Planetary Orbits


The orbits of the planets were something that astronomers struggled to explain. Planets appeared to wander around the sky, sometimes reversing direction. There were two main schools of thought about planetary orbits in the 16th century; one that the planets orbited the Earth in the Geocentric model, and the other that the planets orbited the Sun in the Heliocentric model. Unfortunately, both models struggled to explain the corkscrew like behaviour of planetary motion.

It was not until the 17th Century when Johannes Kepler, working as an assistant for the famous astronomer Tacho Brahe, was given the task of explaining the orbit of the planet Mars. After six years of studying and thousands of pages of calculations, Kepler finally deduced that the orbit of Mars around the Sun was in fact not perfectly circular but was elliptical. 
The more elliptical an object the higher its eccentricity
The ellipse does not have one centre like a circle, but two foci as it is the product of two competing factors (the motion of the planet and the pull of gravity). Because the Sun has over 98% of all the matter in the solar system its gravitational pull is MASSIVE!
Kepler’s First Law states all planetary orbits are elliptical – where planets orbit around two foci. This image is greatly exaggerated, with most planets having an eccentricity of less than 0.2, meaning they are very close to circular.
Investigate how the spacing between the foci effects the eccentricity of an ellipse by following the method shown on this hands-on video tutorial.             

The word eccentric means “off centre”, and although we like to save the term for our favourite quirky relative, it is originally a mathematical term. The eccentricity of an ellipse depends on how flattened it is. The eccentricity ranges from 0 – 1, where zero has no flattening and is a circle, the closer to 1 it is the more flattened the circle is.
Ellipse with eccentricity of ~ 0.2 similar to the orbit of Mercury. (https://www.mathopenref.com/ellipseeccentricity.html, accessed 29/06/2020)
The simulation on this website allows you to adjust the distance between the foci and see how this effects eccentricity: Eccentricity and Ellipse

Below is a table of the eccentricity of different planets in our solar system.
Planet
Major axis (AU)
Eccentricity
Mercury
0.774
0.2056
Venus
1.446
0.0068
Earth
2
0.0167
Mars
3.048
0.0934
Jupiter
10.406
0.0484
Saturn
19.074
0.0542
Neptune
60.14
0.0086

As you can see, there is no relationship between distance from the Sun and the eccentricity of a planets orbit. In fact, Mercury has the most eccentric orbit. However, even an ellipse with eccentricity of 0.2 appears very circular. This is perhaps why it took so long for astronomers to realise that planets were orbiting the Sun in ellipses.