Library

abstract type AstroCoordTransformation <: AstrodynamicsTransformation

An abstract type representing a Transformation Between Astrodynamics Coordinates with no Time Regularization

abstract type AstrodynamicsTransformation <: Transformation

An abstract type representing a Transformation Between Astrodynamics Coordinates

Cartesian{T} <: AstroCoord

Cartesian Orbital Elements. 6D parameterziation of the orbit. x - X-position y - Y-position z - Z-position ẋ - X-velocity ẏ - Y-velocity ż - Z-velocity

Constructors Cartesian(x, y, z, ẋ, ẏ, ż) Cartesian(X::AbstractArray) Cartesian(X::AstroCoord, μ::Number)

abstract type AstroCoord{N, T} <: StaticMatrix{N, 1, T}

An abstract type representing a N-Dimensional Coordinate Set

Cylindrical{T} <: AstroCoord

Cylindrical Orbital Elements. 6D parameterziation of the orbit ρ - in-plane radius θ - in-plane angle z - out-of-plane distance ρdot - instantaneous rate of change of in-plsne radius θdot - instantaneous rate of change of θ ż - instantaneous rate of change of z

Constructors Cylindrical(r, θ, z, ṙ, θdot, ż) Cylindrical(X::AbstractArray) Cylindrical(X::AstroCoord, μ::Number)

Delaunay{T} <: AstroCoord

Delaunay Orbital Elements. 6D parameterziation of the orbit. L - Canonical Keplerian Energy G - Canonical Total Angular Momentum H - Canonical Normal Angular Momentum (Relative to Equator) M - Mean Anomaly ω - Argument of Periapsis Ω - Right Ascention of the Ascending Node

Constructors Delaunay(L, G, H, M, ω, Ω) Delaunay(X::AbstractVector{<:Number}) Delaunay(X::AstroCoord, μ::Number)

The IdentityTransformation is a singleton Transformation that returns the input unchanged, similar to identity.

J2EqOE{T} <: AstroCoord

Modified Equinoctial Orbital Elements. 6D parameterziation of the orbit. n - mean motion h - eccetricity projection onto longitude of perigee k - eccetricity projection onto ⟂ longitude of perigee p - projection of half inclination onto RAAN q - projection of half inclination onto ⟂ RAAN L - true longitude

Constructors J2EqOE(n, h, k, p, q, L) J2EqOE(X::AbstractArray) J2EqOE(X::AstroCoord, μ::Number)

Keplerian{T} <: AstroCoord

Keplerian Orbital Elements. 6D parameterziation of the orbit. a - semi-major axis e - eccetricity i - inclination Ω - Right Ascension of Ascending Node ω - Argument of Perigee f - True Anomaly

Constructors Keplerian(a, e, i, Ω, ω, f) Keplerian(X::AbstractArray) Keplerian(X::AstroCoord, μ::Number)

Milankovich{T} <: AstroCoord

Milankovich Orbital Elements. 7D parameterziation of the orbit. hx - X-component of Angular Momentum Vector hy - Y-component of Angular Momentum Vector hz - Z-component of Angular Momentum Vector ex - X-component of Eccentricity Vector ey - Y-component of Eccentricity Vector ez - Z-component of Eccentricity Vector L - True Longitude

Constructors Milankovich(hx, hy, hz, ex, ey, ez, L) Milankovich(X::AbstractArray) Milankovich(X::AstroCoord, μ::Number)

ModEq{T} <: AstroCoord

Modified Equinoctial Orbital Elements. 6D parameterziation of the orbit. p - semi-parameter f - eccetricity projection onto longitude of perigee g - eccetricity projection onto ⟂ longitude of perigee h - projection of half inclination onto RAAN k - projection of half inclination onto ⟂ RAAN L - true longitude

Constructors ModEq(p, f, g, h, k, l) ModEq(X::AbstractArray) ModEq(X::AstroCoord, μ::Number)

Spherical{T} <: AstroCoord

Spherical Orbital Elements. 6D parameterziation of the orbit r - radius θ - in-plane angle ϕ - out-of-plane angle ṙ - instantaneous rate of change of radius θdot - instantaneous rate of change of θ ϕdot - instantaneous rate of change of ϕ

Constructors Spherical(r, θ, ϕ, ṙ, ω, Ω) Spherical(X::AbstractArray) Spherical(X::AstroCoord, μ::Number)

The Transformation supertype defines a simple interface for performing transformations. Subtypes should be able to apply a coordinate system transformation on the correct data types by overloading the call method, and usually would have the corresponding inverse transformation defined by Base.inv(). Efficient compositions can optionally be defined by compose() (equivalently ∘).

USM6{T} <: AstroCoord

Unified State Model Orbital Elements. 6D parameterziation of the orbit using Velocity Hodograph and MRP's C - Velocity Hodograph Component Normal to the Radial Vector Laying in the Orbital Plane Rf1 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame X-Axis Rf2 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame Y-Axis σ1 - First Modified Rodriguez Parameter σ2 - Second Modified Rodriguez Parameter σ3 - Third Modified Rodriguez Parameter

Constructors USM6(C, Rf1, Rf2, σ1, σ2, σ3) USM6(X::AbstractArray) USM6(X::AstroCoord, μ::Number)

USM7{T} <: AstroCoord

Unified State Model Orbital Elements. 7D parameterziation of the orbit using Velocity Hodograph and Quaternions C - Velocity Hodograph Component Normal to the Radial Vector Laying in the Orbital Plane Rf1 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame X-Axis Rf2 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame Y-Axis ϵO1 - First Imaginary Quaternion Component ϵO2 - Second Imaginary Quaternion Component ϵO3 - Third Imaginary Quaternion Component η0 - Real Quaternion Component

Constructors USM7(C, Rf1, Rf2, ϵO1, ϵO2, ϵO3, η0) USM7(X::AbstractArray) USM7(X::AstroCoord, μ::Number)

USMEM{T} <: AstroCoord

Unified State Model Orbital Elements. 6D parameterziation of the orbit using Velocity Hodograph and Exponential Mapping C - Velocity Hodograph Component Normal to the Radial Vector Laying in the Orbital Plane Rf1 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame X-Axis Rf2 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame Y-Axis a1 - First Exponential Mapping Component a2 - Second Exponential Mapping Component a3 - Third Exponential Mapping Component

Constructors USMEM(C, Rf1, Rf2, a1, a2, a3) USMEM(X::AbstractArray) USMEM(X::AstroCoord, μ::Number)

EP2MRP(β::AbstractVector{<:Number})

Converts Euler Parameter rotation description into Modified Rodriguez Parameters.

Arguments

• β::AbstractVector{<:Number}: The Euler Parameter description of a rotation.

Returns

• σ::AbstractVector{<:Number}: The Modified Rodriguez Parameter description of a rotation.

function IOE2J2IOE(u::IOE{T}, μ::V) where {T<:Number, V<:Number}

Computes the J2 Perturbed Intermediate Orbit Elements from a Intermediate Orbit Element set.

Arguments

-u::AbstractVector{<:Number}: The Intermediate Orbit Element vector [I1; I2; I3; I4; I5; I6]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_J2IOR::SVector{6, <:Number}: The J2 Perturbed Intermediate Orbit Element vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)].

function IOE2koeM(u::AbstractVector{T}, μ::V) where {T<:Number, V<:Number}

Computes the Keplerian orbital elements from a Intermediate Orbit Element set.

Arguments

-u::AbstractVector{<:Number}: The Intermediate Orbit Element vector [I1; I2; I3; I4; I5; I6]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_koeM::SVector{6, <:Number}: The Keplerian state vector [a; e; i; Ω(RAAN); ω(AOP); M(Mean Anomaly)].

function IOE2modEq(u::AbstractVector{T}, μ::V) where {T<:Number, V<:Number}

Computes the Modified Equinoctial orbital elements from a Intermediate Orbit Element set.

Arguments

-u::AbstractVector{<:Number}: The Intermediate Orbit Element vector [I1; I2; I3; I4; I5; I6]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_modEq::SVector{6, <:Number}: The Modified Equinoctial state vector [n; f; g; h; k; L].

function J2EqOE2cart(u::AbstractVector{<:Number}, μ::Number)

Computes the Cartesian state vector from a J2 Perturbed Equinoctial Orbit Elements.

Arguments

-u::AbstractVector{<:Number}: The J2 Perturbed Equinoctial Orbit Element vector [n; h; k; p; q; L]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_cart::SVector{6, <:Number}: The Cartesian state vector [x; y; z; ẋ; ẏ; ż].

function J2IOE2IOE(J2::J2IOE{T}, μ::V) where {T<:Number, V<:Number}

Computes the Intermediate Orbit Elements from a J2 Perturbed Intermediate Orbit Element set.

Arguments

-J2::J2IOE{<:Number}: The J2 Perturbed Intermediate Orbit Element vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_IOE::SVector{6, <:Number}: The Intermediate Orbit Element vector [I1; I2; I3; I4; I5; I6].

KeplerSolver(M::T, e::Number; tol::Float64=10 * eps(T)) where {T<:Number}

Solves for true anomaly given the mean anomaly and eccentricity of an orbit.

Arguments

-M::Number: Mean Anomaly of the orbit [radians]. -e::Number: Eccentricity of the orbit.

Keyword Arguments

-tol::Float64: Convergence tolerance of Kepler solver. [Default=10*eps(T)]

Returns

-f::Number`: True Anomaly of the orbit [radians]

MRP2EP(σ::AbstractVector{<:Number})

Converts Modified Rodriguez Parameters rotation description into Euler Parameter.

Arguments

• σ::AbstractVector{<:Number}: The Modified Rodriguez Parameter description of a rotation.

Returns

• β::AbstractVector{<:Number}: The Euler Parameter description of a rotation.

Mil2cart(u::AbstractVector{T}, μ::V) where {T<:Number,V<:Number}

Converts Milankovich state vector into the Cartesian state vector.

Arguments

-u::AbstractVector{<:Number}: The Milankovich state vector [H; e; L]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_cart::SVector{6, <:Number}: The Cartesian state vector [x; y; z; ẋ; ẏ; ż].

ModEq2koe(u::AbstractVector{T}, μ::Number) where {T<:Number}

Converts Modified Equinoctial elements into the Keplerian elements.

Arguments

-u:AbstractVector{<:Number}: The Modified Equinoctial state vector [p; f; g; h; k; l]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_koe::SVector{6, <:Number}: The Keplerian state vector [a; e; i; Ω(RAAN); ω(AOP); ν(True Anomaly)].

USM62USM7(u::AbstractVector{T}, μ::Number) where {T<:Number}

Converts USM with Modified Rodrigue Parameters to USM with quaternions.

Arguments

-u::AbstractVector{<:Number}: The USM6 vector [C; Rf1; Rf2; σ1; σ2; σ3]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_USM::SVector{6, <:Number}: The Unified State Model vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0].

USM72USM6(u::AbstractVector{T}, μ::Number) where {T<:Number}

Converts USM with quaternions to USM with Modified Rodrigue Parameters.

Arguments

-u::AbstractVector{<:Number}: The Unified State Model vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_USM6::SVector{6, <:Number}: The USM6 State vector [C; Rf1; Rf2; σ1; σ2; σ3].

USM72USMEM(u::AbstractVector{T}, μ::Number) where {T<:Number}

Converts USM with quaternions to USM with exponential mapping.

Arguments

-u::AbstractVector{<:Number}: The Unified State Model vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_USMEM::SVector{6, <:Number}: The USMEM State Vector [C; Rf1; Rf2; a1; a2; a3, Φ].

USM72koe(u::AbstractVector{T}, μ::V) where {T<:Number,V<:Number}

Converts Unified State Model elements into the Keplerian orbital element set. Van den Broeck, Michael. "An Approach to Generalizing Taylor Series Integration for Low-Thrust Trajectories." (2017). https://repository.tudelft.nl/islandora/object/uuid%3A2567c152-ab56-4323-bcfa-b076343664f9

Arguments

-u::AbstractVector{<:Number}: The Unified State Model vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_koe:SVector{6, <:Number}: The Keplerian State vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)].

USMEM2USM7(u::AbstractVector{T}, μ::Number) where {T<:Number}

Converts USM with exponential mapping to USM with quaternions.

Arguments

-u::AbstractVector{<:Number}: The USMEM vector [C; Rf1; Rf2; a1; a2; a3, Φ]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_USM::SVector{7, <:Number}: The Unified State Model vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0].

angle_between_vectors(
    v1::AbstractVector{T1}, v2::AbstractVector{T2}
) where {T1<:Number,T2<:Number}

Computes the angle between two vectors in a more numerically stable way than dot product.

Arguments

-v1::AbstractVector{<:Number}: The first vector of the computation -v2::AbstractVector{<:Number}: The second vector of the computation

Returns

-angle::Number: The angle between the two vectors

angularMomentumQuantity(u::AbstractVector{<:Number})

Computes the instantaneous angular momentum.

Arguments

-u::AbstractVector{<:Number}: The Cartesian state vector [x; y; z; ẋ; ẏ; ż].

Returns

-angular_momentum::Number: Angular momentum of the body.

angularMomentumQuantity(X::AstroCoord, μ::Number)

Computes the instantaneous angular momentum.

Arguments

-X::AstroCoord: An coordinate set describing the orbit. -μ::Number: Standard graviational parameter of central body.

Returns

-angular_momentum::Number: Angular momentum of the body.

angularMomentumVector(u::AbstractVector{<:Number})

Computes the instantaneous angular momentum vector from a Cartesian state vector.

Arguments

-u::AbstractVector{<:Number}: The Cartesian state vector [x; y; z; ẋ; ẏ; ż].

Returns

-'angular_momentum::Vector{<:Number}': 3-Dimensional angular momemtum vector.

angularMomentumVector(X::AstroCoord, μ::Number)

Computes the instantaneous angular momentum vector from a Cartesian state vector.

Arguments

-X::AstroCoord: An coordinate set describing the orbit. -μ::Number: Standard graviational parameter of central body.

Returns

-angular_momentum::Vector{<:Number}: 3-Dimensional angular momemtum vector.

function cart2J2EqOE(u::AbstractVector{<:Number}, μ::Number)

Computes the J2 Perturbed Equinoctial Orbit Elements from a Cartesian state vector.

Arguments

-u::AbstractVector{<:Number}: The Cartesian state vector [x; y; z; ẋ; ẏ; ż]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_J2EqOE::SVector{6, <:Number}: The J2 Perturbed Equinoctial Orbit Element vector [n; h; k; p; q; L].

cart2Mil(u::AbstractVector{T}, μ::V) where {T<:Number,V<:Number}

Converts Cartesian state vector into the Milankovich state vector.

Arguments

-u::AbstractVector{<:Number}: The Cartesian state vector [x; y; z; ẋ; ẏ; ż]. -μ::Number: Standard graviational parameter of central body.

Keyword Arguments

-equatorial_tol::Float64: The tolerance on what is considered an equatorial orbit (no inclination). [Default=1e-15] -circular_tol::Float64: The tolerance on what is considered a circular orbit (no eccentricity). [Default=1e-15]

Returns

-u_Mil::SVector{7, <:Number}: The Milankovich state vector [H; e; L].

cart2cylind(u::AbstractVector{T}, μ::Number) where {T<:Number}

Computes the cylindrical orbital elements from a Cartesian set.

Arguments

-u::AbstractVector{<:Number}: Cartesian state vector [x; y; z; ẋ; ẏ; ż]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_cylind::SVector{6, <:Number}`: The cylindrical orbital element vector [r; θ; z; ṙ; θdot; ż].

cart2delaunay(u::AbstractVector{T}, μ::V) where {T<:Number,V<:Number}

Computes the Delaunay orbital elements from a Cartesian set. Laskar, Jacques. "Andoyer construction for Hill and Delaunay variables." Celestial Mechanics and Dynamical Astronomy 128.4 (2017): 475-482.

Arguments

-u::AbstractVector{<:Number}: The Cartesian orbital element vector [x; y; z; ẋ; ẏ; ż]. -μ::Number: Standard graviational parameter of central body.

Returns

-'u_cart::SVector{6, <:Number}': Delaunay Orbital Element Vector [L; G; H; M; ω; Ω]

function cart2koe(
    u::AbstractVector{T}, μ::V; equatorial_tol::Float64=1E-15, circular_tol::Float64=1E-15
) where {T<:Number,V<:Number}

Computes the Keplerian orbital elements from a cartesian set.

Arguments

-u::AbstractVector{<:Number}: The Cartesian state vector [x; y; z; ẋ; ẏ; ż]. -μ::Number: Standard graviational parameter of central body.

Keyword Arguments

-equatorial_tol::Float64: The tolerance on what is considered an equatorial orbit (no inclination). [Default=1e-15] -circular_tol::Float64: The tolerance on what is considered a circular orbit (no eccentricity). [Default=1e-15]

Returns

-u_koe::SVector{6, <:Number}`: Keplerian orbital element vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)].

cart2sphere(u::AbstractVector{T}, μ::Number) where {T<:Number}

Computes the spherical orbital elements from a spherical set.

Arguments

-u::AbstractVector{<:Number}: The Cartesian state vector [x; y; z; ẋ; ẏ; ż]. -μ::Number: Standard graviational parameter of central body.

Returns

-'u_sphere::SVector{6, <:Number}': Spherical Orbital Element Vector [r; θ; ϕ; ṙ; θdot; ϕdot]

cylind2cart(u::AbstractVector{T}, μ::Number) where {T<:Number}

Computes the Cartesian orbital elements from a cylindrical set.

Arguments

-u::AbstractVector{<:Number}: The cylindrical state vector [r; θ; z; ṙ; θdot; ż]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_cart::SVector{6, <:Number}: The Cartesian orbital element vector [x; y; z; ẋ; ẏ; ż].

delaunay2cart(u::AbstractVector{T}, μ::V) where {T<:Number,V<:Number}

Computes the Cartesian orbital elements from a Delaunay set. Laskar, Jacques. "Andoyer construction for Hill and Delaunay variables." Celestial Mechanics and Dynamical Astronomy 128.4 (2017): 475-482.

Argument

-u::AbstractVector{<:Number}: The Delaunay orbital element vector [L; G; H; M; ω; Ω]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_cart::SVector{6, <:Number}`: The cartesian orbital element vector [x; y; z; ẋ; ẏ; ż].

eccentricAnomaly2MeanAnomaly(E::Number, e::Number)

Converts the true anomaly into the mean anomaly.

Arguments

-E::Number: Eccentric anomaly of the orbit [radians]. -e::Number: Eccentricity of the orbit.

Returns

-'M::Number': Mean anomaly of the orbit [radians].

eccentricAnomaly2TrueAnomaly(E::Number, e::Number)

Converts the eccentric anomaly into the true anomaly.

Arguments

-E::Number: Eccentric anomaly of the orbit [radians]. -e::Number: Eccentricity of the orbit.

Returns

-f::Number: True anomaly of the orbit [radians].

function koeM2IOE(u::AbstractVector{T}, μ::V) where {T<:Number, V<:Number}

Computes the Intermediate Orbit Elements from a Keplerian set.

Arguments

-u::AbstractVector{<:Number}: The Keplerian state vector [a; e; i; Ω(RAAN); ω(AOP); M(Mean Anomaly)]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_IOE::SVector{6, <:Number}: The Intermediate Orbit Element vector [I1; I2; I3; I4; I5; I6].

koe2ModEq(u::AbstractVector{T}, μ::Number) where {T<:Number}

Converts Keplerian elements into the Modified Equinoctial elements.

Arguments

-u:AbstractVector{<:Number}: The Keplerian State vector [a; e; i; Ω(RAAN); ω(AOP); ν(True Anomaly)]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_ModEq::SVector{6, <:Number}: The Modified Equinoctial state vector [p; f; g; h; k; l].

koe2USM7(u::AbstractVector{T}, μ::V) where {T<:Number,V<:Number}

Converts Keplerian orbital elements into the Unified State Model set. Van den Broeck, Michael. "An Approach to Generalizing Taylor Series Integration for Low-Thrust Trajectories." (2017). https://repository.tudelft.nl/islandora/object/uuid%3A2567c152-ab56-4323-bcfa-b076343664f9

Arguments

-u:AbstractVector{<:Number}: The Keplerian state vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_USM::SVector{7, <:Number}: The Unified State Model vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0].

koe2cart(u::AbstractVector{T}, μ::V) where {T<:Number,V<:Number}

Computes the Cartesian orbital elements from a Keplerian set.

Arguments

-u::AbstractVector{<:Number}: The Keplerian state vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_cart::Vector{6, <:Number}: The Keplerian orbital element vector [x; y; z; ẋ; ẏ; ż].

meanAnomaly2EccentricAnomaly(M::T, e::Number; tol::Float64=10 * eps(T)) where {T<:Number}

Converts the Mean Anomaly into the Eccentric Anomaly

Arguments

-M::Number: Mean Anomaly of the orbit [radians] -e::Number: Eccentricity of the orbit

Keyword Arguments

-tol::Float64: Convergence tolerance of Kepler solver. [Default=10*eps(T)]

Returns

-E::Number: Eccentric Anomaly of the orbit [radians]

meanAnomaly2TrueAnomaly(M::T, e::Number; tol::Float64=10 * eps(T)) where {T<:Number}

Converts the mean anomaly into the true anomaly.

Arguments

-M::Number: Mean anomaly of the orbit [radians]. -e::Number: Eccentricity of the orbit.

Keyword Arguments

-tol::Float64: Convergence tolerance of Kepler solver. [Default=10*eps(T)]

Returns

-f::Number: Mean anomaly of the orbit [radians].

meanMotion(X::AstroCoord, μ::Number)

Computes the Keplerian mean motion about a central body.

Arguments

-X::AstroCoord: An coordinate set describing the orbit. -μ::Number: Standard graviational parameter of central body.

Returns

• n::Number: The orbital mean motion.

meanMotion(a::Number, μ::Number)

Computes the Keplerian mean motion about a central body.

Arguments

-a::Number: The semi-major axis of the orbit. -μ::Number: Standard graviational parameter of central body.

Returns

• n::Number: The orbital mean motion.

function modEq2IOE(u::AbstractVector{T}, μ::V) where {T<:Number, V<:Number}

Computes the Intermediate Orbit Elements from a Modified Equinoctial set.

Arguments

-u::AbstractVector{<:Number}: The Modified Equinoctial state vector [p; f; g; h; k; L]. -μ::Number: Standard graviational parameter of central body.

Returns

-u_IOE::SVector{6, <:Number}: The Intermediate Orbit Element vector [I1; I2; I3; I4; I5; I6].

orbitalNRG(X::AstroCoord, μ::Number)

Computes the keplerian orbital energy.

Arguments

-X::AstroCoord: An coordinate set describing the orbit. -μ::Number: Standard graviational parameter of central body.

Returns

-NRG::Number: The orbital energy.

orbitalNRG(a::Number, μ::Number)

Computes the keplerian orbital energy.

Arguments

-a::Number: The semi-major axis of the orbit. -μ::Number: Standard graviational parameter of central body.

Returns

-NRG::Number: The orbital energy.

orbitalPeriod(X::AstroCoord, μ::Number)

Computes the Keplerian orbital period about a central body.

Arguments

-X::AstroCoord: An coordinate set describing the orbit. -μ::Number: Standard graviational parameter of central body.

Returns

-T::Number: The orbital period.

orbitalPeriod(a::Number, μ::Number)

Computes the Keplerian orbital period about a central body.

Arguments

-a::Number: The semi-major axis of the orbit. -μ::Number: Standard graviational parameter of central body.

Returns

-T::Number: The orbital period.

sphere2cart(u::AbstractVector{T}, μ::Number) where {T<:Number}

Computes the Cartesian orbital elements from a spherical set.

Arguments

-u::AbstractVector{<:Number}: The spherical orbital element vector [r; θ; ϕ; ṙ; θdot; ϕdot]. -μ::Number: Standard graviational parameter of central body.

Returns

-'u_cart::SVector{6, <:Number}': The Cartesian orbital element vector [x; y; z; ẋ; ẏ; ż].

trueAnomaly2EccentricAnomaly(f::Number, e::Number)

Converts the true anomaly into the mean anomaly.

Arguments

-f::Number: True anomaly of the orbit [radians]. -e::Number: Eccentricity of the orbit.

Returns

-E::Number: Eccentric anomaly of the orbit [radians].

trueAnomaly2MeanAnomaly(f::Number, e::Number)

Converts the true anomaly into the mean anomaly.

Arguments

-f::Number: True anomaly of the orbit [radians]. -e::Number: Eccentricity of the orbit.

Returns

-M::Number: Mean anomaly of the orbit [radians].

inv(trans::Transformation)

Returns the inverse (or reverse) of the transformation trans