# Kepler’s Laws

Tycho Brahe was a man with an awesome moustache:

Evidence he was a man with an awesome moustache, possibly a crazy, crazy man

Despite this, this post is titled “Kepler’s Laws” since Brahe’s version of the Solar System is both confusing and wrong, but he did have one.  So, we will give him credit for creating the data used by Johannes Kepler (Brahe’s assistant, shown below), who found some fascinating aspects in the orbits of planets in our Solar System.  Kepler was given the task of understanding the orbit of Mars by Brahe†, but little did Brahe know, Kepler would be making some laws now, and they are quite eccentric.

A man also with a moustache (obviously it helps with Astronomy), but maybe the beard helped make him slightly less crazy than Brahe

Before we go into Kepler’s laws a major aspect of them is the ellipse.  These have a few important properties, essentially being non-perfect circles.  The more “ellipse-like” and unequally round an ellipse is, the more eccentric it is,  going from zero (a circle, a special kind of ellipse) to one (a parabola, not an ellipse).  The orbits of bodies around stars tend to be elliptical, since it is difficult to make things perfectly circular in nature.  Interestingly, the orbits of planets in our Solar System are oddly less elliptical than orbits normally would be.  Confusingly, this would then be called “less eccentric”.  Another aspect of ellipses is the major and minor axes, the major being longer than the minor.

There are three laws of Planetary Motion.

1. The ellipses:

Kepler noticed that Copernicus had planets which had circular orbits  with epicycles, both of which made no sense compared to the models he constructed.  With work, Kepler found that the orbits were actually ellipses, with planets orbiting around the Sun at one focus, as shown below.

2. The perihelion and aphelion:

Kepler next found that the area created over equal times between a planet and the Sun is equal around the ellipse.  A planet moves faster near perihelion (when it is closest to the Sun) and slower near aphelion (when it is furthest from the Sun).  This is shown below, greatly exaggerated:

3. A relation forms:

Lastly, the ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes.  Far easier shown is:

where the 1 to the bottom right of the letter represents the quantities for one planet, and the 2 to the bottom right of the same letter represents the quantities for the second planet.  P is revolutionary period, and R is the semimajor axis or half the major axis of the ellipse.

To conclude, the man is quite important.  It is incredibly impressive that he could create highly accurate laws describing large bodies without even technically using a telescope (he used Brahe’s data from sextant observations), such that it can be taught in schools. It may not sound good that there is more to test on because of him, but it is better than  keeping presumptions that create inaccuracies in our interpretation of the universe.  Now it may not seem as necessary, since we can take far better images of space, but whenever Astronomers try to look into space, a model or predictions are made (good science requires hypothesizing and planning).  Kepler’s Laws can be used to check a model of ANY TWO ORBITING BODIES.  He is so respected he even has a satellite named for him looking for planets outside our Solar System.

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† Luckily for Kepler and modern astronomy, Mars has one of the most eccentric orbits in the Solar System.

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TL;DR — After looking towards the Copernican Model and using Brahe’s data, Kepler was able to greatly help Astronomy with his three laws of Planetary Motions, which help for explaining motions of any two orbiting bodies.  Essentially, instead of circles, he found that planets revolve around the Sun in an ellipse, and he made certain relations from this.

For more on this one can go to:

http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html

http://www-spof.gsfc.nasa.gov/stargaze/Kep3laws.htm

http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

http://www.drennon.org/science/kepler.htm

http://projects.astro.illinois.edu/data/KeplersLaws/