If you look in the night sky you can see the planets (well, Uranus, Neptune, and Pluto require a telescope), and in fact Jupiter and Saturn appear brighter in the sky than even the brightest star (other than our own Sun, which is also a star!) Night to night they change their position in the sky though.

The ancient Greeks, Romans, and Egyptians, such as Ptolemy, came up with a geocentric system in which the planets went about the Earth in circles. In order to account for all the details, such as retrograde motion, Ptolemy needed to add epicycles. Planets went around on circles attached to other circles.

Copernicus came up with a system that had the Sun in the center of the Universe, with the planets (including the Earth) going in circular orbits. The Moon also went around the Earth. However, Copernicus was careful not to upset the authorities of his time. He only agreed for his book to be published as he was dying, and even then he declared that it was only a method of predicting where planets were, not the truth of how they actually moved.

However, even Copernicus's system was not so great at figuring out where planets would be. His system still needed epicycles, athough his system had a better explanation for retrograde motion (that the Earth catches up and passes other planets.)

Tycho Brahe was a very colorful character. He had part of his nose sliced off in a duel when he was 20 (the fight was over who was the best mathematician.) For the rest of his life, he wore a gold or silver nose, and carried around putty to keep it attached. He and his assistants made the most accurate naked-eye observations of all time. This was all before the invention of the telescope, so Brahe had to rely on mechanical devices to help him figure out the angle of where a star or planet were in the sky. These observations were accurate to 1' (one arc minute, or 1/60 of a degree, or about 1/30 of the angle of the Full Moon in the sky.)

But the predictions of Copernicus and Ptolemy were about 8' off! Something was wrong.

However, Tycho was not the person to figure it out. Story has it that Tycho died after eating and drinking to excess. He couldn't excuse himself from the presence of the King, who he was dining with. How could you say to a King that going to the bathroom was more important than his presence? So, according to legend, Tycho's bladder burst and he died.

But Tycho is supposed to have said to his assistant, "Make it so that I did not live in vain."

Kepler had a more quiet, serious personality than Tycho. And in keeping with his character, he took very seriously his mission of trying to understand how the planets moved. (Kepler wasn't boring though--he wrote some of the first science fiction, and his mother was accused of being a witch.)

Actually I once got a phone call at 3am. A friend of mine (same friend who named her baby Perihelion) needed to know Kepler's laws. Apparently, she had been at a party and was showing off a bit to much. "Ok, if you're so smart, what are Kepler's laws?" she was asked. Her only hope for an answer was to call me.

Now, one good reason for you to learn Kepler's laws is that my friend may call you too! And in case you're ever showing off at a party in Japan, don't expect me to help you remember what Kepler's laws are!

Seriously, Kepler was in some ways the first modern scientist, because he gave up his own cherished beliefs in the face of evidence. Kepler's pet theory was that the reason there were 6 planets in the Solar System (we've since learned about Uranus, Neptune, and Pluto, but before the telescope only Mercury, Venus, Earth, Mars, Jupiter, and Saturn were known) was that they moved on spheres that sandwiched "perfect solids" between them. The "perfect solids" had been studied by the Greeks; they were shapes in which all the faces were equal. Here's a picture of Kepler's (wrong) model:

But faced with the incredibly accurate data of Tycho Brahe, Kepler came up with 3 "laws" that we accept today. These 3 laws also led to Newton's theory of gravity, but in Kepler's time, nobody knew why they were true. Kepler himself thought that magnetism was the force that kept the Solar System together. Now we know it's gravity.

An ellipse is to a circle as a rectangle is to a square.

That is to say, an ellipse is round like a circle, but doesn't have to have its sides equal, just like a rectangle has one side longer than the other.

A circle has a center, and can be defined as all the points at the same distance (the radius) from that center.

An ellipse can be defined as given by two "centers" actually called foci (each one is a focus.) You go from one focus to the curve and then back to the other focus. That distance is the same for the entire ellipse.

You can think about nailing down to ends of a string, and then using a pencil to trace out the ellipse by stretching the string as far as it goes in all directions.

This figure is from your textbook (The Cosmic Perspective, Bennett, Donahue, Schneider, and Voit). It shows the definition of an ellipse. Planets orbit the Sun in the shape of an ellipse, as found from painstaking observations of Tycho and calculations of Kepler.

According to Kepler's 1st law, the Sun is at one of the foci of the ellipse. What's at the other focus? Nothing special!

Each planet moves in its own ellipse. All of them have the Sun at one focus, but they don't have to all have the same second focus. And there's absolutely nothing special about the 2nd focus of the Earth's orbit.

So this is from an Appendix in our textbook, showing the eccentricity of each planet's orbit:

Kepler's 2nd law tells you how fast a planet moves at different times in its elliptical orbit. The law says--and I know this sounds like a political slogan, but it's really part of the science of astronomy--Equal Areas in Equal Times.

Over any time period--say a week--when a planet goes around on its ellipse, you can imagine a "pie wedge" shaped area that it sweeps up. When it's far away (apehelion) and when it's close (perihelion) it will, over a week, still sweep out the same area. When it's further away, the pie wedge will have to be narrower to compensate for the fact that the distance to the Sun is greater. So the planet won't go as far in a week when it's far away as when it's close in. It goes faster close in, and slower when it's further away. We now understand this as a result of the conservation of angular momentum, which I'll tell you about in more detail later. It's the real reason the world goes 'round!

In words, this means that as a becomes larger (the orbit is larger), then P becomes larger too. You would expect this. A planet in a larger orbit has further to go, so it should take longer, even if it goes at the same speed.

Galileo didn't invent the telescope, but he was the first to use it for serious astronomy. With his telescope, he made several discoveries that reinforced the Copernican view that the planets (including Earth) went around the Sun and not the Earth:

• The Phases of Venus
• The Moons of Jupiter (not everything was in orbit around the Earth)
• Sunspots (the Sun isn't "perfect")
• Craters on the Moon
• The Milky Way is made of many many stars

And here are some actual astronomical photographs: