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IO Aerospace

Lambert Solver

Lambert Solver¶

The Lambert solver computes transfer orbits between two positions and a time of flight, enabling interplanetary and rendezvous mission design.

LambertSolver¶

LambertSolver finds departure and arrival velocities that satisfy the Lambert boundary-value problem. It supports multi-revolution transfers via Battin, Lagrange, and Lancaster formulations with Halley root-finding.

Solve Method¶

public LambertResult Solve(
    bool isRetrograde,
    OrbitalParameters initialOrbitalParameters,
    OrbitalParameters targetObjectOrbitalParameters,
    CelestialItem centerOfMotion,
    ushort maxRevolution)

Parameter	Type	Description
`isRetrograde`	`bool`	Whether the transfer is retrograde
`initialOrbitalParameters`	`OrbitalParameters`	Spacecraft state at departure
`targetObjectOrbitalParameters`	`OrbitalParameters`	Target state at arrival
`centerOfMotion`	`CelestialItem`	Central body for the transfer
`maxRevolution`	`ushort`	Maximum number of full revolutions

LambertResult¶

Member	Description
`Solutions`	`IReadOnlyCollection<LambertSolution>` of all computed transfer solutions
`MaxRevolutions`	Maximum revolutions used
`GetZeroRevolutionSolution()`	Get the direct (zero-revolution) solution
`GetMultiRevolutionSolutions(uint n)`	Get solutions for a given revolution count

LambertSolution¶

Each solution contains the velocity vectors and delta-V information for one transfer arc.

Property	Type	Description
`V1`	`Vector3`	Departure velocity (m/s)
`V2`	`Vector3`	Arrival velocity (m/s)
`DeltaV1`	`Vector3`	Required delta-V at departure
`DeltaV2`	`Vector3`	Required delta-V at arrival
`DeltaV`	`double`	Total delta-V magnitude (m/s)
`Revolutions`	`uint`	Number of full revolutions
`Branch`	`LambertBranch?`	`Left` or `Right` branch (null for direct transfer)
`Iterations`	`uint`	Number of solver iterations

Example¶

var solver = new LambertSolver();
var result = solver.Solve(
    isRetrograde: false,
    initialOrbitalParameters: departureState,
    targetObjectOrbitalParameters: arrivalState,
    centerOfMotion: earth,
    maxRevolution: 0);

var solution = result.GetZeroRevolutionSolution();
var transferOrbit = new StateVector(
    departureState.ToStateVector().Position, solution.V1,
    earth, departureState.Epoch, Frame.ICRF);

Console.WriteLine($"Total Delta-V: {solution.DeltaV:F1} m/s");

See Also¶