Core routines

Construct HighFidelityEphemerisModelParameters struct.

Arguments

• et0::Float64: reference epoch in seconds past J2000
• DU::Real: canonical distance unit
• GMs::Vector{Float64}: gravitational constants of the bodies, in km^3/s^2
• naif_ids::Vector{String}: NAIF IDs of the bodies
• naif_frame::String: inertial frame in which dynamics is integrated
• abcorr::String: aberration correction for querying ephemerides of third bodies
• filepath_spherical_harmonics::Union{Nothing,String}: path to spherical harmonics data file
• nmax::Int: maximum degree of spherical harmonics to be included
• frame_PCPF::Union{Nothing,String}: NAIF frame of planet-centered planet-fixed frame
• get_jacobian_func::Bool: whether to construct symbolic Jacobian function (only for Nbody dynamics)
• interpolate_ephem_span::Union{Nothing,Vector{Float64}}: span of epochs to interpolate ephemerides
• interpolation_time_step::Real: time step for interpolation
• include_srp::Bool: whether to include SRP terms
• srp_Cr::Float64: SRP radiation pressure coefficient
• srp_Am::Float64: SRP area-to-mass ratio in m^2/kg
• srp_P0::Float64: SRP power in W

Overload method for showing InterpolatedEphemeris

Interpolate ephemeris position at a given epoch

Arguments

• ephem::InterpolatedEphemeris: interpolated ephemeris struct
• et::Float64: epoch to interpolate

Interpolate ephemeris state at a given epoch

Arguments

• ephem::InterpolatedEphemeris: interpolated ephemeris struct
• et::Float64: epoch to interpolate

InterpolatedEphemeris struct

Fields

• naif_id::String: NAIF ID of the body
• et_range::Tuple{Float64, Float64}: span of epochs to interpolate
• splines::Array{Spline1D, 1}: splines for the interpolated ephemeris
• rescale_epoch::Bool: whether to rescale the epoch to the canonical time unit
• tstar::Float64: canonical time unit

Arguments

• naif_id::String: NAIF ID of the body
• ets::Vector{Float64}: epochs to interpolate
• rvs::Array{Float64, 2}: position and velocity vectors of the body, in km and km/s
• rescale_epoch::Bool: whether to rescale the epoch to the canonical time unit
• tstar::Float64: canonical time unit
• spline_order::Int: order of the spline

Overload method for showing InterpolatedTransformation

Interpolate Euler angles at a given epoch

Arguments

• transformation::InterpolatedTransformation: interpolated transformation struct
• et::Float64: epoch to interpolate

Interpolate transformation matrix at a given epoch

Arguments

• transformation::InterpolatedTransformation: interpolated transformation struct
• et::Float64: epoch to interpolate

InterpolatedTransformation struct

Fields

• et_range::Tuple{Float64, Float64}: span of epochs to interpolate
• frame_from::String: frame from which the transformation is computed
• frame_to::String: frame to which the transformation is computed
• axis_sequence::Tuple{Int, Int, Int}: sequence of axes for the Euler angles
• splines::Array{Spline1D, 1}: splines for the interpolated transformation
• rescale_epoch::Bool: whether to rescale the epoch to the canonical time unit
• TU::Float64: canonical time unit

Arguments

• ets::Vector{Float64}: epochs to interpolate
• frame_from::String: frame from which the transformation is computed
• frame_to::String: frame to which the transformation is computed
• rescale_epoch::Bool: whether to rescale the epoch to the canonical time unit
• TU::Float64: canonical time unit
• spline_order::Int: order of the spline

dfdx_Nbody_Interp(x, u, params, t)

Evaluate Jacobian of N-body problem

eom_Nbody_Interp!(dx, x, params, t)

Right-hand side of N-body equations of motion compatible with DifferentialEquations.jl

eom_Nbody_Interp(x, params, t)

Right-hand side of N-body equations of motion compatible with DifferentialEquations.jl

eom_stm_Nbody_Interp!(dx_stm, x_stm, params, t)

Right-hand side of N-body equations of motion with STM compatible with DifferentialEquations.jl

eom_stm_Nbody_Interp_fd!(dx_stm, x_stm, params, t)

Right-hand side of N-body equations of motion with STM compatible with DifferentialEquations.jl

dfdx_Nbody_SPICE(x, u, params, t)

Evaluate Jacobian of N-body problem

eom_Nbody_SPICE!(dx, x, params, t)

Right-hand side of N-body equations of motion compatible with DifferentialEquations.jl

eom_Nbody_SPICE(x, params, t)

Right-hand side of N-body equations of motion compatible with DifferentialEquations.jl

eom_stm_Nbody_SPICE!(dx_stm, x_stm, params, t)

Right-hand side of N-body equations of motion with STMcompatible with DifferentialEquations.jl

eom_stm_Nbody_SPICE_fd!(dx_stm, x_stm, params, t)

Right-hand side of N-body equations of motion with STM compatible with DifferentialEquations.jl

dfdx_NbodySH_Interp_fd(x, u, params, t)

Evaluate Jacobian of N-body problem

eom_NbodySH_Interp!(dx, x, params, t)

Right-hand side of N-body equations of motion compatible with DifferentialEquations.jl

eom_NbodySH_Interp(x, params, t)

Right-hand side of N-body equations of motion compatible with DifferentialEquations.jl

eom_stm_NbodySH_Interp_fd!(dx_stm, x_stm, params, t)

Right-hand side of N-body equations of motion with STM compatible with DifferentialEquations.jl

eom_NbodySH_SPICE!(dx, x, params, t)

Right-hand side of N-body equations of motion compatible with DifferentialEquations.jl

eom_NbodySH_SPICE(x, params, t)

Right-hand side of N-body equations of motion compatible with DifferentialEquations.jl

eom_stm_NbodySH_SPICE_fd!(dx_stm, x_stm, params, t)

Right-hand side of N-body equations of motion with STM compatible with DifferentialEquations.jl

eom_hessian_fd(eom::Function, x, u, params, t)

Evaluate Hessian of equations of motion using ForwardDiff. The second argument u is a place-holder for control input.

Arguments

• eom: "static" equations of motion, with signature eom(x, params, t) –> dx
• x: State vector
• u: Control input
• params: Parameters
• t: Time

Returns

• hess: Hessian of the equations of motion

eom_jacobian_fd(eom::Function, x, u, params, t)

Evaluate Jacobian of equations of motion using ForwardDiff. The second argument u is a place-holder for control input.

Arguments

• eom: "static" equations of motion, with signature eom(x, params, t) –> dx
• x: State vector
• u: Control input
• params: Parameters
• t: Time

Returns

• jac: Jacobian of the equations of motion

Get multipliers into gravity potential c.f. Montenbruck & Gill pg.66 eqn (3.27)

Arguments

• phi::Real: latitude
• lambda::Real: longitude
• R::Real: radius of Earth
• r::Real: radius of spacecraft
• n::Int: degree
• m::Int: order

Returns

• Vnm::Real: Vnm component
• Wnm::Real: Wnm component

Compute Legendre function of degree n order m

Arguments

• n::Int: degree (must be >= m)
• m::Int: order
• t::Real: argument (cosine of latitude)

Returns

• Pnm::Real: Legendre function value

Get acceleration due to potential up to degree nmax in planet-centered planet-fixed frame

Arguments

• phi::Real: latitude
• lambda::Real: longitude
• CS::Matrix: coefficient matrix
• GM::Real: gravitational parameter
• R::Real: reference radius
• r::Real: radius of spacecraft
• nmax::Int: maximum degree

Returns

• accel_PCPF::Vector{Real}: acceleration in planet-centered planet-fixed frame

Get acceleration due to (n,m) potential in planet-centered planet-fixed frame c.f. Montenbruck & Gill pg.68 eqn (3.33)

Arguments

• phi::Real: latitude
• lambda::Real: longitude
• Cnm_dict::Dict: dictionary of Cnm coefficients (de-normalized)
• Snm_dict::Dict: dictionary of Snm coefficients (de-normalized)
• GM::Real: gravitational parameter
• R::Real: reference radius
• r::Real: radius of spacecraft
• n::Int: degree
• m::Int: order

Returns

• accel_PCPF::Vector{Real}: acceleration in planet-centered planet-fixed frame

third_body_accel(r_spacecraft, r_3body, mu_3body)

Compute third-body acceleration via Battin's formula (eqn (8.60) ~ (8.62) in [1])

[1] Battin, R. H. (1987). An introduction to the mathematics and methods of astrodynamics. American Institute of Aeronautics and Astronautics, Inc.

get_srp_cannonball_coefficient(srp_P0, srp_Cr, srp_Am, DU, TU; AU = 149.6e6)

Get the cannonball coefficient in canonical units for solar radiation pressure.

Arguments

• DU: canonical distance unit, in km
• TU: canonical time unit, in s
• srp_Cr: reflectivity coefficient, dimensionless
• srp_Am: area-to-mass ratio in units of m^2/kg
• srp_P0: solar radiation pressure at 1 AU, in units of N/m^2
• AU: Astronomical unit, in km

srp_cannonball(r, r_sun, k_srp_cannonball)

Compute acceleration due to solar radiation pressure using the cannonball model.

Arguments

• r: position of the spacecraft, in km
• r_sun: position of the sun, in km
• k_srp_cannonball: cannonball coefficient in canonical units DU^3/TU^2

angle_difference(ϕ_fwd::Real, ϕ_bck::Real)

Compute angle difference for periodic angles between 0 and 2π

Compute osculating true anomaly from state and mu

Arguments

• state::Vector: state vector in Cartesian coordinates, in order [x, y, z, vx, vy, vz]
• mu::Float64: gravitational parameter
• to2pi::Bool: if true, return the true anomaly in the range [0, 2π]

Get event function to detect target osculating true anomaly

Arguments

• θ_target::Real: target osculating true anomaly
• t_bounds::Tuple{Real,Real}: time bounds
• radius_bounds::Tuple{Real,Real}: radius bounds
• θ_check_range::Float64: check range for true anomaly

Returns:

• _condition: event function with signature (x, t, integrator) -> Union{Float64, NaN}

mod_custom(a, n)

Custom modulo function Ref: https://stackoverflow.com/questions/1878907/how-can-i-find-the-difference-between-two-angles