Kepler's six planets
In 1619 Johannes Kepler published Harmonices Mundi and gave each planet a voice. He knew six (Uranus wasn't found until 1781), and the Orrery's six rings are his six, Mercury nearest the sun. As he worked out, the inner planets go round faster, so here they sing higher.
Where they really were
Each position comes from NASA JPL's Keplerian elements: six numbers for each planet's orbit, and how they drift over a century, fitted by E. M. Standish to JPL's full ephemeris. Solving Kepler's own equation turns them into each planet's direction from the sun, right here in the page.
From 1800 to 2050 they agree with JPL's full ephemeris to within a fifth of a degree; we checked every tenth day. Outside those years the elements aren't valid, so the Orrery doesn't guess. Positions are for 00:00 UTC: Mercury, the fastest, moves up to about 6° in a day.
Which way is up
You're looking down on the solar system from the north, where every planet goes round counterclockwise. The line above the sun points toward 0°: the vernal equinox, the direction we see the sun in at the March equinox. Astronomers measure from it, as it was in 2000 (the standard J2000 frame), and each planet's angle counts counterclockwise from there.
Earth itself reaches 0° every September, at the equinox, when we see the sun on the far side of the sky, at 180°.
Check it yourself
Each Horizons link in the table opens JPL's own answer for that planet on this date, from Horizons, JPL's high-precision ephemeris service. Find the hEcl-Lon column: it matches the table to within a few tenths of a degree.
Two ways to hear it
Kepler's song plays this day's sky as the Orrery's music: the planets start where they were and circle its rings, coming back to this exact sky every 12 seconds, on repeat. With exact timing off, each chime lands on the nearest beat; on, each planet chimes the moment it crosses the line.
Real speeds lets the real solar system run on from this day, about 30 days a second. Each planet chimes as it passes 0°: Mercury every three seconds or so, Earth every 12, Saturn every six minutes. It never comes round to the same sky again, so it runs until you pause it.
Skies worth a listen