init

world/orbit.go

@@ -0,0 +1,39 @@
+// Package world defines the static shape of the belt: bodies on analytic
+// (on-rails) orbits and the procedural generation that creates them.
+//
+// The star pulls with acceleration v^2/r (v = config OrbitSpeed), so a circular
+// orbit at any radius has the same speed v. Every body on rails is therefore
+// on a circle traversed at speed v; only the period (2*pi*r/v) varies.
+package world
+
+import "wh/fixed"
+
+// Orbit is a circular orbit around the origin (the star).
+type Orbit struct {
+	A      fixed.F // radius, km
+	Period int64   // seconds
+	M0     fixed.F // phase at t=0, radians
+	Inc    fixed.F // inclination to the ecliptic (XY plane), radians
+	Node   fixed.F // longitude of the ascending node, radians
+}
+
+// PeriodFor returns the period in seconds of a circle of radius a at speed v.
+func PeriodFor(a, v fixed.F) int64 {
+	return fixed.TwoPi.Mul(a).Div(v).Int()
+}
+
+// State returns position (km) and velocity (km/s) at absolute time t seconds.
+func (o Orbit) State(t int64) (pos, vel fixed.Vec) {
+	frac := fixed.FromInt(t % o.Period).Div(fixed.FromInt(o.Period))
+	s, c := fixed.SinCos(o.M0 + fixed.TwoPi.Mul(frac))
+	k := fixed.TwoPi.Mul(o.A).Div(fixed.FromInt(o.Period)) // speed
+	pos = fixed.Vec{X: o.A.Mul(c), Y: o.A.Mul(s)}
+	vel = fixed.Vec{X: -k.Mul(s), Y: k.Mul(c)}
+	return o.orient(pos), o.orient(vel)
+}
+
+// orient rotates a vector from the orbital plane into the ecliptic frame:
+// Rz(Node) * Rx(Inc).
+func (o Orbit) orient(v fixed.Vec) fixed.Vec {
+	return v.RotateX(o.Inc).RotateZ(o.Node)
+}