Orbit view shows the planets going around the Sun. Travel view shows the whole Solar System flying through the galaxy, so each planet draws a spiral. Planet sizes are made bigger so you can see them.
The Sun comes back to the same place in the sky every year. The planets come back too. Anything that repeats so exactly must be following a rule, and I wanted to find the shape behind that rule.
Every orbit looks like a circle, but it is a little stretched. This shape is called an ellipse. Pick Mercury in the model and look closely: the Sun is not in the middle.
Turn the model sideways. All eight orbits lie almost flat, like rings drawn on one dinner plate. A flat surface like this is called a plane.
Mercury races. Neptune crawls. The farther a planet is from the Sun, the longer one lap takes, and the pattern is very exact.
The Sun is moving too. Switch to Travel view: a circle that also moves forward becomes a spiral, called a helix. It is the shape of a spring.
Most patterns are something you look at. This one we are standing on. Earth is drawing an ellipse right now, at 30 kilometres every second, and nobody feels it.
Johannes Kepler found the first three rules about 400 years ago by studying the planet Mars. Isaac Newton later showed that all of them come from one thing: gravity.
An ellipse has two special points inside it, called foci (say: FOH-sigh). The Sun sits on one of them. The other one is empty.
Watch the two lines in the picture. One gets longer, the other gets shorter, but together they always add up to the same length. That is what makes an ellipse an ellipse.
The number e tells how squished it is. 0 is a perfect circle. Close to 1 is very long and thin.
Draw a line from the Sun to the planet. As the planet moves, that line sweeps over a slice of space, like a windscreen wiper.
Near the Sun the slice is short, so it has to be wide. The planet must move fast to make it wide. Far from the Sun the slice is long and thin, so the planet moves slowly.
The 3D model above uses this rule to move every planet.
Measure distance in AU (1 AU = the distance from Earth to the Sun). Measure time in Earth years. Then:
In words: year × year = distance × distance × distance. Check the table. The last two columns match for every planet.
Try it: Jupiter is 5.2 AU away. 5.2 × 5.2 × 5.2 ≈ 141. Which number times itself gives 141? About 11.9. And Jupiter's year really is 11.9 Earth years.
All eight planets land on one straight line. Each step on these axes is 10 times bigger than the one before, so tiny Mercury and far Neptune both fit.
The Sun flies around the centre of our galaxy at about 230 km every second. The planets come along. So a planet does two moves at once: it goes around, and it goes forward.
You do not need to know cos and sin yet. They are just the maths way of saying “go around a circle”. Put the three parts together and you get the shape of a spring.
The planets’ plate is tilted about 60° to the direction the Sun travels. That is why the spirals in Travel view lean.
The Sun pulls every planet. The r² on the bottom is the key: twice as far away means the pull is 4 times weaker. Three times as far means 9 times weaker.
A weaker pull means a planet needs less speed to stay in orbit. That is why far planets are slow, and it is where Rule 3 comes from.
“Orbits are circles.” That was my first guess. Earth’s squish is only 0.017, so by eye it looks like a circle. I could only see the ellipse when I checked the numbers: Earth is 147 million km from the Sun in January and 152 million km in July.
“The planets trail behind the Sun like a tail.” Some videos online show this. It is wrong. A planet is in front of the Sun for half of its lap and behind it for the other half. Fixing this made my Travel view correct.
“Real distances will look good.” They do not. Turn on Real distances in the model: the four inner planets squeeze into a dot. This made me see how empty space is.
My creation is the 3D model at the top of this page. Nothing in it is a recorded video. Every frame, the computer uses the rules from Section 2 to work out where each planet should be.
Each path is a real ellipse with the Sun on one focus (Rule 1). Each planet speeds up near the Sun (Rule 2). Each lap time comes from T² = a³ (Rule 3). Travel view adds the forward motion (Rule 4).
Neptune is really about 78 times farther out than Mercury. On a screen, the inner planets would vanish. So I used the square root of each distance. Now Neptune is only about 6 times farther, and the order stays the same. The Real distances switch shows the true picture.
I squeezed space but I did not squeeze time. The lap times are the real ones. Count for yourself: Mercury goes around about 4 times while Earth goes around once.
The Sun moves almost 8 times faster than Earth, so the real helix is stretched out very long. I made the forward speed smaller so the coils are easy to see. The 60° tilt is real.