Add arealVelocity

src/Physics/Orbit.hs

@@ -29,6 +29,8 @@ module Physics.Orbit
   , apoapsis
   , meanMotion
   , period
+  , arealVelocity
+    -- *** Geometry
   , semiMajorAxis
   , semiMinorAxis
   , semiLatusRectum
@@ -292,3 +294,17 @@ hyperbolicDepartureAngle o =
 -- and -π when given a parabolic orbit.
 hyperbolicApproachAngle :: (Floating a, Ord a) => Orbit a -> Maybe (Angle a)
 hyperbolicApproachAngle = fmap negate' . hyperbolicDepartureAngle
+
+-- | Calculate the areal velocity, A, of the orbit.
+--
+-- The areal velocity is the area <https://xkcd.com/21/ swept out> by the line
+-- between the orbiting body and the primary per second.
+arealVelocity :: (Ord a, Floating a) => Orbit a -> Quantity a [u|m^2/s|]
+arealVelocity o = case classify o of
+                    Elliptic -> sqrt' (μ *: a *: (1 + e) /: (1 - e))
+                    Parabolic -> sqrt' (μ *: q /: 2)
+                    Hyperbolic -> sqrt' (μ *: (negate' a) *: (1 + e) /: (1 - e))
+  where μ = primaryGravitationalParameter o
+        Just a = semiMajorAxis o
+        e = eccentricity o
+        q = periapsis o