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diff --git a/src/space/mod.rs b/src/space/mod.rs
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+//! Space: star systems with proper orbits, the places in them you can fly
+//! around, and the rules of flight.
+//!
+//! There are two scales. A system is measured in AU and days: planets follow
+//! Kepler orbits around the star, moons around their planets, and the
+//! calendar moves them on. You never fly at that scale. Instead you travel
+//! between places (a planet's orbit, a moon, a belt, a station), and each
+//! place is a small local map you fly around in, measured in local units:
+//! one unit is one terminal cell across and half a cell down (cells are about
+//! twice as tall as they are wide), so circles come out round on screen.
+//! Local maps use screen-style coordinates, with y pointing down.
+//!
+//! Above both is the galaxy: star systems in light-years, joined by lanes
+//! you jump along (see `galaxy`).
+
+pub mod flight;
+pub mod galaxy;
+pub mod locale;
+pub mod orbit;
+pub mod survey;
+pub mod system;
+
+use std::f64::consts::{PI, TAU};
+use std::ops::{Add, AddAssign, Mul, Neg, Sub, SubAssign};
+
+use crate::seed;
+
+/// The star system a universe first started everyone in. It's one of the
+/// four peoples' seats in its galaxy (see `galaxy`).
+pub fn home_system(universe: u64) -> system::System {
+    system::generate(seed::derive(universe, "system", 0))
+}
+
+#[derive(Clone, Copy, Debug, Default, PartialEq)]
+pub struct Vec2 {
+    pub x: f64,
+    pub y: f64,
+}
+
+impl Vec2 {
+    pub const ZERO: Vec2 = Vec2::new(0.0, 0.0);
+
+    pub const fn new(x: f64, y: f64) -> Vec2 {
+        Vec2 { x, y }
+    }
+
+    /// On a local map, the unit vector pointing along `heading`: 0 is up the
+    /// screen, and headings increase clockwise.
+    pub fn from_heading(heading: f64) -> Vec2 {
+        Vec2::new(heading.sin(), -heading.cos())
+    }
+
+    /// The heading this vector points along, the inverse of `from_heading`.
+    pub fn heading(self) -> f64 {
+        self.x.atan2(-self.y).rem_euclid(TAU)
+    }
+
+    pub fn rotated(self, angle: f64) -> Vec2 {
+        let (s, c) = angle.sin_cos();
+        Vec2::new(self.x * c - self.y * s, self.x * s + self.y * c)
+    }
+
+    pub fn length(self) -> f64 {
+        self.x.hypot(self.y)
+    }
+
+    pub fn distance(self, other: Vec2) -> f64 {
+        (self - other).length()
+    }
+
+    pub fn dot(self, other: Vec2) -> f64 {
+        self.x * other.x + self.y * other.y
+    }
+
+    /// This vector at length 1, or zero if it has no length.
+    pub fn normalised(self) -> Vec2 {
+        let len = self.length();
+        if len > 0.0 { self * (1.0 / len) } else { Vec2::ZERO }
+    }
+}
+
+impl Add for Vec2 {
+    type Output = Vec2;
+    fn add(self, o: Vec2) -> Vec2 {
+        Vec2::new(self.x + o.x, self.y + o.y)
+    }
+}
+
+impl Sub for Vec2 {
+    type Output = Vec2;
+    fn sub(self, o: Vec2) -> Vec2 {
+        Vec2::new(self.x - o.x, self.y - o.y)
+    }
+}
+
+impl Mul<f64> for Vec2 {
+    type Output = Vec2;
+    fn mul(self, k: f64) -> Vec2 {
+        Vec2::new(self.x * k, self.y * k)
+    }
+}
+
+impl Neg for Vec2 {
+    type Output = Vec2;
+    fn neg(self) -> Vec2 {
+        Vec2::new(-self.x, -self.y)
+    }
+}
+
+impl AddAssign for Vec2 {
+    fn add_assign(&mut self, o: Vec2) {
+        *self = *self + o;
+    }
+}
+
+impl SubAssign for Vec2 {
+    fn sub_assign(&mut self, o: Vec2) {
+        *self = *self - o;
+    }
+}
+
+/// The signed angle to turn through to get from `from` to `to`, the short
+/// way round: between -π and π.
+pub fn turn_between(from: f64, to: f64) -> f64 {
+    (to - from + PI).rem_euclid(TAU) - PI
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn headings_round_trip() {
+        for i in 0..16 {
+            let h = TAU * f64::from(i) / 16.0;
+            assert!((Vec2::from_heading(h).heading() - h).abs() < 1e-9);
+        }
+        let up = Vec2::from_heading(0.0);
+        assert!(up.x.abs() < 1e-9 && (up.y + 1.0).abs() < 1e-9, "heading 0 points up the screen");
+        assert!((Vec2::from_heading(TAU / 4.0).x - 1.0).abs() < 1e-9, "a quarter turn is right");
+    }
+
+    #[test]
+    fn turning_takes_the_short_way() {
+        assert!((turn_between(0.1, TAU - 0.1) + 0.2).abs() < 1e-9);
+        assert!((turn_between(TAU - 0.1, 0.1) - 0.2).abs() < 1e-9);
+    }
+
+    #[test]
+    fn rotation_is_anticlockwise() {
+        let v = Vec2::new(1.0, 0.0).rotated(PI / 2.0);
+        assert!(v.x.abs() < 1e-9 && (v.y - 1.0).abs() < 1e-9);
+    }
+}