HPR2598: Calculating planetary orbits in Haskell

Hacker Public Radio

Function signatures (it might or might not be helpful to have these at hand while listening):

• Helpers:

 radToDeg :: Floating a => a -> a degToRad :: Floating a => a -> a clamp :: Float -> Float

• Time:

 day :: Int -> Int -> Int -> Float -> Day Float

• Orbital parameters:

 longitudeOfAscendingNode :: Orbit body center => body -> center -> Day d -> LongAscNode body center inclinationToEcliptic :: Orbit body center => body -> center -> Day d -> InclToEcl body center argumentOfPeriapsis :: Orbit body center => body -> center -> Day d -> ArgPeri body center semiMajorAxis :: Orbit body center => body -> center -> Day d -> SemiMajor body center eccentricity :: Orbit body center => body -> center -> Day d -> Ecc body center meanAnomaly :: Orbit body center => body -> center -> Day d -> MeanAno body center

• Calculating location on orbital plane:

 eccAnomaly :: MeanAno a b -> Ecc a b -> EccAnomaly a b trueAnomaly :: EccAnomaly a b -> Ecc a b -> TrueAnomaly a b dist :: EccAnomaly a b -> Ecc a b -> SemiMajor a b -> Distance a b

• Translating between coordinate systems:

 toEclCoord :: TrueAnomaly a b -> Distance a b -> LongAscNode a b -> ArgPeri a b -> InclToEcl a b -> EclCoord a b toEqCoordinates :: EclCoord body Earth -> Day Float -> EqCoord body

Some helpful links:

• Guide by Paul Schlyter - https://www.stjarnhimlen.se/comp/ppcomp.html
• Sample calculations by Paul Schlyter - https://www.stjarnhimlen.se/comp/tutorial.html
• Tuula's blog post - https://engineersjourney.wordpress.com/2018/06/29/planetary-orbits-and-haskell/
• Definition of orbital elements in Wikipedia - https://en.wikipedia.org/wiki/Orbital_elements
• Units of angle in Wikipedia - https://en.wikipedia.org/wiki/Degree_(angle) and https://en.wikipedia.org/wiki/Radian