Orbits

The core idea

A handful of bodies share a single circle, spaced evenly around it, all sweeping at the same angular speed. There is no gravity and no interaction here — just clean circular motion. The beauty is in what gets left behind: each frame fades rather than clears, so the orbiters smear into glowing arcs that turn a static loop into a living, luminous ring.

How it works

The position is pure trigonometry. Body i of n sits on the circle at angle

$a_i = t\,v + \frac{i}{n}\,2\pi$

where $t$ is elapsed time and $v$ is the speed. The $\frac{i}{n}\,2\pi$ offset distributes the bodies at equal angular spacing, and the shared $t\,v$ term advances them all in lockstep — so they stay rigidly evenly spaced as they rotate. Each orbiter is then drawn at

x = cx + R·cos(a)
y = cy + R·sin(a)

with $R$ a fraction of the canvas half-width. A small central dot marks the shared centre.

The trails are a rendering trick, not physics. Instead of wiping the canvas each frame, we paint a translucent rectangle in the stage's background colour over everything. Old pixels survive, dimmed a little more on every pass, so the recent history of each body lingers as a fading tail. The Trail value is that per-frame opacity: a lower value fades more gently, leaving longer light streaks.

What to watch for

This is the same accumulation-buffer technique behind motion blur, phosphor-decay oscilloscope displays, and long-exposure photography — the image is an integral over time, not a single instant. Push the orbiter count up and the trails overlap into a near-solid annulus; drop Trail low and a single body paints a complete glowing hoop before its own tail catches up. Because the motion is perfectly periodic and uniform, the eye reads the trails as a frozen ring even though every dot is moving — a small lesson in how persistence of vision builds shape out of speed.

Knobs

• Orbiters — how many bodies share the circle.
• Speed — angular velocity.
• Radius — circle size relative to the canvas.
• Trail — per-frame fade; lower = longer light trails.
• Color — orbiter + glow colour.