úÎ!xt@@      !"#$%&'()*+,-./0123456789:;<=>?None.MUVX†orbits"One complete revolution in radiansorbits À radiansorbitsMultiply by 1 radianorbitsDivide by 1 radianNone.MUVX@ABNone.=>?@AHMUVXr¤1orbitsDWhat for the orbit's geometry takes. This is dependant only on the , e >= 0, of the orbit.orbits 0 <= e < 1This includes circular orbits.orbitse == 1orbitse > 1 orbits Along with   the  3 describes orbital elements extra to its geometry. orbitsThe orbit is not circular orbits+The orbit has an eccentricity of 0 so the   is indeterminate. orbitsThe argument of periapsis, É.The  [ is the angle of the periapsis relative to the reference direction in the orbital plane. orbits Along with   the  3 describes orbital elements extra to its geometry.orbits6The orbit does not lie exactly in the reference planeorbits%The orbit lies in the reference planeorbits(The longitude of the ascending node, ©.‹The angle between the reference direction and the point where the orbiting body crosses the reference plane in the positive z direction.orbitsThe orbit's inclination, i.<The angle between the reference plane and the orbital planeorbitsOData type defining an orbit parameterized by the type used to represent valuesorbitsThe orbit's eccentricity, e. must be non-negative.0An eccentricity of 0 describes a circular orbit.<An eccentricity of less than 1 describes an elliptic orbit.7An eccentricity equal to 1 describes a parabolic orbit.=An eccentricity greater than 1 describes a hyperbolic orbit.orbitsThe orbit's periapsis, q. must be positive.LThe periapsis is the distance between the bodies at their closest approach.orbitsThe H describes the angle between the obtital plane and the reference plane.orbits is   iff  is 0wThe periapsis specifier describes any rotation of the orbit relative to the reference direction in the orbital plane.orbits8The gravitational parameter of the system's primary, ¼..¼ is equal to the mass of the primary times < 4https://en.wikipedia.org/wiki/Gravitational_constant G>. must be positive.orbitsA unitless measure.orbitsA measure in radians.orbitsA measure in kilograms.orbitsA measure in meters per second.orbitsA measure in meters.orbitsA measure in seconds.orbits Return true is the orbit is valid and false if it is invalid. The behavior of all the other functions in this module is undefined when given an invalid orbit. orbits / is a funciton which returns the orbit's class.!orbits)Calculate the semi-major axis, a, of the  . Returns C‡ when given a parabolic orbit for which there is no semi-major axis. Note that the semi-major axis of a hyperbolic orbit is negative."orbits)Calculate the semi-minor axis, b, of the . Like ! 'semiMinorAxis' o is negative when o: is a hyperbolic orbit. In the case of a parabolic orbit " returns 0m.#orbits)Calculate the semiLatusRectum, l, of the $orbitsPCalculate the distance between the bodies when they are at their most distant. $ returns C- when given a parabolic or hyperbolic orbit.%orbits)Calculate the mean motion, n, of an orbitDThis is the rate of change of the mean anomaly with respect to time.&orbits6Calculate the orbital period, p, of an elliptic orbit.&: returns Nothing if given a parabolic or hyperbolic orbit.'orbits.Calculate the areal velocity, A, of the orbit.The areal velocity is the area  https://xkcd.com/21/ swept outC by the line between the orbiting body and the primary per second.(orbitsÿCalculate the angle at which a body leaves the system when on an escape trajectory relative to the argument of periapsis. This is the limit of the true anomaly as time tends towards infinity minus the argument of periapsis. The departure angle is in the closed range (À/2..À).+This is the negation of the approach angle.(R returns Nothing when given an elliptic orbit and À when given a parabolic orbit.)orbitsÿCalculate the angle at which a body leaves the system when on a hyperbolic trajectory relative to the argument of periapsis. This is the limit of the true anomaly as time tends towards -infinity minus the argument of periapsis. The approach angle is in the closed range (-À..À/2).,This is the negation of the departure angle.)X returns Nothing when given a non-hyperbolic orbit and -À when given a parabolic orbit.*orbitsCCalculate the time since periapse, t, when the body has the given  *https://en.wikipedia.org/wiki/Mean_anomaly mean anomalyU, M. M may be negative, indicating that the orbiting body has yet to reach periapse.DThe sign of the time at mean anomaly M is the same as the sign of M.The returned time is unbounded.+orbitsXCalculate the time since periapse, t, of an elliptic orbit when at eccentric anomaly E.+; returns Nothing if given a parabolic or hyperbolic orbit.,orbitsRCalculate the time since periapse given the true anomaly, ½, of an orbiting body.-orbitsCalculate the  *https://en.wikipedia.org/wiki/Mean_anomaly mean anomaly{, M, at the given time since periapse, t. t may be negative, indicating that the orbiting body has yet to reach periapse.DThe sign of the mean anomaly at time t is the same as the sign of t.'The returned mean anomaly is unbounded..orbitsPCalculate the mean anomaly, M, of an elliptic orbit when at eccentric anomaly E.; returns Nothing if given a parabolic or hyperbolic orbit.HThe number of orbits represented by the anomalies is preserved; i.e. M D 2À = E D 2À/orbitsVCalculate the mean anomaly, M, of an orbiting body when at the given true anomaly, ½.HThe number of orbits represented by the anomalies is preserved; i.e. M D 2À = ½ D 2À/Currently only implemented for elliptic orbits.0orbitsCCalculate the eccentric anomaly, E, of an elliptic orbit at time t.0= returns Nothing when given a parabolic or hyperbolic orbit.CThe number of orbits represented by the time is preserved; i.e. t D p = E D 2À1orbitsÞCalculate the eccentric anomaly, E, of an elliptic orbit when at mean anomaly M. This function is considerably slower than most other conversion functions as it uses an iterative method as no closed form solution exists.HThe number of orbits represented by the anomalies is preserved; i.e. M D 2À = E D 2À1= returns Nothing when given a parabolic or hyperbolic orbit.2orbits1 specialized to E.:This function is used to calculate the initial guess for 1.3orbitsUCalculate the eccentric anomaly, E, of an orbiting body when it has true anomaly, ½.HThe number of orbits represented by the anomalies is preserved; i.e. ½ D 2À = E D 2À9Returns Nothing if given a parabolic or hyperbolic orbit.4orbitsCCalculate the true anomaly, ½, of a body at time since periapse, t.5orbits[Calculate the true anomaly, ½, of an orbiting body when it has the given mean anomaly, _M.6orbits`Calculate the true anomaly, ½, of an orbiting body when it has the given eccentric anomaly, _E.HThe number of orbits represented by the anomalies is preserved; i.e. ½ D 2À = E D 2À6orbitsAn elliptic orbitorbitsThe eccentric anomaly _EorbitsThe true anomaly, ½3  !"#$%&'()*+,-./01234563   $%&'!"#)(*+,-./0123456F      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJHKLMNOPorbits-0.3-inplace Physics.OrbitData.Constants.Mechanics.ExtraData.Metrology.Extra(exact-real-0.12.2-AtpXl3xbCQF7J4oERPtwDAData.CReal.ConvergeConvergeturnhalfTurnaddRaddelRadClassificationElliptic Parabolic HyperbolicPeriapsisSpecifier EccentricCircularargumentOfPeriapsisInclinationSpecifierInclined NonInclinedlongitudeOfAscendingNode inclinationOrbit eccentricity periapsisinclinationSpecifierperiapsisSpecifierprimaryGravitationalParameterUnitlessAngleMassSpeedDistanceTimeisValidclassify semiMajorAxis semiMinorAxissemiLatusRectumapoapsis meanMotionperiod arealVelocityhyperbolicDepartureAnglehyperbolicApproachAngletimeAtMeanAnomalytimeAtEccentricAnomalytimeAtTrueAnomalymeanAnomalyAtTimemeanAnomalyAtEccentricAnomalymeanAnomalyAtTrueAnomalyeccentricAnomalyAtTimeeccentricAnomalyAtMeanAnomaly"eccentricAnomalyAtMeanAnomalyFloateccentricAnomalyAtTrueAnomalytrueAnomalyAtTimetrueAnomalyAtMeanAnomalytrueAnomalyAtEccentricAnomaly$fShowInclinationSpecifier$fEqInclinationSpecifier$fShowPeriapsisSpecifier$fEqPeriapsisSpecifier $fShowOrbit $fEqOrbit$fShowClassification$fReadClassification$fEqClassificationmod'div'divMod'base GHC.MaybeNothingGHC.Realdivghc-prim GHC.TypesFloat