Full state transformations (position and velocity)

[stevenhughes73]

Hello,

Thanks for all the great work on astrodynamics coordinate transformations! I need to convert a full Cartesian state between coordinate systems. I've used the library and read the docs, but I don't see a way to transform velocities which requires the omega x position term. Omega ultimately contains the time derivative of the coordinate transformation (which is a LOT of work in general). Am I missing where the library supports that and if not have you considered adding it?

Thanks again,

Steve

[ronisbr]

Hi @stevenhughes73 !

You can convert the state vector using those functions here:

https://juliaspace.github.io/SatelliteToolboxTransformations.jl/stable/man/orbit_representations/

If you are converting between ECI and ECEF, it automatically takes into account the Earth rotation.

[ronisbr]

By the way, notice that the only effect we need to consider is the Earth rotation. All other motions of the reference frame are so small that they will not change the velocity at all.

[stevenhughes73]

Ah, perfect. Thanks for the lighting fast response ! I guess I didn't do enough RTFM! I have coded these in other languages and made the same assumptions for velocity transformations.

While we're on this thread, are these libraries differentiable with ForwardDiff.jl and/or other packages? I haven't looked into that yet but guessing you could answer quickly. I am working on some optimization that will require derivatives.

BTW, I need transformations for planets and moons and have started coding them from "Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015". The angles computed can be used in R1(), R2(), R3(), Rdot(1),Rdot2(), and Rdot3() rotations to easily transform positions and velocities. I'd be happy to contribute them if you are interested once I have finished testing. I have coded all of the planets, no moons yet. Sample code here

const ACRCSEC_TO_RAD = π / 648000
const MILLIARCSEC_TO_RAD = ACRCSEC_TO_RAD / 1000
const SECONDS_PER_DAY = 86400.0
const DEG_TO_RADIANS = π / 180

    neptune_orientation_parameters_iau2015(jd::J) where {J<:Real}

Return Neptune pole orientation and spin angle with time derivatives.

# Arguments
- `jd`: Julian date in TDB

# Returns
NamedTuple with:
- `α₀`     : Right ascension of pole (ICRF) [rad]
- `δ₀`     : Declination of pole (ICRF) [rad]
- `W₀`     : Prime meridian angle (body-fixed longitude) [rad]
- `dα₀_dt` : Right ascension rate (rad/sec)
- `dδ₀_dt` : Declination rate (rad/sec)
- `dW_dt`  : Spin rate (rad/sec)

# Notes
- All angles are in radians; rates are in radians/sec.
"""
function neptune_orientation_iau2015(jd::J) where {J<:Real}
    d = jd - 2451545.0
    T = d / 36525.0

    N_deg = 357.85 + 52.316 * T
    N_rad = N_deg * DEG_TO_RADIANS

    # α₀, δ₀, W₀
    α₀ = (299.36 + 0.70 * sin(N_rad)) * DEG_TO_RADIANS
    δ₀ = (43.46 - 0.51 * cos(N_rad)) * DEG_TO_RADIANS
    W₀ = (249.978 + 541.1397757 * d - 0.48 * sin(N_rad)) * DEG_TO_RADIANS

    # Derivatives
    dN_dt = (52.316 / 36525.0)*DEG_TO_RADIANS/SECONDS_PER_DAY  # radians per second
    # TODO, check this derivative
    dα₀_dt = 0.70 * cos(N_rad) * dN_dt * DEG_TO_RADIANS 
    dδ₀_dt = 0.51 * sin(N_rad) * dN_dt * DEG_TO_RADIANS 
    dW_dt  = (deg2rad(541.1397757)/SECONDS_PER_DAY - deg2rad(0.48) * cos(N_rad) * dN_dt ) 

    return (; α₀, dα₀_dt, δ₀, dδ₀_dt, W₀, dW_dt)
    
end

[ronisbr]

While we're on this thread, are these libraries differentiable with ForwardDiff.jl and/or other packages? I haven't looked into that yet but guessing you could answer quickly. I am working on some optimization that will require derivatives.

Yes, for some functions, due to the amazing work of @jmurphy6895 !

BTW, I need transformations for planets and moons and have started coding them from "Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015". The angles computed can be used in R1(), R2(), R3(), Rdot(1),Rdot2(), and Rdot3() rotations to easily transform positions and velocities. I'd be happy to contribute them if you are interested once I have finished testing. I have coded all of the planets, no moons yet. Sample code here

This would be awesome! However, isn't those algorithm more suitable inside some package in the JuliaAstro org?

[stevenhughes73]

This would be awesome! However, isn't those algorithm more suitable inside some package in the JuliaAstro org?

I am relatively new to the Julia language and community... happy to contribute to wherever is most appropriate.

[jmurphy6895]

Hey @stevenhughes73, just to provide a bit more context on the differentiability of astrodynamics software in Julia. There are three main places to look

• SatelliteToolbox provides a ton of fantastic functionality for base models and the following packages should be compatible with ForwardDiff, Zygote, Mooncake, Enzyme, FIniteDiff, and PolyesterForwardDiff. SatelliteToolboxCelestialBodies.jl, SatelliteToolboxTransformations.jl, SatelliteToolboxGravityModels.jl, SatelliteToolboxAtmosphericModels.jl, and SpaceIndices.jl. These should also work through DCM math in ReferenceFrameRotations.jl.
• I've also wrapped these into a high-fidelity modular and differentiable propagation schemes for HAMMERHEAD-Space in AstroForceModels.jl and AstroPropagators.jl. There's also an extensive coordinate translation library AstroCoords.jl. These should all be compatible with the same autodiff libraries
• Then there's JuliaSpaceMissionDesign, which I believe has a differentiable time and binary ephemeris readers in Tempo.jl and Ephemerides.jl. I am not sure which autodiff libraries are currently supported there, but I believe ForwardDiff is.

Some other notable ones are JuliaAstro which I don't think has explicit autodiff support and OrbitalTrajectories.jl for some CR3BP analyses that take advantage of autodiff.

It would be nice to coalesce into a singular framework at some point but I think we all have internal use cases that make it difficult to do that currently.

If you come across any errors here, want help making something compatible with autodiff, or want to collaborate on some astro packages in the future don't hesitate to reach out!