A star, its planets and their moons in four dimensions of space with gravity pinned like charge (the pull falls as 1/r², so orbits close, as ours do). Nothing is on rails: every body pulls every other, stepped forward live, from the results of the planetary-systems chapter.

• computed The planes. A 4D nebula spinning at two rates, 1 and q, ends a thick lens. Every orbit's left half of turning lines up with the cloud's, and its right half only to a mean cosine just under (1 − q)/(1 + q) (measured). So any two planets' planes are tilted by the same angle in both of 4D's directions at once. A random spin's q is typically about a fifth.
• computed The spacing. Each planet sits past the one inside at the closest ratio the stability map kept for 100,000 orbits at their tilt and mass, with a margin. The system is run before it's shown, and redrawn if anything strays.
• computed The moons. Each in its planet's completely orthogonal plane, the one the star can't tug (the moon runs), a third of the way to where the star would take it. Drawn farther out than they are until you zoom in.
• follows Temperatures. Starlight thins as 1/r³ and a planet glows as T⁵, so T falls as r^−3/5: our water's liquid band runs from 57 to 96 star radii.
• a choice The star is as hot as our Sun (a 4D star's surface temperature isn't known yet). How many planets and their masses (Jupiter's or a tenth of it) aren't derived: this is a possible system, checked by running it.
• computed Tides. A star's tide locks a planet's spin in its orbit's plane and can't touch its turning in the completely orthogonal plane: a locked 4D planet keeps turning, with a fixed day side and night side under a wheeling sky (the tides section).
• open Spins, seasons, magnetic fields. The spins planets are born with, and how soon tides lock them, aren't worked out yet, so the planets here don't turn. A spinning planet with a conducting core makes a magnetic field shaped like its spin (fields, toy 7). Next: those, and the star's wind meeting them.