Two men were to have such significant bearing on man's understanding of astronomy and physics that it can be said that they were responsible for the arrival of the modern era of these sciences. This is due not only to their contributions in their own right, but for also for the groundwork that they laid down. Both were later to be of great inspiration to Sir Isaac Newton and he was to use their principles as the foundations for his great work.

These two men were Johannes Kepler and Galileo Galilei.

It was Johannes Kepler who was the first man to finally understand planetary motion correctly, including of course retrograde motion. Kepler was primarily working on understanding Mars' motion, as it had held a special interest for him, due to the relatively high regularity of the predicted motion of the planet being inconsistant with the observed motion.

Kepler was a long time believer of the Copernican system (the heliocentric system) and he was to add mathematical credibility to the work. It wasn't until 1609 that his conclusions were announced to the world when he published his first two laws of planetary motion together.

This law, also known as the Law of Ellipses, realises that planets do not move in perfectly circular orbits around the Sun but actually move in elliptical orbits with the Sun at one focus.
It is important to realise that the sun is not at the centre of the ellipse; unlike a circle that only has one focal point an ellipse has two and the Sun is at one of these focal points.

A diagram to show the elliptical orbit of a planet and the position of the sun as a focal point.

(Note: the ellipse shown is greatly exaggerated).

Also known as the Law of Equal Areas - The key concept here is that the radius Vector describes equal areas in equal times.
Ok so this is a little more complicated at first glance, however it is not too difficult to grasp with a little explanation and a diagram!

All this means that if you draw a line between any of the planets and the Sun this line will sweep over equal areas in equal time periods.
Why is this? A planet will travel faster as it approaches its perihelion and will be at at its slowest when it is around its aphelion.

So in an equal time period the planet will clearly travel a greater distance along its orbital path at its perihelion than at it's aphelion as it has a greater velocity, but by definition, the distance to the Sun at a planet's perihelion is much less. This results in, as Kepler calculated, that in an equal amount of time the radius vector will cover equal areas.

In this diagram the time period between 1 and 2 is the same as that between 3 and 4, we can see that as the planet is travelling faster at its perihelion (period 1 to 2) it covers a greater distance along its orbital path than at its aphelion (period 3 to 4). We can also see that the distance to the Sun is much less between periods 1 and 2, than between periods 3 and 4. Kepler found that the area A equals area B, in other words equal areas in equal times.

(Note again the ellipse shown is exaggerated).

Following this work, in 1619 Kepler published his third and final law of planetary motion, also known as the Harmonic Law, which was the brilliant conclusion that:

The squares of the periodic times are to each other as the cubes of the mean distances.
Again this seems complicated but it is in fact fairly straight forward, what this is demonstrating is that if you take any two planets the ratio of the squares of the time it takes for them to complete one orbit is equal to the ratio of the cubes of their semimajor axes. Or for a single planet the square of the revolutionary period is proportionate to the cube of its semimajor axis.

Where P is the planet's period of revolution, R is the average distance of the planet from the Sun then:

Equation For Two Planets	Equation For A Single Planet

where K is a constant for all planets

The result of this work is that finally, for the first time, we had a model that was based upon the results of observation rather than having an assumed model and trying to make the observations fit into it. This together with the simplicity of the model made this the strongest argument yet against the geocentric belief.

It can easily be argued that Johannes Kepler was part of the birth of modern science and was probably one of the fathers of modern astronomy. His third law undoubtedly provided some inspiration in the future for Isaac Newton to develop his Law of Gravitation. Due to this Kepler has even been called the founder of celestial mechanics, which would probably be a fair assessment of his work.

Go on to the Dawn of Modern Astronomy and Physics (Galileo)
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