feat(cockpit): ride a tracked satellite in an orbital view

With a satellite tracked and no aircraft tracked, Cockpit can ride the
satellite. Entry needs only the Satellites layer; debris can be tracked but
not entered, and voice stays aircraft-only. Double-clicking the tracked
satellite or the entry buttons (reading ORBIT) enter it.

The camera sits on the satellite's per-frame SGP4 position and looks
straight down, turned to the ground track (north-up for a satellite with
none). The optical zoom steps 1x to 8x with a focus pull, the arrows tilt
the view up to 45 degrees off nadir, and Home or 0 returns to nadir. Off
nadir the tilt reads its total angle first and the swath readout becomes an
approximation marked with ≈. While in orbit the map leases flat Esri
imagery, the cloud pass stays off and the view opens in the optical style.

The orbital HUD names the satellite with its owner's flag (from the
flag-icons package, loaded per country) or an organisation badge, its
operator, class, NORAD and COSPAR ids and TLE epoch with the element lines
on request, altitude, orbital speed and the sub-satellite point. CURRENTLY
OVER names the country and its first-level division, or the sea, and from
8x the most prominent populated place nearby, looked up offline from the
bundled Natural Earth packs (populated places are a new pack). The
satellites layer hides the ridden satellite's own marks, dims the other
orbit rings and ignores scene clicks and Escape while held. Exit restores
the camera's field of view and the satellite's follow camera.

C no longer enters or leaves Cockpit, bridge or orbit: it is left to the
app-wide CCTV shortcut, and Escape or the exit button leave first person.

src/cockpitOrbital.test.mjs

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+import test from 'node:test';
+import assert from 'node:assert/strict';
+import {
+  ORBITAL_ZOOM_LADDER,
+  ORBITAL_BASE_FOV_LEO_RAD,
+  ORBITAL_EARTH_RADIUS_M,
+  ORBITAL_SETTLE_MAX_MS,
+  cesiumFrustumFovRad,
+  earthAngularRadiusRad,
+  footprintWidthKm,
+  fovForZoom,
+  interpolateZoomFov,
+  nadirOrientation,
+  nextOrbitalZoom,
+  offNadirAngleDeg,
+  offNadirSwathScale,
+  offNadirOrientation,
+  orbitalBaseFovRad,
+  previousOrbitalZoom,
+  zoomSettleHolding,
+  zoomTransitionBlurPx,
+  zoomTransitionProgress,
+  zoomTransitionState,
+} from './cockpitOrbital.js';
+
+const RAD = Math.PI / 180;
+const dot = (a, b) => a.x * b.x + a.y * b.y + a.z * b.z;
+const norm = (v) => Math.hypot(v.x, v.y, v.z);
+
+/** ECEF position on the mean sphere at a latitude, longitude and altitude. */
+function ecef(latDeg, lonDeg, altitudeM) {
+  const r = ORBITAL_EARTH_RADIUS_M + altitudeM;
+  const lat = latDeg * RAD;
+  const lon = lonDeg * RAD;
+  return {
+    x: r * Math.cos(lat) * Math.cos(lon),
+    y: r * Math.cos(lat) * Math.sin(lon),
+    z: r * Math.sin(lat),
+  };
+}
+
+/** Local north unit vector at a latitude and longitude. */
+function localNorth(latDeg, lonDeg) {
+  const lat = latDeg * RAD;
+  const lon = lonDeg * RAD;
+  return {
+    x: -Math.sin(lat) * Math.cos(lon),
+    y: -Math.sin(lat) * Math.sin(lon),
+    z: Math.cos(lat),
+  };
+}
+
+function assertOrthonormal(orientation) {
+  const { direction, up, right } = orientation;
+  for (const v of [direction, up, right])
+    assert.ok(Math.abs(norm(v) - 1) < 1e-9);
+  assert.ok(Math.abs(dot(direction, up)) < 1e-9);
+  assert.ok(Math.abs(dot(direction, right)) < 1e-9);
+  assert.ok(Math.abs(dot(up, right)) < 1e-9);
+}
+
+test('the nadir view points at the Earth centre with north up', () => {
+  for (const [lat, lon, alt] of [
+    [0, 0, 420e3],
+    [51.6, -97.3, 420e3],
+    [-33.9, 151.2, 20.2e6],
+    [0.05, 75, 35.786e6],
+  ]) {
+    const position = ecef(lat, lon, alt);
+    const orientation = nadirOrientation(position);
+    const toCentre = {
+      x: -position.x / norm(position),
+      y: -position.y / norm(position),
+      z: -position.z / norm(position),
+    };
+    assert.ok(dot(orientation.direction, toCentre) > 1 - 1e-12);
+    assert.ok(dot(orientation.up, localNorth(lat, lon)) > 1 - 1e-9);
+    assertOrthonormal(orientation);
+    // North up puts east on the right of a picture looking down.
+    const east = { x: -Math.sin(lon * RAD), y: Math.cos(lon * RAD), z: 0 };
+    assert.ok(dot(orientation.right, east) > 1 - 1e-9);
+  }
+});
+
+test('over a pole the orientation stays valid and keeps the previous up', () => {
+  for (const z of [1, -1]) {
+    const position = { x: 0, y: 0, z: z * (ORBITAL_EARTH_RADIUS_M + 800e3) };
+    const fallback = nadirOrientation(position);
+    assertOrthonormal(fallback);
+    assert.equal(fallback.direction.z, -z);
+    // The prime-meridian limit of north.
+    assert.ok(Math.abs(fallback.up.x - -z) < 1e-9);
+    const kept = nadirOrientation(position, {
+      previousUp: { x: 0, y: 1, z: 0 },
+    });
+    assertOrthonormal(kept);
+    assert.ok(kept.up.y > 1 - 1e-9);
+  }
+  // Just off the pole, north still points over it.
+  const nearPole = nadirOrientation(ecef(89.9999, 30, 500e3));
+  assertOrthonormal(nearPole);
+  assert.ok(dot(nearPole.up, localNorth(89.9999, 30)) > 1 - 1e-6);
+});
+
+test('a degenerate position has no orientation', () => {
+  assert.equal(nadirOrientation(null), null);
+  assert.equal(nadirOrientation({ x: 0, y: 0, z: 0 }), null);
+  assert.equal(nadirOrientation({ x: NaN, y: 0, z: 0 }), null);
+});
+
+test('each zoom step divides the tangent of the half-angle', () => {
+  const base = ORBITAL_BASE_FOV_LEO_RAD;
+  for (const zoom of ORBITAL_ZOOM_LADDER) {
+    const fov = fovForZoom(base, zoom);
+    assert.ok(Math.abs(Math.tan(fov / 2) - Math.tan(base / 2) / zoom) < 1e-12);
+  }
+  assert.ok(
+    Math.abs(
+      Math.tan(fovForZoom(base, 4) / 2) / Math.tan(fovForZoom(base, 2) / 2) -
+        0.5,
+    ) < 1e-12,
+  );
+  assert.equal(fovForZoom(base, 1), base);
+  assert.equal(fovForZoom(base, 0), base);
+});
+
+test('zoom steps clamp at both ends without wrapping', () => {
+  assert.equal(nextOrbitalZoom(1), 2);
+  assert.equal(nextOrbitalZoom(4), 8);
+  assert.equal(nextOrbitalZoom(8), 8);
+  assert.equal(previousOrbitalZoom(8), 4);
+  assert.equal(previousOrbitalZoom(2), 1);
+  assert.equal(previousOrbitalZoom(1), 1);
+  assert.equal(nextOrbitalZoom(undefined), 2);
+});
+
+test('the base frame is regional in low orbit and fits the disk from GEO', () => {
+  assert.equal(orbitalBaseFovRad(420e3), ORBITAL_BASE_FOV_LEO_RAD);
+  const geo = orbitalBaseFovRad(35.786e6);
+  const disk = 2 * earthAngularRadiusRad(35.786e6);
+  assert.ok(geo > disk && geo < ORBITAL_BASE_FOV_LEO_RAD);
+  // Continuous across the crossover: no jump as an orbit climbs.
+  let previous = orbitalBaseFovRad(1e6);
+  for (let alt = 1e6; alt <= 40e6; alt += 50e3) {
+    const fov = orbitalBaseFovRad(alt);
+    assert.ok(fov <= previous + 1e-12);
+    assert.ok(previous - fov < 0.01);
+    previous = fov;
+  }
+});
+
+test('the footprint shrinks with zoom and stops at the limb', () => {
+  const alt = 420e3;
+  const widths = [1, 2, 4, 8].map((zoom) =>
+    footprintWidthKm(alt, fovForZoom(orbitalBaseFovRad(alt), zoom)),
+  );
+  for (let i = 1; i < widths.length; i++) assert.ok(widths[i] < widths[i - 1]);
+  assert.ok(widths[0] > 400 && widths[0] < 600, `1x ${widths[0]} km`);
+  assert.ok(widths[3] > 40 && widths[3] < 80, `8x ${widths[3]} km`);
+  // A wider frame covers more ground across.
+  assert.ok(
+    footprintWidthKm(alt, ORBITAL_BASE_FOV_LEO_RAD, 16 / 9) > widths[0],
+  );
+  // From GEO a frame wider than the disk spans the visible cap only.
+  const cap =
+    (2 *
+      ORBITAL_EARTH_RADIUS_M *
+      Math.acos(ORBITAL_EARTH_RADIUS_M / (ORBITAL_EARTH_RADIUS_M + 35.786e6))) /
+    1000;
+  assert.ok(Math.abs(footprintWidthKm(35.786e6, 40 * RAD) - cap) < 1e-6);
+  assert.equal(footprintWidthKm(0, 1), null);
+  assert.equal(footprintWidthKm(420e3, NaN), null);
+});
+
+test('Cesium frustum fov widens to the horizontal on a landscape canvas', () => {
+  const vertical = 30 * RAD;
+  assert.equal(cesiumFrustumFovRad(vertical, 0.75), vertical);
+  const horizontal = cesiumFrustumFovRad(vertical, 2);
+  assert.ok(
+    Math.abs(Math.tan(horizontal / 2) - 2 * Math.tan(vertical / 2)) < 1e-12,
+  );
+});
+
+test('zoom transition curves stay bounded and settle', () => {
+  assert.equal(zoomTransitionProgress(0), 0);
+  assert.equal(zoomTransitionProgress(400), 1);
+  assert.equal(zoomTransitionProgress(9999), 1);
+  assert.equal(zoomTransitionProgress(-50), 0);
+  assert.equal(zoomTransitionProgress(0, { reducedMotion: true }), 1);
+  let previous = 0;
+  for (let ms = 0; ms <= 500; ms += 10) {
+    const p = zoomTransitionProgress(ms);
+    assert.ok(p >= previous && p >= 0 && p <= 1);
+    previous = p;
+    const blur = zoomTransitionBlurPx(ms / 400);
+    assert.ok(blur >= 0 && blur <= 6);
+  }
+  assert.equal(zoomTransitionBlurPx(0), 0);
+  assert.ok(zoomTransitionBlurPx(1) < 1e-9);
+  assert.ok(Math.abs(zoomTransitionBlurPx(0.5) - 6) < 1e-9);
+  assert.equal(zoomTransitionBlurPx(0.5, { reducedMotion: true }), 0);
+
+  const from = fovForZoom(1, 1);
+  const to = fovForZoom(1, 2);
+  assert.equal(interpolateZoomFov(from, to, 0).toFixed(12), from.toFixed(12));
+  assert.equal(interpolateZoomFov(from, to, 1).toFixed(12), to.toFixed(12));
+  const mid = interpolateZoomFov(from, to, 0.5);
+  assert.ok(mid < from && mid > to);
+});
+
+test('the transition state blurs, then ticks the lock, then rests', () => {
+  const moving = zoomTransitionState(200);
+  assert.equal(moving.active, true);
+  assert.ok(moving.blurPx > 5);
+  assert.equal(moving.lockTick, false);
+  const settled = zoomTransitionState(450);
+  assert.equal(settled.active, false);
+  assert.equal(settled.lockTick, true);
+  assert.equal(settled.progress, 1);
+  assert.ok(settled.blurPx < 1e-9);
+  const rest = zoomTransitionState(2000);
+  assert.equal(rest.lockTick, false);
+  assert.deepEqual(zoomTransitionState(100, { reducedMotion: true }), {
+    active: false,
+    progress: 1,
+    blurPx: 0,
+    lockTick: false,
+  });
+});
+
+test('an off-nadir tilt turns the view by its angle from the nadir frame', () => {
+  const nadir = nadirOrientation(ecef(30, -97, 420_000));
+  assert.equal(offNadirOrientation(nadir), nadir, 'no tilt is nadir itself');
+  const angle = (v) => Math.acos(Math.min(1, dot(v, nadir.direction))) / RAD;
+  const north = offNadirOrientation(nadir, { northDeg: 10 });
+  assert.ok(Math.abs(angle(north.direction) - 10) < 1e-9);
+  assert.ok(dot(north.direction, nadir.up) > 0, 'toward north');
+  assert.ok(Math.abs(dot(north.direction, nadir.right)) < 1e-12);
+  const west = offNadirOrientation(nadir, { eastDeg: -20 });
+  assert.ok(Math.abs(angle(west.direction) - 20) < 1e-9);
+  assert.ok(dot(west.direction, nadir.right) < 0, 'toward west');
+  const both = offNadirOrientation(nadir, { northDeg: 45, eastDeg: 45 });
+  const expected = Math.acos(Math.cos(45 * RAD) ** 2) / RAD;
+  assert.ok(Math.abs(angle(both.direction) - expected) < 1e-9);
+  for (const view of [north, west, both]) {
+    assert.ok(Math.abs(norm(view.direction) - 1) < 1e-12);
+    assert.ok(Math.abs(norm(view.up) - 1) < 1e-12);
+    assert.ok(Math.abs(dot(view.direction, view.up)) < 1e-12);
+  }
+});
+
+test('a landed zoom step holds for its imagery, but never past the cap', () => {
+  assert.equal(zoomSettleHolding(0, false), true, 'still loading');
+  assert.equal(zoomSettleHolding(ORBITAL_SETTLE_MAX_MS - 1, false), true);
+  assert.equal(zoomSettleHolding(ORBITAL_SETTLE_MAX_MS, false), false, 'cap');
+  assert.equal(zoomSettleHolding(0, true), false, 'loaded: lock at once');
+  assert.equal(zoomSettleHolding(Number.NaN, false), true);
+});
+
+test('a heading turns the nadir frame, keeping north to fall back on', () => {
+  // Over the equator at 0°E: north is +z, east is +y.
+  const position = { x: ORBITAL_EARTH_RADIUS_M + 500_000, y: 0, z: 0 };
+  const northUp = nadirOrientation(position);
+  const east = nadirOrientation(position, { headingDeg: 90 });
+  const close = (a, b) =>
+    Math.abs(a.x - b.x) < 1e-9 &&
+    Math.abs(a.y - b.y) < 1e-9 &&
+    Math.abs(a.z - b.z) < 1e-9;
+  assert.ok(close(northUp.up, { x: 0, y: 0, z: 1 }));
+  assert.ok(close(east.up, { x: 0, y: 1, z: 0 }), 'east at the top');
+  assert.ok(close(east.north, northUp.up), 'north kept for the next frame');
+  assert.ok(
+    close(nadirOrientation(position, { headingDeg: 0 }).up, northUp.up),
+  );
+});
+
+test('the total off-nadir angle combines both tilts', () => {
+  assert.equal(offNadirAngleDeg(), 0);
+  assert.ok(Math.abs(offNadirAngleDeg({ northDeg: 10 }) - 10) < 1e-9);
+  // FWD 15° and RIGHT 10° read OFF-NADIR 18.0°.
+  const total = offNadirAngleDeg({ northDeg: 15, eastDeg: 10 });
+  assert.equal(total.toFixed(1), '18.0');
+  assert.equal(offNadirAngleDeg({ northDeg: -15, eastDeg: -10 }), total);
+});
+
+test("a tilted view's width grows faster across the frame than along it", () => {
+  assert.equal(offNadirSwathScale(), 1, 'nadir');
+  const cos = (deg) => Math.cos((deg * Math.PI) / 180);
+  assert.ok(
+    Math.abs(offNadirSwathScale({ northDeg: 30 }) - 1 / cos(30)) < 1e-9,
+  );
+  assert.ok(
+    Math.abs(offNadirSwathScale({ eastDeg: 30 }) - 1 / cos(30) ** 2) < 1e-9,
+  );
+  let last = 1;
+  for (const deg of [5, 15, 25, 35, 45]) {
+    const scale = offNadirSwathScale({ northDeg: deg, eastDeg: deg });
+    assert.ok(scale > last, `${deg}°`);
+    last = scale;
+  }
+  assert.equal(offNadirSwathScale({ northDeg: Number.NaN }), 1);
+});