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Chaotic Orbit

Find the speed and angle
to achieve a stable orbit.

🏆 Best0 orbits
🔥 Daily streak0 days
NumCalcX

How Orbital Mechanics Works

Every planet in this game pulls on your satellite with Newton's law of gravitation: the force is proportional to the planet's mass and falls off with the square of the distance — twice as far away means a quarter of the pull, not half. That inverse-square relationship is why a stable orbit exists at all: launch too slowly and gravity wins, pulling you into a collision; launch too fast and you escape into space before gravity can curve your path into a loop. Between those extremes sits a range of speed-and-angle combinations that trace a closed, repeating path around the planet — the same balance that keeps real satellites, moons, and planets in orbit.

With a single planet, the game runs a straightforward two-body problem: Newton solved this case completely, and it has a fairly forgiving, well-understood range of launch conditions that produce a stable orbit. From level 3 onward, a second (and eventually third) planet's gravity pulls on your satellite at the same time, and there's no exact formula for that — it's the same fundamental difficulty as the three-body problem, one of the oldest unsolved questions in physics. Every frame, the game numerically re-calculates the real gravitational pull from every planet and steps your satellite's position forward accordingly, so a launch angle that orbits cleanly around one planet can be flung into a wildly different — and much harder to predict — path once a second planet's gravity is added.

Frequently Asked Questions

Why does the right launch angle change depending on the speed I pick?

Because an orbit is a balance between your satellite's forward motion and the planet's inward pull, and both speed and direction determine where that balance lands. The same speed launched straight up falls back down or flies off; launched sideways at the right height it can curve into a loop. There's no single "correct" speed or angle in isolation — only combinations of the two that balance.

Why do 2-3 planet levels feel so much less predictable than the single-planet ones?

With one planet, gravity always pulls toward the same point, and the physics has an exact, well-behaved solution — that's the two-body problem Newton solved centuries ago. Add a second planet and the pull on your satellite constantly shifts between two competing sources with no exact formula for the result, which is the same reason the general three-body problem is still, in a real mathematical sense, unsolved: small changes in launch speed or angle can send you into a stable-looking loop or a collision with almost no warning.

Is the orbit actually simulated with real physics, or is the path just an animation?

It's a real simulation, not a scripted animation. Every frame, the game calculates the actual inverse-square gravitational force from each planet on your satellite's current position, updates its velocity and position accordingly, and checks whether it collided, escaped, or is still in flight — the trajectory you see is the direct result of that physics, recalculated fresh on every launch.