Orbit design from a genetic algorithm

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Introduction

This is step by step guide to basic interplanetary mission design with Nyx using B-Plane targeting. This is a clone of GMAT's Ex_LunarTransfer.script example script provided with GMAT 2020a. By the end of this guide, you'll see how to setup a B-Plane targeting in Nyx using either the TOML scenario setup¹ or the pure Rust setup. The former is especially useful to work with a simple scenario without much customization

Spacecraft setup

Nyx (Rust)Nyx (CLI)GMAT

// Initialize the cosm which stores the ephemeris
let cosm = Cosm::de438();
// Grab the frames we'll use
let eme2k = cosm.frame("EME2000");
let iau_earth = cosm.frame("IAU Earth");
// Define the epoch
let epoch = Epoch::from_gregorian_utc(2014, 7, 22, 11, 29, 10, 811_000);
// Define the initial orbit
let orbit = Orbit::cartesian(
    -137380.1984338506,
    75679.87867537055,
    21487.63875187856,
    -0.2324532014235503,
    -0.4462753967758019,
    0.08561205662877103,
    epoch,
    eme2k,
);

// Define the spacecraft
let sat = Spacecraft::new(orbit, 1000.0, 0.0, 1.0, 15.0, 1.7, 2.2);

TODO in version beta-2.

Create Spacecraft Sat;
GMAT Sat.DateFormat = UTCGregorian;
GMAT Sat.Epoch = '22 Jul 2014 11:29:10.811';
GMAT Sat.CoordinateSystem = EarthMJ2000Eq;
GMAT Sat.DisplayStateType = Cartesian;
GMAT Sat.X = -137380.1984338506;
GMAT Sat.Y = 75679.87867537055;
GMAT Sat.Z = 21487.63875187856;
GMAT Sat.VX = -0.2324532014235503;
GMAT Sat.VY = -0.4462753967758019;
GMAT Sat.VZ = 0.08561205662877103;
GMAT Sat.DryMass = 1000;
GMAT Sat.Cd = 2.2;
GMAT Sat.Cr = 1.7;
GMAT Sat.DragArea = 15;
GMAT Sat.SRPArea = 1;

Set up acceleration and force models

Nyx (Rust)Nyx (CLI)GMAT

// Set up the harmonics first because we need to pass them to the overarching orbital dynamics
// Load the harmonics from the JGM3 file (GMAT uses the JGM2 in this case).
// It's gunzipped (hence `true` as the last parameter)
let stor = HarmonicsMem::from_cof("JGM3.cof.gz", 20, 20, true)?;
// Set up the orbital dynamics: we need to specify the models one by one here
// because the usual functions wrap the dynamics so that they can be used in a Monte Carlo
// setup.
let orbital_dyn = OrbitalDynamics::new(vec![
    // Note that we are only accounting for Sun, Moon and Jupiter, in addition to the integration frame's GM
    PointMasses::new(
        eme2k,
        &[Bodies::Sun, Bodies::Luna, Bodies::JupiterBarycenter],
        cosm.clone(),
    ),
    // Specify that these harmonics are valid only in the IAU Earth frame. We're using the
    Harmonics::from_stor(iau_earth, stor, cosm.clone()),
]);


// Set up SRP and Drag second, because we need to pass them to the overarching spacecraft dynamics
let srp = SolarPressure::default(eme2k, cosm.clone());
let drag = Drag::std_atm1976(cosm.clone());
// Set up the spacecraft dynamics
let sc_dyn = SpacecraftDynamics::from_models(orbital_dyn, vec![srp, drag]);

TODO in version beta-2.

Create ForceModel AllForces;
GMAT AllForces.CentralBody = Earth;
GMAT AllForces.PrimaryBodies = {Earth};
GMAT AllForces.PointMasses = {Sun, Luna, Venus, Mars, Jupiter, Saturn, Uranus, Neptune};
GMAT AllForces.SRP = On;
GMAT AllForces.RelativisticCorrection = Off;
GMAT AllForces.ErrorControl = RSSStep;
GMAT AllForces.GravityField.Earth.Degree = 20;
GMAT AllForces.GravityField.Earth.Order = 20;
GMAT AllForces.GravityField.Earth.StmLimit = 100;
GMAT AllForces.GravityField.Earth.PotentialFile = 'JGM2.cof';
GMAT AllForces.GravityField.Earth.TideModel = 'None';
GMAT AllForces.SRP.Flux = 1367;
GMAT AllForces.SRP.SRPModel = Spherical;
GMAT AllForces.SRP.Nominal_Sun = 149597870.691;
GMAT AllForces.Drag.AtmosphereModel = MSISE90;
GMAT AllForces.Drag.HistoricWeatherSource = 'ConstantFluxAndGeoMag';
GMAT AllForces.Drag.PredictedWeatherSource = 'ConstantFluxAndGeoMag';
GMAT AllForces.Drag.CSSISpaceWeatherFile = '../samples/SupportFiles/CSSI_2004To2026.txt';
GMAT AllForces.Drag.SchattenFile = 'SchattenPredict.txt';
GMAT AllForces.Drag.F107 = 150;
GMAT AllForces.Drag.F107A = 150;
GMAT AllForces.Drag.MagneticIndex = 3;
GMAT AllForces.Drag.SchattenErrorModel = 'Nominal';
GMAT AllForces.Drag.SchattenTimingModel = 'NominalCycle';
GMAT AllForces.Drag.DragModel = 'Spherical';

Propagate until periapse

Nyx (Rust)Nyx (CLI)GMAT

// Propagate until periapse
let prop = Propagator::default(sc_dyn);

let (out, traj) = prop
    .with(sat)
    .until_event(0.5 * TimeUnit::Day, &Event::periapsis(), 0)
    .unwrap();

TODO in version beta-2.

Create Propagator EarthFull;
GMAT EarthFull.FM = AllForces;
GMAT EarthFull.Type = RungeKutta89;
GMAT EarthFull.InitialStepSize = 60;
GMAT EarthFull.Accuracy = 9.999999999999999e-12;
GMAT EarthFull.MinStep = 0.001;
GMAT EarthFull.MaxStep = 45000;
GMAT EarthFull.MaxStepAttempts = 50;
GMAT EarthFull.StopIfAccuracyIsViolated = true;

% (...)

BeginMissionSequence;

%------------------------------
%  Propagate to Earth periapsis
%------------------------------

Propagate 'Prop to Perigee' EarthFull(Sat) {Sat.Periapsis};

% (...)

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1. If this footnote still exists, then the TOML setup hasn't yet been added to this tutorial. I'm currently reworking how the TOML is handled. ↩