Nib asked, and Nib — askNib's tutor — drew the answer live at a whiteboard. This is the spoken transcript; enable JavaScript to watch it drawn.
why do stars twinkle but planets don't
A star's light never flickers. In space it shines perfectly steady. The twinkling happens at the very end of its trip, in the air above you.
Air isn't uniform. Pockets of warm and cold air have different densities, and each bends light a little. They swirl, so the path wobbles hundreds of times a second.
A star is so far away it is just a point: Sirius is only 0.006 arcseconds wide. All its light squeezes down one thread, so the whole star jumps and flickers.
A planet is different. It is close enough to be a tiny disc: Jupiter is thirty to fifty arcseconds across. Light from each spot of the disc takes its own path.
Some spots flare while others fade, and the flickers average out. So the planet glows steadily. Not perfectly: low near the horizon, even planets shimmer.
So here's the whole idea. A star is one thread of light and the air shakes it. A planet is many threads that average out. Same air, different sizes.
Twinkling is the air shaking a point of light, and a planet's spread-out glow is too big for it to shake.