal Gravitation, which states that the gravitational constant distributed to the product of any two objects masses and divided by their distance from each other squared would equal the magnitude of the objects attractive force (Encyclopedia Britannica, n.d.).
Kepler’s Third Law
In Kepler’s Third Law, he would go on to form the calculation required to measure any bodies orbit based off average distance. This is what scientists use today to calculate moons, satellites, and any other objects orbit. The law states that the cube of the average distance between the planet and the Sun is equal to the square of an orbits period. Technically, the correlation is that a period (in seconds) squared is proportional to the semimajor axis (in kilometers) cubed (Sellers, 2014).
Impact on Modern Life
Isaac Newton
Largely considered the greatest physicist to ever live, Sir Isaac Newton developed numerous things that still are hold true to today, such as calculus, the famous three laws of motion and the law of universal gravitation. However, a lot of these findings are based on the groundwork that others set. Specifically, Newton’s law of universal gravitation was developed with influences from Kepler’s second law. To start, Newton’s law of universal gravitation states that the attracting force between two masses is equal to the product of their masses and inversely proportional to the distance between them squared (Sellers, 2014).
This equation explains what Kepler was seeing in Brahe’s journals on Mars and what was developed in his second law. It is also the explanation that was needed for science to label Kepler’s laws as laws. Explaining elliptical orbits and why the area of an orbit matches timed segment from one side of the Sun and the other side. In modern science, these two laws are still used to make the inference that the force that holds a planet to its elliptical orbit is the planet’s change in velocity (Tanona, 2000).
Classic Orbital Elements (COEs)
To visualize an orbit and a spacecraft’s position within it, you require six different descriptors. Kepler was able to develop these, which are now called the COEs and are still used today. They consist of: Orbital size (using the semimajor axis), orbital shape (using the eccentricity), orientation of the orbital plane in space (using two descriptors, inclination, and right ascension of the ascending node), orientation of the orbit within the plane is defined by argument of perigee, and the spacecraft’s location in the orbit is represented by true anomaly (Sellers, 2014).
Kepler’s Equation
His life didn’t just have three discoveries that resulted in monumental laws of planetary motion, he would continue to solve some of the problems that his laws would create. A good example is the resulting Kepler’s Equation from the discovery of elliptical orbits. After discovering that Mars’ orbit was elliptical in his first law, Kepler found that calculating a circular orbit was far easier to do than an elliptical one. So, he formulated an equation to relate an elliptical orbits motion to a circular orbits motion so that future positions could be calculated. This is important for today because it allows us to predict orbits and it’s used to calculate time of flight with space craft and satellites (Sellers, 2014).
Outside of Astrology
On the topic of Kepler’s contributions to modern life, the focus must deviate away from orbital mechanics and into vision science. Kepler stated, “therefore vision occurs through a picture of the visible things on the white, concave surface of the retina”. This was regarded as impossible because it meant that the image would culminate in the back of the eye, and it would be inverted. Years later, modern science would realize that Kepler’s assumption was correct. It appears that the laws of projective geometry are universally applied to astronomy and vision science (Gilchrist, 2014).
Conclusion
Throughout Kepler’s life he was fighting a battle for his life based on the conflict between the results of his science and the religious beliefs that surrounded him. This outward pressure is what stopped scientist and ceased innovation through the years during and before Kepler. His ability to stay dedicated to the science may be what allowed him to come out with such innovation.
His three laws were undoubtably the highlight of his life and it’s what he is predominantly known for. The reason being for their direct influence the modern world and on the scientists that came in between the times, like Newton. Outside of the three laws, Kepler was able to question many other problems and create solutions. The Kepler equation, COE and light observance through the retina are three examples outside of the laws that contributed to modern life.
References
Boantza, V. (2019). The Astronomer and the Witch: Johannes Kepler’s Fight for his Mother. History: Reviews of New Books, 47(2), 38–39. https://doi.org/10.1080/03612759.2019. 1565013.
Encyclopedia Britannica, inc. (n.d.). Newton's Law of Gravitation. Encyclopedia Britannica. Retrieved January 5, 2022, from https://www.britannica.com/science/Newtons-law-of-gravitation.
Gilchrist, A. (2014). Johannes Kepler: The Sky as a retinal image. Perception, 43(12), 1283–1285. https://doi.org/10.1068/p4312ed.
Sellers, J. (2014). Understanding Space: An Introduction to Astronautics (3rd Edition). McGraw-Hill Learning Solutions.
Tanona, S. (2000). The Anticipation of Necessity: Kant on Kepler’s Laws and Universal Gravitation. Philosophy of Science, 67(3), 421–443. https://doi.org/10.1086/392789.
