Kepler’s Laws of Planetary Motion

Ethan Siegel’s article, “The Scientific Failure of the Original Elegant Universe,” talks about how Kepler came about to bring forth his three laws of planetary motion. Siegel discusses how Kepler had developed an idea, but it did not succeed and found himself having to abandon his hypothesis. Siegel expresses his admiration towards Kepler for allowing himself to open “to whatever the data [showed], and be willing to follow it, no matter where it leads.” Kepler being open to what the data showed helped him develop his three laws; “that planets move in ellipses around the Sun, that they sweep out equal areas in equal times, and that the ratio of the squares of the orbital period to the cube of the semi-major axis are a constant for any central mass. ”
In connection to the class, this article relates because we covered Kepler’s laws, but mostly the second and third law in our lecture tutorials.


As you can see by the image above, the lecture tutorial uses the picture to help represent Kepler’s second law, equal areas in equal times, because in the tutorial it says “note that the time between each position shown is exactly one month.”


Now in the lecture tutorial to cover Kepler’s third law they used a table to show that there is no relationship between the mass of a planet with the orbital period (i.e. Mars and Saturn).

Overall, I think it was interesting to read about Kepler’s original idea and how he had to have an open mind to come up with his laws of planetary motion. Learning about Kepler’s laws has given me a better understanding of how planets move in our universe and what relationships do exist when is comes to planets motion.



We used to think the planets travelled in circles, but now we’re so OVAL it.

In class, we learned Kepler’s three laws of planetary motion, which describe how planets orbit around a star. The three laws are as follows:

  1. A planet orbits around its sun in an ellipses.
  2. A radius vector joining any planet to its sun sweeps out equal areas in equal lengths of time.
  3. The revolution of a planet squared is directly proportional to the length of the orbits semimajor axis cubed. (This can be mathematically expressed as T^2/a^3 equals a constant. This constant is the same for every planet in its solar system.)

Before the discovery of these laws, we assumed that the planets travelled around the sun in a circular motion. Retrograde motion, such as that of Mars and Mercury, was unexplainable under this mindset. Kepler not only gave us an explanation for this retrograde motion, but also provided a basis for Newton to derive his laws of gravity from.

The article I found, titled “Mercury Retrograde” via, explains retrograde motion using Mercury as a specific example. Like we learned in class, the article explains that retrograde motion is an illusion caused by the elliptical path of planets. During its farthest point from the sun, planets move the slowest. So while Earth passes up Mercury when it’s at its farthest point, it appears to be going backwards from our point of view, even though it isn’t.

I liked the article because it helped reinforce the laws of planetary motion that we learned in class. I also liked the article because it talked about how people who closely follow astrology believe that mercury’s retrograde motion has an emotional affect on human behavior. This belief apparently derives from a time when the geocentric model of our solar system was accepted, so I find it interesting that people still takes these beliefs into consideration even though the information it was founded on has long ago proven to be complete garbage.

The Universal Movement of the Planets

The fifth conceptual objective, I can apply Kepler’s laws of planetary motion, has been recently discussed in class. In class, we primarily defined and explained Kepler’s three laws of planetary motion. These laws were eventually exercised by the class in the Lecture-Tutorial book. Kepler’s first law says that the orbit of a planet is an ellipse with the sun at one focus. Kepler’s second law says that the line joining a planet and the sun sweeps out equal amounts of area in equal intervals of time. Finally, Kepler’s third law states that the square of a planet’s period is proportional to the cube length of the orbits semi-major axis. This concept can be expressed mathematically with the equation: T^2/a^3=constant. That said constant is the same for all objects orbiting the sun. Multiple illustrations in the Lecture-Tutorial book allowed me to get a better understanding of these three laws and concepts involving planetary motion. The article I chose, “Living on the Trappist-1 Planets Would Be Very Strange”, discusses the differences that would exist when living on one of the seven planets compared to Earth. This article closely relates to the fifth conceptual objective. As opposed to Earth, those who were standing on a planet in the Trappist-1 system would be able to see all six of the other planets. Due to their close proximity and orbits. This article relates to the fifth conceptual objective because it discusses the orbital periods of these seven planets, much like Kepler’s laws that are accepted here. These laws are universal and can even be applied to a planetary system that is nearly 40 light years away. All seven of the known planets in this system orbit closer to their star than Mercury orbits the Sun. Even in this instance, Kepler’s laws can be applied. The article the mentions the reason these planets can still support life, “The reason these seven planetary siblings can fit into such tight orbits is because their parent star is an ultra-cool dwarf star. It’s about 2,000 times dimmer than the sun, and only slightly larger than the planet Jupiter”. The article then begins to mention that the planets would appear to be dim to a person visiting one of these planets, regardless of the close orbits. The planets in this system take almost no time at all to make one complete orbit around their star. The article then discusses what life would be like on these planets. Kepler’s laws of planetary motion ultimately paved the way for universally accepted laws that define any orbit. Before Kepler came along, astronomers attempted to understand how the planets move. As discussed in our fourth conceptual objective, the geocentric theory was believed to be the truth by many. Eventually, this belief was overtaken by Copernicus. The concept of heliocentrism simplified models of planetary motion, and made the motions more explainable. However, it did not carefully explain retrograde motion. The elliptical orbits of planets is said to be caused by our altered perspective here on Earth. Although planetary motion was better demonstrated, it wasn’t until Kepler came along that planetary motion was explained with accepted laws. Kepler made countless calculations in order to prove his laws of planetary motion. This article is very comparable to what we exercised and discussed in class. This article clarifies the concept of planetary motion as defined by Kepler and shows that these laws can be applied elsewhere. The universal laws that originated from Kepler that define planetary motion seem to be consistent with other planetary systems. It is amazing that a man with very little technology could come up with three widely accepted laws that still exist today. The article provides useful information of this concept, further explaining our fifth conceptual objective. The precise layout of this article allows the reader to fully understand the material and apply it to other, real-world situations.