Why does my planet fly away or crash?

It was thrown too fast to stay bound, or it passed close to another world, whose gravity changed its orbit. Close encounters are chaotic, which is why real stable systems keep their planets far apart. Try a tap, which gives a circular orbit, and leave plenty of room between neighbours.

How do I give a planet a moon?

Choose the moon, then tap or drag just outside a ringed giant, inside the yellow dotted circle that appears around it. Your moon is launched relative to the giant, and a tap puts it on a circular orbit around it. Moons have to stay well inside the planet’s Hill sphere, or the Sun pulls them away.

How do I catch a Trojan?

Add a giant, then tap a small world onto one of the faint L4 or L5 crosses that ride along the giant’s orbit, 60° ahead or behind it. Keep it there for three of the giant’s orbits.

Why is T²÷a³ not exactly 1?

The other worlds tug on each other, so orbits are never perfect ellipses, and Newton’s version of Kepler’s law includes the planet’s own mass, which matters for the heavy giants. Moons orbit their planet rather than the Sun, so their constant is set by the planet’s mass instead.

Keep Them Orbiting

Fling planets around a painted sun and try to keep them there. Every orbit plays a note. Back to the game

How to play

Pick a world from the strip at the bottom: a rocky planet, an ocean world, a ringed giant or a small moon. Tap anywhere on the sky to drop it into a perfectly circular orbit, or press and drag to fling it: the direction and length of your drag set its velocity. While you drag, a dotted line shows where it will go, worked out by running the real simulation ahead of time. If your fling is close to a circular orbit, it snaps to one. Start a drag close to a big planet (inside the yellow dotted circle) and your new world is flung around that planet instead, which is how you give it a moon.

Your score is in planet-years: every year that passes earns one point for each world still in the picture. The clock starts the moment you first touch the sky, and a world flung far off the page stops counting until it comes back. One year is the time a world takes to go once around the Sun at 1 AU, the dotted circle closest to the Sun. Each world chimes as it crosses the faint line straight above whatever it orbits, with a pitch set by its orbital period: fast inner worlds ring high, slow outer giants hum low. Tick off the goals on the list, try new sky for an empty sky or the sky of the day (the same system for everyone, all day), use the speed buttons to fast-forward the centuries, and press frame it to see and share your system. On a keyboard, keys 1 to 4 choose a world, the arrow keys place it (Shift with up and down changes its speed), Space launches it and P pauses.

Kepler’s three laws

Johannes Kepler worked out from Tycho Brahe’s observations that planets move on ellipses with the Sun at one focus, and that a line from the Sun to a planet sweeps out equal areas in equal times, so planets speed up when they are close to the Sun (published in 1609). Ten years later, in Harmonices Mundi (1619), he found his third law: the square of a planet’s period is proportional to the cube of its distance. In years and astronomical units it is simply T² = a³, which is why the T²÷a³ column in the notebook stays close to 1 for every world circling the Sun. Isaac Newton later showed that all three laws follow from gravity weakening with the square of distance, and that the constant depends on the mass being orbited, which is why moons of the same planet share a different constant. The same book is where Kepler, chasing the ancient idea of a music of the spheres, assigned musical notes to the planets according to their speeds.

Why most random systems fall apart

Two bodies alone orbit each other forever in a neat ellipse. Add a third and there is no general formula for what happens next. Henri Poincaré showed in the 1890s that the three-body problem is chaotic: a tiny change in the starting positions can grow until the whole future is different. Planets that pass close to each other trade energy until one is flung inward, crashes into a neighbour or is thrown out of the system entirely. Astronomers think this really happens, and that the galaxy holds huge numbers of these lonely rogue planets. Stable systems keep their planets well spaced (several times the zone each planet controls, its Hill sphere) or lock them into resonances: Neptune goes round the Sun three times for every two orbits of Pluto, and Jupiter’s moons Io, Europa and Ganymede are locked in a 1:2:4 rhythm. Some systems chain several resonances together: the seven Earth-sized planets of TRAPPIST-1, 40 light-years away, have neighbouring periods in ratios close to 8:5, 5:3, 3:2, 3:2, 4:3 and 3:2. Rare, delicate periodic solutions exist too, like the figure-eight in which three equal masses chase each other along a single curve, found by computer by Cris Moore in 1993 and proved to exist by Alain Chenciner and Richard Montgomery in 2000.

Lagrange points and Trojans

Around any planet orbiting the Sun there are five places where a small object can keep pace with it. Two of them, L4 and L5, sit 60° ahead of and behind the planet on its orbit, and they are stable as long as the planet has less than about a twenty-fifth of the Sun’s mass. Jupiter shares its orbit with more than ten thousand known Trojan asteroids gathered around its L4 and L5 points, the first found in 1906. The game marks L4 and L5 for every giant you add.

Is our solar system stable?

Probably, for a while yet. Computer simulations by Jacques Laskar and colleagues show that the planets’ orbits are chaotic over tens of millions of years, so their exact positions can’t be predicted that far ahead, but the system as a whole holds together. In 2009 Laskar and Mickaël Gastineau ran 2,501 versions of the next five billion years and found that in about 1% of them Mercury’s orbit stretches enough to collide with Venus or the Sun. The other 99% stay calm until the Sun itself grows into a red giant.

What’s real and what isn’t

The physics is a genuine n-body simulation: every world pulls on every other world and on the Sun, which wobbles in response, just as real stars wobble when planets tug on them. It uses a leapfrog integrator with a fixed time step, the kind of method astronomers use because it doesn’t make orbits slowly spiral in or out. Some things are fudged so you can actually see them. The worlds are drawn far larger than real planets would be, collisions just merge two worlds, and the masses are exaggerated: the ringed giant is about 26 times heavier than Jupiter, so that it can hold moons and Trojans you can see.

Questions people ask

Why does my planet fly away or crash?: It was thrown too fast to stay bound, or it passed close to another world, whose gravity changed its orbit. Close encounters are chaotic, which is why real stable systems keep their planets far apart. Try a tap, which gives a circular orbit, and leave plenty of room between neighbours.
How do I give a planet a moon?: Choose the moon, then tap or drag just outside a ringed giant, inside the yellow dotted circle that appears around it. Your moon is launched relative to the giant, and a tap puts it on a circular orbit around it. Moons have to stay well inside the planet’s Hill sphere, or the Sun pulls them away.
How do I catch a Trojan?: Add a giant, then tap a small world onto one of the faint L4 or L5 crosses that ride along the giant’s orbit, 60° ahead or behind it. Keep it there for three of the giant’s orbits.
Why is T²÷a³ not exactly 1?: The other worlds tug on each other, so orbits are never perfect ellipses, and Newton’s version of Kepler’s law includes the planet’s own mass, which matters for the heavy giants. Moons orbit their planet rather than the Sun, so their constant is set by the planet’s mass instead.