Kepler formulated three laws governing planetary motion. The first law stated that: all planets move around the sun in elliptical orbits rather than in circles; although the sun itself is one of the focal points. The second law states that: the speed of a single planet is not uniform but is designed in a manner that the radius vector between the sun and the planet sweeps out equal areas in equal durations. Finally, the third law states that: the duration a planet takes to complete one orbit around the sun if divided by 3/2 power of the average distance between the same planet and the sun should be the same constant (Nave, n.d). From the foregoing, the third law is very important and it provides insight into Newton’s law of universal gravitation between the moon and the earth as well as between the sun and other planets.
According to the first law, the ellipses are the paths or orbits that the planets follow during revolution and the sun is one of the foci of the ellipse. An orbit’s size is the average distance from the sun, which can be represented mathematically by letter a . However, Kepler defined the shape of an orbit by the ellipticity of the celestial body. The ellipticity is the relationship between the length of the minor axis and the major axis of the orbit; hence, giving the ellipses their descriptions based on mathematical fictions although without physical reality.
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Kepler’s first law of planetary motion implies that although ellipses may have the same size, they may have overly different centers when their shapes are dissimilar. For example, an ellipse may have the same focus although the centers may differ as the ellipse stretches out because the eccentric nature pushes the focus further away. Notably, Kepler considered eccentricity as the fraction of the size of the ellipse that distinguishes the focus from the center. These assertions are attributed to Kepler’s efforts, which involved a critical study of Mars in its orbital motion. Therefore, he concluded that the true path of the planet (Mars) is an ellipse, which is oval (Byrne, 2016). Ideally, Kepler’s ideas were based on the fact that the radius of the ellipse is subject to change regarding the angle through the full orbit. Therefore, the first law proves that the movement of planets occurs in elliptical orbits because of the existing set of points at specific distances from the two points. This means that the distance from the center is not fixed.
Kepler’s second law provides two different perspectives of the planets as they move in their orbits. He argues that there is an inverse relationship between a planet’s velocity and its distance from the sun. Also, Kepler elucidates that the variation in the planet’s velocity depends on the line joining the planet and the sun and that the same radius must sweep equal areas in equal times. From this perspective, Kepler did not consider the concept of instantaneous velocity; hence, making his inferences simply superfluous. However, his implications are quite accurate within the perspective of modern physics. For instance, he argues that the duration that a planet takes to traverse the same elements of its orbit must be proportional to the distance between the same planet and the sun. In this regard, Kepler provides distance law and area laws in explaining the second law of planetary motion. Consequently, we can deduce that the angular momentum of a planet, say, Mars, is unchanging about its axis with the sun as the point of reference and perpendicular to its orbital plane.
Kepler’s third law provides a direct relationship between the square of a planet’s orbital period and the cube of its orbit’s semi-major axis. Precisely, Kepler meant that if you square the year of Mass and divide the result by the cube of the distance between Mass and the Sun, you should obtain a similar result for all planets (OpenStax HS Physics, 2016). This concept has been proved to work for all other dwarf planets including asteroids and satellites around the Earth. A typical example of this case is the comet, specifically Halley’s Comet that has an orbital duration of 75.3 years and a distance averaging 17.55 au (Future Learn, 2019). Therefore, using the relationship T = AR2/3, we can compute the data and arrive at 1.048, which should remain the same for all planets.
In conclusion, Kepler made significant contributions through his three laws of planetary motion, especially concerning the movement of natural and artificial satellites. Similarly, his laws are applicable in unpowered spacecraft in orbit, with special reference to stellar systems. Notably, the three laws did not consider gravitational forces and the influence of other planets on each other; hence, complicating the possibility of predicting how two celestial bodies move under their mutual attractions. Therefore, solving problems associated with the three-body concept becomes unobtainable unless under special conditions. Finally, the three laws play significant roles in relativistic and quantum effects with regards to electromagnetic forces in an atom, especially when dealing with the inverse-square-laws forces.
References
Byrne, C. (2016). Kepler’s Laws of Planetary Motion. Lowell: University of Massachusetts Lowell. http://faculty.uml.edu/cbyrne/Kepler.pdf
Future Learn. (2019). Maths for Humans: Inverse Relations. Kepler's Third Law: the law of harmonies. UNSW Sydney. https://www.futurelearn.com/courses/maths-power-laws/0/steps/12172
Nave, R. (n.d). Kepler's Laws. http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html
OpenStax HS Physics. (2016). Kepler's Laws of Planetary Motion. Version 1.2. file:///C:/Users/d/Downloads/keplers-laws-of-planetary-motion-2.pdf
