diff --git a/DECISIONS.md b/DECISIONS.md
index 6ebac1c..8cef03f 100644
--- a/DECISIONS.md
+++ b/DECISIONS.md
@@ -87,3 +87,10 @@ Implementation decisions not spelled out in `memory-bank/implementation-plan.md`
 
 - **Seeds are 32-bit unsigned integers.** The PRNG is mulberry32; child seeds are an FNV-1a hash of the label, started from the parent seed, plus a final mixing step.
 - **`createRng` returns an object with internal state.** It is still deterministic: the same seed always gives the same sequence. Each use (a board, a name) creates its own generator from a derived seed, so draws never depend on call order elsewhere.
+
+## Step 3.3
+
+- **Positions are heliocentric, in the J2000 mean ecliptic plane** (`HelioVector` rotated by `Rotation_EQJ_ECL`), keeping x and y and dropping the small out-of-plane z.
+- **The Moon is Earth plus 0.384M km on the +x axis**, as the plan specifies; its real orbit is ignored.
+- **Ceres uses a circular orbit** (astronomy-engine has no Ceres): radius 2.7675 AU (~414M km), period 1,680.5 days, mean longitude ~160° at J2000. The angle is approximate, which is fine for gameplay.
+- **Test date is 2100-03-01**, close to the placeholder game epoch.
diff --git a/memory-bank/progress.md b/memory-bank/progress.md
index c021c48..b01614b 100644
--- a/memory-bank/progress.md
+++ b/memory-bank/progress.md
@@ -21,7 +21,7 @@
 
 - [x] **Step 3.1 — Game clock conversion.** `src/clock.ts`: `realToGame` / `gameToReal` using the config epoch and compression; times are Unix-ms numbers.
 - [x] **Step 3.2 — Seeded RNG.** `src/rng.ts`: `createRng(seed)` (mulberry32) with `next`, `int`, `pick`; `deriveSeed(parent, label)` for child seeds.
-- [ ] Step 3.3 — Location positions
+- [x] **Step 3.3 — Location positions.** `src/positions.ts`: heliocentric ecliptic positions (million km) from `astronomy-engine` for Earth, Mars and Jupiter; Moon = Earth + fixed offset; Ceres on a circular orbit.
 - [ ] Step 3.4 — Route distance
 - [ ] Step 3.5 — Travel time
 - [ ] Step 3.6 — Fuel cost
diff --git a/packages/sim/package.json b/packages/sim/package.json
index 6027bf4..56d4633 100644
--- a/packages/sim/package.json
+++ b/packages/sim/package.json
@@ -9,6 +9,7 @@
     "typecheck": "tsc --noEmit"
   },
   "dependencies": {
-    "@deadhead/content": "workspace:*"
+    "@deadhead/content": "workspace:*",
+    "astronomy-engine": "^2.1.19"
   }
 }
diff --git a/packages/sim/src/index.ts b/packages/sim/src/index.ts
index 984edf2..1dc91a0 100644
--- a/packages/sim/src/index.ts
+++ b/packages/sim/src/index.ts
@@ -1,2 +1,3 @@
 export * from "./clock";
 export * from "./rng";
+export * from "./positions";
diff --git a/packages/sim/src/positions.ts b/packages/sim/src/positions.ts
new file mode 100644
index 0000000..8de0a28
--- /dev/null
+++ b/packages/sim/src/positions.ts
@@ -0,0 +1,60 @@
+import type { AstronomyBody, Location } from "@deadhead/content";
+import { Body, HelioVector, KM_PER_AU, RotateVector, Rotation_EQJ_ECL } from "astronomy-engine";
+import type { GameTime } from "./clock";
+
+/** A heliocentric point in the ecliptic plane, in million km. */
+export interface Position {
+  x: number;
+  y: number;
+}
+
+const MILLION_KM_PER_AU = KM_PER_AU / 1e6;
+const MS_PER_DAY = 86_400_000;
+const J2000 = Date.UTC(2000, 0, 1, 12);
+
+/** Fixed Earth→Moon offset (mean lunar distance); the Moon's orbit is ignored. */
+const MOON_OFFSET_MILLION_KM = 0.384;
+
+/**
+ * Ceres is not in astronomy-engine, so it follows a circular orbit with its
+ * real mean radius and period, starting from its approximate J2000 mean longitude.
+ */
+const CERES_RADIUS_AU = 2.7675;
+const CERES_PERIOD_DAYS = 1680.5;
+const CERES_J2000_LONGITUDE_DEG = 160;
+
+const eqjToEcliptic = Rotation_EQJ_ECL();
+
+function planetPosition(body: Body, gameTime: GameTime): Position {
+  const ecliptic = RotateVector(eqjToEcliptic, HelioVector(body, new Date(gameTime)));
+  return { x: ecliptic.x * MILLION_KM_PER_AU, y: ecliptic.y * MILLION_KM_PER_AU };
+}
+
+function ceresPosition(gameTime: GameTime): Position {
+  const days = (gameTime - J2000) / MS_PER_DAY;
+  const angle = ((CERES_J2000_LONGITUDE_DEG + (360 * days) / CERES_PERIOD_DAYS) * Math.PI) / 180;
+  const radius = CERES_RADIUS_AU * MILLION_KM_PER_AU;
+  return { x: radius * Math.cos(angle), y: radius * Math.sin(angle) };
+}
+
+export function bodyPosition(body: AstronomyBody, gameTime: GameTime): Position {
+  switch (body) {
+    case "earth":
+      return planetPosition(Body.Earth, gameTime);
+    case "moon": {
+      const earth = planetPosition(Body.Earth, gameTime);
+      return { x: earth.x + MOON_OFFSET_MILLION_KM, y: earth.y };
+    }
+    case "mars":
+      return planetPosition(Body.Mars, gameTime);
+    case "ceres":
+      return ceresPosition(gameTime);
+    case "jupiter":
+      return planetPosition(Body.Jupiter, gameTime);
+  }
+}
+
+/** A location's 2D position at a game time, in million km from the Sun. */
+export function locationPosition(location: Location, gameTime: GameTime): Position {
+  return bodyPosition(location.body, gameTime);
+}
diff --git a/packages/sim/test/positions.test.ts b/packages/sim/test/positions.test.ts
new file mode 100644
index 0000000..9091cf8
--- /dev/null
+++ b/packages/sim/test/positions.test.ts
@@ -0,0 +1,42 @@
+import { content } from "@deadhead/content";
+import { describe, expect, it } from "vitest";
+import { locationPosition } from "../src/index";
+
+const when = Date.parse("2100-03-01T00:00:00Z");
+const fromSun = (id: string) => {
+  const { x, y } = locationPosition(content.location(id)!, when);
+  return Math.hypot(x, y);
+};
+
+describe("location positions", () => {
+  it("puts Earth about 150 million km from the Sun", () => {
+    expect(fromSun("earth")).toBeGreaterThan(147);
+    expect(fromSun("earth")).toBeLessThan(153);
+  });
+
+  it("puts Mars 206–250 million km from the Sun", () => {
+    expect(fromSun("mars")).toBeGreaterThan(206);
+    expect(fromSun("mars")).toBeLessThan(250);
+  });
+
+  it("puts Jupiter Cloud Platform 740–820 million km from the Sun", () => {
+    expect(fromSun("jupiter-cloud-platform")).toBeGreaterThan(740);
+    expect(fromSun("jupiter-cloud-platform")).toBeLessThan(820);
+  });
+
+  it("puts Ceres Station on its ~414 million km orbit", () => {
+    expect(fromSun("ceres-station")).toBeCloseTo(414, 0);
+  });
+
+  it("keeps the Moon within 1 million km of Earth", () => {
+    const earth = locationPosition(content.location("earth")!, when);
+    const moon = locationPosition(content.location("moon")!, when);
+    expect(Math.hypot(moon.x - earth.x, moon.y - earth.y)).toBeLessThan(1);
+  });
+
+  it("returns identical values for the same time", () => {
+    for (const location of content.locations) {
+      expect(locationPosition(location, when)).toEqual(locationPosition(location, when));
+    }
+  });
+});
diff --git a/pnpm-lock.yaml b/pnpm-lock.yaml
index 2bb74b2..4895d26 100644
--- a/pnpm-lock.yaml
+++ b/pnpm-lock.yaml
@@ -53,6 +53,9 @@ importers:
       '@deadhead/content':
         specifier: workspace:*
         version: link:../content
+      astronomy-engine:
+        specifier: ^2.1.19
+        version: 2.1.19
 
 packages:
 
@@ -350,6 +353,9 @@ packages:
     resolution: {integrity: sha512-Izi8RQcffqCeNVgFigKli1ssklIbpHnCYc6AknXGYoB6grJqyeby7jv12JUQgmTAnIDnbck1uxksT4dzN3PWBA==}
     engines: {node: '>=12'}
 
+  astronomy-engine@2.1.19:
+    resolution: {integrity: sha512-8yWKNf7UeNbH458h3sAJ6ZgAjE5jTXp/mNNRFoC20j2SHwZIjAQeEsBB2Q3uCFRaTCCJRv33K2XhkhZQMXoX6w==}
+
   balanced-match@4.0.4:
     resolution: {integrity: sha512-BLrgEcRTwX2o6gGxGOCNyMvGSp35YofuYzw9h1IMTRmKqttAZZVU67bdb9Pr2vUHA8+j3i2tJfjO6C6+4myGTA==}
     engines: {node: 18 || 20 || >=22}
@@ -1119,6 +1125,8 @@ snapshots:
 
   assertion-error@2.0.1: {}
 
+  astronomy-engine@2.1.19: {}
+
   balanced-match@4.0.4: {}
 
   brace-expansion@5.0.12: