/
ReturnFromMoon.cs
531 lines (424 loc) · 22.4 KB
/
ReturnFromMoon.cs
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/*
* Copyright Lamont Granquist, Sebastien Gaggini and the MechJeb contributors
* SPDX-License-Identifier: LicenseRef-PD-hp OR Unlicense OR CC0-1.0 OR 0BSD OR MIT-0 OR MIT OR LGPL-2.1+
*/
#nullable enable
using System;
using System.Diagnostics;
using MechJebLib.Core;
using MechJebLib.Core.TwoBody;
using MechJebLib.Primitives;
using static MechJebLib.Utils.Statics;
using static System.Math;
namespace MechJebLib.Maneuvers
{
public static class ReturnFromMoon
{
private struct Args
{
public double MoonSOI;
public double PeR;
public double Inc;
public V3 R0;
public V3 V0;
public V3 MoonR0;
public V3 MoonV0;
public Scale MoonToPlanetScale;
public Scale MoonScale;
public Scale PlanetScale;
}
/* I was going to try to implement the differnetial correction procedure in Ocampo and Saudemont as a
least-squares minimization problem, but decided not to, but this is the constraint function if I ever
come back to it
private static void GuessFunction(double[] x, double[] fi, object o)
{
var args = (Args)o;
double moonSOI = args.MoonSOI;
double peR = args.PeR;
double inc = args.Inc;
V3 r0 = args.R0;
V3 v0 = args.V0;
V3 moonR0 = args.MoonR0;
V3 moonV0 = args.MoonV0;
Scale moonToPlanetScale = args.MoonToPlanetScale;
double tf = x[0];
var rf = new V3(x[1], x[2], x[3]);
var vf = new V3(x[4], x[5], x[6]);
double tsoiMinus = x[7];
double tsoiPlus = x[8];
double burnTime = x[9];
var dv = new V3(x[10], x[11], x[12]);
(V3 rburn, V3 vburn) = Shepperd.Solve(1.0, burnTime, r0, v0);
(V3 rsoi, V3 vsoi) = Shepperd.Solve(1.0, tsoiMinus, rburn, vburn + dv);
(V3 moonR2, V3 moonV2) = Shepperd.Solve(1.0, tsoiMinus, moonR0, moonV0);
V3 rsoiMinus = rsoi / moonToPlanetScale.LengthScale + moonR2;
V3 vsoiMinus = vsoi / moonToPlanetScale.VelocityScale + moonV2;
(V3 rsoiPlus, V3 vsoiPlus) = Shepperd.Solve(1.0, tf - tsoiPlus, rf, vf);
fi[0] = rsoiPlus.x - rsoiMinus.x;
fi[1] = rsoiPlus.y - rsoiMinus.y;
fi[2] = rsoiPlus.z - rsoiMinus.z;
fi[3] = vsoiPlus.x - vsoiMinus.x;
fi[4] = vsoiPlus.y - vsoiMinus.y;
fi[5] = vsoiPlus.z - vsoiMinus.z;
fi[6] = tsoiPlus - tsoiMinus;
fi[7] = V3.Dot(rf.normalized, vf.normalized);
fi[8] = rf.sqrMagnitude - peR * peR;
}
*/
private static void NLPFunction(double[] x, double[] fi, double[,] jac, object o)
{
/*
* unpacking constants
*/
var args = (Args)o;
double moonSOI = args.MoonSOI;
double peR = args.PeR;
double inc = args.Inc;
V3 r0 = args.R0;
V3 v0 = args.V0;
V3 moonR0 = args.MoonR0;
V3 moonV0 = args.MoonV0;
Scale moonToPlanetScale = args.MoonToPlanetScale;
/*
* unpacking optimizer variables
*/
var dv = new V3(x[0], x[1], x[2]);
double burnTime = x[3];
double moonDt1 = x[4];
double moonDt2 = x[5];
V3 rsoi = new V3(moonSOI, x[6], x[7]).sph2cart;
V3 vsoi = new V3(x[8], x[9], x[10]).sph2cart;
double moonDt = x[11];
double planetDt1 = x[12];
double planetDt2 = x[13];
var rf = new V3(x[14], x[15], x[16]);
var vf = new V3(x[17], x[18], x[19]);
// forward propagation in the moon SOI
(V3 rburn, V3 vburn) = Shepperd.Solve(1.0, burnTime, r0, v0);
V3 aburn = -rburn / (rburn.sqrMagnitude * rburn.magnitude);
(V3 r1Minus, V3 v1Minus, M3 v1MinusS00, M3 v1MinusS01, M3 v1MinusS10, M3 v1MinusS11) = Shepperd.Solve2(1.0, moonDt1, rburn, vburn + dv);
V3 a1Minus = -r1Minus / (r1Minus.sqrMagnitude * r1Minus.magnitude);
// reverse propagation in the moon SOI
(V3 r1Plus, V3 v1Plus, M3 v1PlusS00, M3 v1PlusS01, M3 v1PlusS10, M3 v1PlusS11) = Shepperd.Solve2(1.0, -moonDt2, rsoi, vsoi);
V3 a1Plus = -r1Plus / (r1Plus.sqrMagnitude * r1Plus.magnitude);
// propagation of the moon via the "ephemeris"
double t2 = moonDt / moonToPlanetScale.TimeScale;
(V3 moonR2, V3 moonV2) = Shepperd.Solve(1.0, t2, moonR0, moonV0);
V3 moonA2 = -moonR2 / (moonR2.sqrMagnitude * moonR2.magnitude);
V3 rsoiPlanet = rsoi / moonToPlanetScale.LengthScale + moonR2;
V3 vsoiPlanet = vsoi / moonToPlanetScale.VelocityScale + moonV2;
// forward propagation in the planet SOI
(V3 r2Minus, V3 v2Minus, M3 v2MinusS00, M3 v2MinusS01, M3 v2MinusS10, M3 v2MinusS11) =
Shepperd.Solve2(1.0, planetDt1, rsoiPlanet, vsoiPlanet);
V3 a2Minus = -r2Minus / (r2Minus.sqrMagnitude * r2Minus.magnitude);
// reverse propagation in the planet SOI
(V3 r2Plus, V3 v2Plus, M3 v2PlusS00, M3 v2PlusS01, M3 v2PlusS10, M3 v2PlusS11) = Shepperd.Solve2(1.0, -planetDt2, rf, vf);
V3 a2Plus = -r2Plus / (r2Plus.sqrMagnitude * r2Plus.magnitude);
// objective
Dual obj = new DualV3(dv, new V3(1, 0, 0)).sqrMagnitude;
fi[0] = obj.M;
jac[0, 0] = obj.D;
jac[0, 1] = new DualV3(dv, new V3(0, 1, 0)).sqrMagnitude.D;
jac[0, 2] = new DualV3(dv, new V3(0, 0, 1)).sqrMagnitude.D;
/*
* meet in the moon's SOI
*/
fi[1] = r1Minus.x - r1Plus.x;
fi[2] = r1Minus.y - r1Plus.y;
fi[3] = r1Minus.z - r1Plus.z;
fi[4] = v1Minus.x - v1Plus.x;
fi[5] = v1Minus.y - v1Plus.y;
fi[6] = v1Minus.z - v1Plus.z;
v1MinusS01.CopyTo(jac, 1, 0);
v1MinusS11.CopyTo(jac, 4, 0);
(v1MinusS00 * vburn + v1MinusS01 * aburn).CopyTo(jac, 1, 3);
(v1MinusS10 * vburn + v1MinusS11 * aburn).CopyTo(jac, 4, 3);
v1Minus.CopyTo(jac, 1, 4);
a1Minus.CopyTo(jac, 4, 4);
v1Plus.CopyTo(jac, 1, 5);
a1Plus.CopyTo(jac, 4, 5);
DualV3 rsoi6 = new DualV3(moonSOI, x[6], x[7], 0, 1, 0).sph2cart;
DualV3 rsoi7 = new DualV3(moonSOI, x[6], x[7], 0, 0, 1).sph2cart;
var d2 = new M3(rsoi6.D, rsoi7.D, V3.zero);
DualV3 vsoi8 = new DualV3(x[8], x[9], x[10], 1, 0, 0).sph2cart;
DualV3 vsoi9 = new DualV3(x[8], x[9], x[10], 0, 1, 0).sph2cart;
DualV3 vsoi10 = new DualV3(x[8], x[9], x[10], 0, 0, 1).sph2cart;
var d3 = new M3(vsoi8.D, vsoi9.D, vsoi10.D);
(-v1PlusS00 * d2).CopyTo(jac, 1, 6);
(-v1PlusS01 * d3).CopyTo(jac, 1, 8);
(-v1PlusS10 * d2).CopyTo(jac, 4, 6);
(-v1PlusS11 * d3).CopyTo(jac, 4, 8);
/*
* meet in the planet's SOI
*/
fi[7] = r2Minus.x - r2Plus.x;
fi[8] = r2Minus.y - r2Plus.y;
fi[9] = r2Minus.z - r2Plus.z;
fi[10] = v2Minus.x - v2Plus.x;
fi[11] = v2Minus.y - v2Plus.y;
fi[12] = v2Minus.z - v2Plus.z;
double l = moonToPlanetScale.LengthScale;
double v = moonToPlanetScale.VelocityScale;
double t = moonToPlanetScale.TimeScale;
DualV3 rsoiPlanet6 = new DualV3(moonSOI, x[6], x[7], 0, 1, 0).sph2cart / l + moonR2;
DualV3 rsoiPlanet7 = new DualV3(moonSOI, x[6], x[7], 0, 0, 1).sph2cart / l + moonR2;
var d0 = new M3(rsoiPlanet6.D, rsoiPlanet7.D, V3.zero);
DualV3 vsoiPlanet8 = new DualV3(x[8], x[9], x[10], 1, 0, 0).sph2cart / v + moonV2;
DualV3 vsoiPlanet9 = new DualV3(x[8], x[9], x[10], 0, 1, 0).sph2cart / v + moonV2;
DualV3 vsoiPlanet10 = new DualV3(x[8], x[9], x[10], 0, 0, 1).sph2cart / v + moonV2;
var d1 = new M3(vsoiPlanet8.D, vsoiPlanet9.D, vsoiPlanet10.D);
(v2MinusS00 * d0).CopyTo(jac, 7, 6);
(v2MinusS01 * d1).CopyTo(jac, 7, 8);
(v2MinusS10 * d0).CopyTo(jac, 10, 6);
(v2MinusS11 * d1).CopyTo(jac, 10, 8);
((v2MinusS00 * moonV2 + v2MinusS01 * moonA2) / t).CopyTo(jac, 7, 11);
((v2MinusS10 * moonV2 + v2MinusS11 * moonA2) / t).CopyTo(jac, 10, 11);
v2Minus.CopyTo(jac, 7, 12);
a2Minus.CopyTo(jac, 10, 12);
v2Plus.CopyTo(jac, 7, 13);
a2Plus.CopyTo(jac, 10, 13);
(-v2PlusS00).CopyTo(jac, 7, 14);
(-v2PlusS01).CopyTo(jac, 7, 17);
(-v2PlusS10).CopyTo(jac, 10, 14);
(-v2PlusS11).CopyTo(jac, 10, 17);
/*
* periapsis condition
*/
Dual p = DualV3.Dot(new DualV3(rf, new V3(1, 0, 0)).normalized, vf.normalized);
fi[13] = p.M;
jac[13, 14] = p.D;
jac[13, 15] = DualV3.Dot(new DualV3(rf, new V3(0, 1, 0)).normalized, vf.normalized).D;
jac[13, 16] = DualV3.Dot(new DualV3(rf, new V3(0, 0, 1)).normalized, vf.normalized).D;
jac[13, 17] = DualV3.Dot(rf.normalized, new DualV3(vf, new V3(1, 0, 0)).normalized).D;
jac[13, 18] = DualV3.Dot(rf.normalized, new DualV3(vf, new V3(0, 1, 0)).normalized).D;
jac[13, 19] = DualV3.Dot(rf.normalized, new DualV3(vf, new V3(0, 0, 1)).normalized).D;
/*
* periapsis constraint
*/
fi[14] = rf.sqrMagnitude - peR * peR;
jac[14, 14] = (new DualV3(rf, new V3(1, 0, 0)).sqrMagnitude - peR * peR).D;
jac[14, 15] = (new DualV3(rf, new V3(0, 1, 0)).sqrMagnitude - peR * peR).D;
jac[14, 16] = (new DualV3(rf, new V3(0, 0, 1)).sqrMagnitude - peR * peR).D;
/*
* time constraints
*/
fi[15] = moonDt1 + moonDt2 + burnTime - moonDt;
jac[15, 3] = 1.0;
jac[15, 4] = 1.0;
jac[15, 5] = 1.0;
jac[15, 11] = -1.0;
/*
* midpoint time constraints
*/
fi[16] = moonDt1 - moonDt2;
jac[16, 4] = 1.0;
jac[16, 5] = -1.0;
fi[17] = planetDt1 - planetDt2;
jac[17, 12] = 1.0;
jac[17, 13] = -1.0;
}
private static double[] GenerateInitialGuess(Args args)
{
var sw = new Stopwatch();
sw.Start();
double[] x = new double[NVARIABLES];
double moonSOI = args.MoonSOI;
double peR = args.PeR;
V3 r0 = args.R0;
V3 v0 = args.V0;
V3 moonR0 = args.MoonR0;
V3 moonV0 = args.MoonV0;
Scale moonToPlanetScale = args.MoonToPlanetScale;
double dt, tt1;
V3 rf, vf, dv, rsoi, vsoi;
// kick the moon's orbit to the new apsis to build the transfer orbit
V3 dv1 = ChangeOrbitalElement.ChangeApsis(1.0, moonR0, moonV0, peR);
// get the transfer orbit keplerian elements
(double sma, double ecc, double inc, double lan, double argp, double tanom, _) =
Maths.KeplerianFromStateVectors(1.0, moonR0, moonV0 + dv1);
// calculate the true anomaly of the SOI point on the transfer orbit (using the planet scale)
double moonSOI2 = moonSOI / moonToPlanetScale.LengthScale;
double nuSOI = TAU - SafeAcos((sma * (1 - ecc * ecc) / moonSOI2 - 1) / ecc); // FIXME: probably assumes we're going to a periapsis?
if (Maths.EccFromStateVectors(1.0, r0, v0) < 1 && Maths.ApoapsisFromStateVectors(1.0, r0, v0) < moonSOI)
{
// get the rsoi/vsoi in the planet-centric coordinates
(V3 _, V3 vsoiPlanet) = Maths.StateVectorsFromKeplerian(1.0, sma, ecc, inc, lan, argp, nuSOI);
// now compute the lunar hyperbolic burn.
V3 vneg, vpos, rburn;
(vneg, vpos, rburn, dt) = Maths.SingleImpulseHyperbolicBurn(1.0, r0, v0, (vsoiPlanet - moonV0) * moonToPlanetScale.VelocityScale);
dv = vpos - vneg;
tt1 = Maths.TimeToNextRadius(1.0, rburn, vpos, moonSOI);
(rsoi, vsoi) = Shepperd.Solve(1.0, tt1, rburn, vpos);
}
else
{
// if we're already on an escape trajectory, try an immediate burn and hope we're reasonably close
dt = 0;
dv = V3.zero;
tt1 = Maths.TimeToNextRadius(1.0, r0, v0, moonSOI);
(rsoi, vsoi) = Shepperd.Solve(1.0, tt1, r0, v0);
}
// get the rsoi/vsoi in planet-coordinates of the forward-propagated feasible orbit from the burn.
(V3 moonR2, V3 moonV2) = Shepperd.Solve(1.0, (dt + tt1) / moonToPlanetScale.TimeScale, moonR0, moonV0);
V3 rsoiPlanet = rsoi / moonToPlanetScale.LengthScale + moonR2;
V3 vsoiPlanet2 = vsoi / moonToPlanetScale.VelocityScale + moonV2;
// construct rf + vf by introducing a discontinuity at the SOI
V3 vsoiPlanet3 = vsoiPlanet2 + ChangeOrbitalElement.ChangeApsis(1.0, rsoiPlanet, vsoiPlanet2, peR);
// forward propagate that to find rf+vf conditions and transfer time
double tt2 = Maths.TimeToNextPeriapsis(1.0, rsoiPlanet, vsoiPlanet3);
(rf, vf) = Shepperd.Solve(1.0, tt2, rsoiPlanet, vsoiPlanet3);
V3 r2Sph = rsoi.cart2sph;
//V3 v2Sph = vsoi.cart2sph;
// taking the average of the mismatch in vsoi and spreading the infeasibility over both SOIs seems to actually
// produce better convergence properties.
V3 v2Sph = (((vsoiPlanet3 - moonV2) * moonToPlanetScale.VelocityScale + vsoi) / 2).cart2sph;
x[0] = dv.x; // maneuver x
x[1] = dv.y; // maneuver y
x[2] = dv.z; // maneuver z
x[3] = dt; // maneuver dt
x[4] = tt1 / 2; // 1/2 coast time through moon SOI
x[5] = tt1 / 2; // 1/2 coast time through moon SOI
x[6] = r2Sph[1]; // theta of SOI position
x[7] = r2Sph[2]; // phi of SOI position
x[8] = v2Sph[0]; // r of SOI velocity
x[9] = v2Sph[1]; // theta of SOI velocity
x[10] = v2Sph[2]; // phi of SOI velocity
x[11] = tt1 + dt; // total time in the moon SOI
x[12] = tt2 / 2; // 1/2 coast time through planet SOI
x[13] = tt2 / 2; // 1/2 coast time thorugh planet SOI
x[14] = rf.x; // final rx
x[15] = rf.y; // final ry
x[16] = rf.z; // final rz
x[17] = vf.x; // final vx
x[18] = vf.y; // final vy
x[19] = vf.z; // final vz
sw.Stop();
Print($"initial guess generation took {sw.ElapsedMilliseconds}ms");
return x;
}
private const double DIFFSTEP = 1e-9;
private const double EPSX = 1e-4;
private const int MAXITS = 10000;
private const int NVARIABLES = 20;
private const int NEQUALITYCONSTRAINTS = 17;
private const int NINEQUALITYCONSTRAINTS = 0;
private static (V3 V, double dt) ManeuverScaled(Args args, double dtmin = double.NegativeInfinity, double dtmax = double.PositiveInfinity)
{
Scale planetScale = args.PlanetScale;
V3 moonR0 = args.MoonR0;
V3 moonV0 = args.MoonV0;
double[] x = GenerateInitialGuess(args);
double[] bndl = new double[NVARIABLES];
double[] bndu = new double[NVARIABLES];
for (int i = 0; i < NVARIABLES; i++)
{
bndl[i] = double.NegativeInfinity;
bndu[i] = double.PositiveInfinity;
}
bndl[3] = dtmin;
bndu[3] = dtmax;
var sw = new Stopwatch();
sw.Start();
//alglib.minnlccreatef(NVARIABLES, x, DIFFSTEP, out alglib.minnlcstate state);
alglib.minnlccreate(NVARIABLES, x, out alglib.minnlcstate state);
alglib.minnlcsetbc(state, bndl, bndu);
alglib.minnlcsetstpmax(state, 1e-2);
//double rho = 1000.0;
//int outerits = 5;
//alglib.minnlcsetalgoaul(state, rho, outerits);
//alglib.minnlcsetalgoslp(state);
alglib.minnlcsetalgosqp(state);
alglib.minnlcsetcond(state, EPSX, MAXITS);
alglib.minnlcsetnlc(state, NEQUALITYCONSTRAINTS, NINEQUALITYCONSTRAINTS);
/*
alglib.minnlcoptguardsmoothness(state);
alglib.minnlcoptguardgradient(state, DIFFSTEP);
*/
double[] fi = new double[NEQUALITYCONSTRAINTS + NINEQUALITYCONSTRAINTS + 1];
double[,] jac = new double[NEQUALITYCONSTRAINTS + NINEQUALITYCONSTRAINTS + 1, NVARIABLES];
NLPFunction(x, fi, jac, args);
alglib.minnlcoptimize(state, NLPFunction, null, args);
alglib.minnlcresults(state, out double[] x2, out alglib.minnlcreport rep);
sw.Stop();
Print($"optimization took {sw.ElapsedMilliseconds}ms: {rep.iterationscount} iter, {rep.nfev} fev");
/*
alglib.minnlcoptguardresults(state, out alglib.optguardreport ogrep);
if (ogrep.badgradsuspected)
throw new Exception(
$"badgradsuspected: {ogrep.badgradfidx},{ogrep.badgradvidx}\nuser:\n{DoubleMatrixString(ogrep.badgraduser)}\nnumerical:\n{DoubleMatrixString(ogrep.badgradnum)}\nsparsity check:\n{DoubleMatrixSparsityCheck(ogrep.badgraduser, ogrep.badgradnum, 1e-2)}");
if (ogrep.nonc0suspected || ogrep.nonc1suspected)
throw new Exception("alglib optguard caught an error, i should report better on errors now");
*/
if (rep.terminationtype < 0)
throw new Exception(
$"ReturnFromMoon.Maneuver(): SQP solver terminated abnormally: {rep.terminationtype}"
);
if (rep.nlcerr > 1e-4)
throw new Exception(
$"ReturnFromMoon.Maneuver() no feasible solution found, constraint violation: {rep.nlcerr}");
(double sma, double ecc, double inc, double lan, double argp, double tanom, _) =
Maths.KeplerianFromStateVectors(1.0, new V3(x2[14], x2[15], x2[16]), new V3(x2[17], x2[18], x2[19]));
Print(
$"Earth transfer orbit:\nsma:{sma * planetScale.LengthScale} ecc:{ecc} inc:{Rad2Deg(inc)} lan:{Rad2Deg(lan)} argp:{Rad2Deg(argp)} tanom:{Rad2Deg(tanom)}");
(sma, ecc, inc, lan, argp, tanom, _) =
Maths.KeplerianFromStateVectors(1.0, moonR0, moonV0);
Print(
$"Lunar orbit:\nsma:{sma * planetScale.LengthScale} ecc:{ecc} inc:{Rad2Deg(inc)} lan:{Rad2Deg(lan)} argp:{Rad2Deg(argp)} tanom:{Rad2Deg(tanom)}");
return (new V3(x2[0], x2[1], x2[2]), x2[3]);
}
private static (V3 V, double dt) Maneuver(double centralMu, double moonMu, V3 moonR0, V3 moonV0, double moonSOI,
V3 r0, V3 v0, double peR, double inc, double dtmin = double.NegativeInfinity, double dtmax = double.PositiveInfinity)
{
var sw = new Stopwatch();
sw.Start();
Print(
$"ReturnFromMoon.Maneuver({centralMu}, {moonMu}, new V3({moonR0}), new V3({moonV0}), {moonSOI}, new V3({r0}), new V3({v0}), {peR}, {inc})");
(double sma, double ecc, double incc, double lan, double argp, double tanom, _) =
Maths.KeplerianFromStateVectors(moonMu, r0, v0);
Print($"sma:{sma} ecc:{ecc} inc:{Rad2Deg(incc)} lan:{Rad2Deg(lan)} argp:{Rad2Deg(argp)} tanom:{Rad2Deg(tanom)}");
var moonScale = Scale.Create(moonMu, Sqrt(r0.magnitude * moonSOI));
var planetScale = Scale.Create(centralMu, Sqrt(moonR0.magnitude * peR));
Scale moonToPlanetScale = moonScale.ConvertTo(planetScale);
var args = new Args
{
MoonSOI = moonSOI / moonScale.LengthScale,
PeR = peR / planetScale.LengthScale,
Inc = inc,
R0 = r0 / moonScale.LengthScale,
V0 = v0 / moonScale.VelocityScale,
MoonR0 = moonR0 / planetScale.LengthScale,
MoonV0 = moonV0 / planetScale.VelocityScale,
MoonToPlanetScale = moonToPlanetScale,
MoonScale = moonScale,
PlanetScale = planetScale
};
(V3 dv, double dt) = ManeuverScaled(args, dtmin / moonScale.TimeScale, dtmax / moonScale.TimeScale);
sw.Stop();
Print($"total calculation took {sw.ElapsedMilliseconds}ms");
return (dv * moonScale.VelocityScale, dt * moonScale.TimeScale);
}
public static (V3 dv, double dt, double newPeR) NextManeuver(double centralMu, double moonMu, V3 moonR0, V3 moonV0,
double moonSOI, V3 r0, V3 v0, double peR, double inc, double dtmin = double.NegativeInfinity, double dtmax = double.PositiveInfinity)
{
double dt;
V3 dv;
int i = 0;
(double _, double ecc) = Maths.SmaEccFromStateVectors(moonMu, r0, v0);
while (true)
{
(dv, dt) = Maneuver(centralMu, moonMu, moonR0, moonV0, moonSOI, r0, v0, peR, inc, dtmin, dtmax);
if (dt > 0 || ecc >= 1)
break;
if (i++ >= 5)
throw new Exception("Maximum iterations exceeded with no valid future solution");
(r0, v0) = Shepperd.Solve(moonMu, Maths.PeriodFromStateVectors(moonMu, r0, v0), r0, v0);
}
(V3 r1, V3 v1) = Shepperd.Solve(moonMu, dt, r0, v0);
double tt1 = Maths.TimeToNextRadius(moonMu, r1, v1 + dv, moonSOI);
(V3 r2, V3 v2) = Shepperd.Solve(moonMu, tt1, r1, v1 + dv);
(V3 moonR2, V3 moonV2) = Shepperd.Solve(centralMu, dt + tt1, moonR0, moonV0);
double newPeR = Maths.PeriapsisFromStateVectors(centralMu, moonR2 + r2, moonV2 + v2);
return (dv, dt, newPeR);
}
}
}