Kepler’s Laws of Planetary Motion, Research Paper Example

In ancient times, astronomers and astrologists were convinced that the Earth was the center of the universe and that all of the observable stars were positioned on a sphere which accounted for their circular movements in the night sky. All of the known planets, being the Earth, Mercury, Venus, Mars, Jupiter, and Saturn, also rotated on what were called “crystal spheres” that moved at different speeds. This understanding of the mechanisms of the observable universe endured until 1543 when Nicholas Copernicus deduced that this system only made sense if all of the planets (including the Earth) revolved around the Sun, and if those planets furthest from the Sun revolved at a slower rate (Stern, “Kepler’s Three Laws of Planetary Motion”).

As it turned out, Copernicus was absolutely correct in his deductions about the movement of the planets in the nighttime sky. Then in 1609, Johannes Kepler, a longtime advocate for the theories of Copernicus, published Astronomia Nova in which he presented his first two laws of planetary motion which came about after realizing that the planets do not orbit the Sun in circular paths (as advocated by Copernicus) but in elliptical paths which mathematicians refer to as an ellipse (“Johannes Kepler: The Laws of Planetary Motion”).

In basic terms, an ellipse is an ovoid or shaped like an oval as contrasted with a circle, and within the center of any given ellipse, there are two specific imaginary points known as foci (a & b). Mathematically, “the sum of the distances to the foci from any point on the ellipse (i.e., from its edge) is a constant” which is expressed by the equation a + b = constant. When any given ellipse is flattened out or stretched, this is known as the eccentricity which results in both foci being further apart (“Johannes Kepler: The Laws of Planetary Motion”).

Much like a circle, an ellipse can be divided into four equal parts with the long axis extending from one end to the other as the major axis and a shorter axis extending from the top to the bottom as the minor axis. When we divide the major axis in half, each half is known as a semimajor axis which is similar to the radius of a circle. Therefore, when a planet (focus one) with the Sun at the center (focus two) revolves around an ellipse, the orbit “is equal to the length of the semimajor axis.” Doubling the semimajor axis gives us the width of the ellipse. Of course, the more eccentric the ellipse (i.e., stretched out), the longer the planet’s orbit (“Johannes Kepler: The Laws of Planetary Motion”). As an example, consider the planet Pluto which lies more than 2 billion miles from the Sun. Pluto’s solar orbit is very eccentric or stretched out; in contrast, the orbit of Mercury is zero eccentric or almost a true circle, due to being less than 50 million miles from the Sun.

When Kepler first realized that the planets orbit the Sun in elliptical paths, he was able to formulate his three laws of planetary motion. The first law is quite simple–“the orbits of the planets are ellipses with the Sun at one focus of the ellipse.” It should be noted that the Sun “is not at the center of the ellipse, but is instead at one focus” which is always stationary, meaning that the Sun does not revolve around anything (yet it does have rotation like the Earth).  As an example, the planet Mars which lies further from the Sun than the Earth, follows the ellipse in its orbit and as it moves around the ellipse, its distance from the Sun constantly changes. The same principle holds true for the Earth which is farther from the Sun during the summer and closer during the winter (“Johannes Kepler: The Laws of Planetary Motion”). It should also be noted that following an elliptical path holds true for all celestial bodies, such as a star orbiting another star, and that if we could look down on the orbit of the Earth around the Sun, the orbit would appear to be circular (“Lesson 34: Kepler’s Three Laws of Planetary Motion”).

Kepler’s second law of planetary motion is a bit more mathematically complex–“The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.” This line is referred to by astronomers as the “radius vector” or an imaginary line that runs length-wise within the ellipse. For instance, when the Earth is at its nearest point to the Sun (perihelion), it sweep out an area that is equal to when the Earth is at its farthest point from the Sun (aphelion). Thus, according to Kepler, a “planet moves fastest when it is near perihelion and slowest when it is near aphelion” (“Johannes Kepler: The Laws of Planetary Motion”), due to the fact that the Sun’s gravitational pull or tug is greater at perihelion and less at aphelion.

Kepler’s third law of planetary motion is perhaps the most complex, due to being based on a specific mathematical equation–“The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes.” This can be expressed via P (period of revolution) or the length of time it takes a planet to make one complete orbit around the Sun, and R which “represents the length of its semimajor axis.” Therefore, the third law “implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit,” meaning that the longer the radius, the more time it takes for planet to orbit the Sun. As an example, the planet Mercury which lies closest to the Sun out of nine planets in our Solar System, orbits the Sun in eighty-eight days, while Pluto which lies farthest from the Sun takes 248 years to make one complete orbit (“Johannes Kepler: The Laws of Planetary Motion”). In essence then, Kepler’s three laws of planetary motion did away with the old notion of the Earth as the center of the Solar System and the idea held by the ancient Greeks that all celestial motion was circular (“Lecture 7: Kepler: Laws of Planetary Motion”).

Works Cited

“Johannes Kepler: The Laws of Planetary Motion.” 2014. Web. 11 April 2014.

“Lecture 7: Kepler: Laws of Planetary Motion.” 2010. Web. 11 April 2014.

“Lesson 34: Kepler’s Three Laws of Planetary Motion.” 2014. Web. 11 April 2014.

Stern, David P. “Kepler’s Three Laws of Planetary Motion.” 2005. Web. 11 April 2014.