Same sine / cosine model, now with the real Sun and eight planets. Periods and distances from NASA JPL. Mercury is a tight coil; Neptune barely turns.
Click a name to focus its sine / cosine shadows. Periods are sidereal.
Each planet is the same helix as the sine / cosine page, with real orbital period and real semi-major axis. The Sun sits at the origin. Time runs into the distance: the front face is “now,” the faded end is the past.
Turns in the window = years of history ÷ the planet’s year. Over 12 Earth years Mercury winds ~50 times and Neptune moves ~7% of one lap. That’s Kepler’s third law in a picture: T² ∝ a³ — farther out is slower, not just bigger.
Orbits are treated as circles using NASA JPL mean longitudes (J2000 elements, 1800–2050). Mercury’s real path is the most elliptical (e ≈ 0.21); everyone else is close to a circle. Inclinations are ignored so the sine / cosine walls stay honest. Phases are approximately where the planets actually are for the simulated date.
Linear AU is true distance — Neptune is 30× Earth and the inner system collapses to a speck. √AU keeps periods exact and only compresses radius so all eight stay readable.
Elements: NASA JPL / Standish & Williams · companion to sine & cosine · space to pause · 1–4 for views