Tools for 2-body orbit propagation, Lambert problem solving, and ejection/insertion trajectory optimization. Put together as a project to get comfortable with Julia. Intended for use to plan simple missions in Kerbal Space Program.
Get the position, velocity, or both (i.e. a state vector) for an orbit as a function of either true anomaly or time:
julia> using KeplerTools
julia> include(joinpath(dirname(pathof(KeplerTools)), "..", "data", "kerbol_system.jl"));
julia> position, velocity = state_vector(3.14, kerbin.orbit)
([-1.3599823007697136e10, 2.1659825247473374e7, 0.0], [-14.786987156243779, -9284.488948751467, 0.0])
julia> position, velocity = time_state_vector(0, kerbin.orbit)
([-1.3599823007697136e10, 2.1659825247473374e7, 0.0], [-14.786987156243779, -9284.488948751467, 0.0])Solve Lambert's problem given two orbits, a start time, and an end time.
julia> starttime = 5091522.;
julia> endtime = starttime + 5588238.;
julia> torb = p_lambert(kerbin.orbit, duna.orbit, starttime, endtime)
Orbit above Kerbol:
semi-major axis: 1.6833240192579033e10 m
eccentricity: 0.1926164653078007
inclination: 0.1434866354451145°
RA of ascending node: 19.065485668978525°
argument of periapsis: 354.82322931318316°
mean anomaly at epoch: 3.4404814375472044°
epoch: 5.091522e6 sObtain an optimal ejection or insertion trajectory given a parking orbit and a relative velocity at escape from/encounter with the sphere of influence.
julia> parking_orb = Orbit(kerbin.eqradius + 100000, kerbin)
Orbit above Kerbin:
semi-major axis: 700000.0 m
eccentricity: 0.0
inclination: 0.0°
RA of ascending node: 0.0°
argument of periapsis: 0.0°
mean anomaly at epoch: 0.0°
epoch: 0.0 s
julia> v̄_ejection = time_orbital_velocity(starttime, torb) - time_orbital_velocity(starttime, kerbin.orbit)
3-element StaticArrays.SVector{3, Float64} with indices SOneTo(3):
-138.4274524214611
853.0248945699786
25.38365880099945
julia> ejection_orb = departure_orbit(parking_orb, v̄_ejection, starttime)[1]
Orbit above Kerbin:
semi-major axis: -5.322430914063159e6 m
eccentricity: 1.1315005119137438
inclination: 3.4432174905445865°
RA of ascending node: 308.4387644550581°
argument of periapsis: 358.686708883049°
mean anomaly at epoch: 0.04289926269835575°
epoch: 5.004695828269423e6 s
julia> target_orb = Orbit(duna.eqradius + 100000, duna)
Orbit above Duna:
semi-major axis: 420000.0 m
eccentricity: 0.0
inclination: 0.0°
RA of ascending node: 0.0°
argument of periapsis: 0.0°
mean anomaly at epoch: 0.0°
epoch: 0.0 s
julia> v̄_insertion = time_orbital_velocity(endtime, torb) - time_orbital_velocity(endtime, duna.orbit)
3-element StaticArrays.SVector{3, Float64} with indices SOneTo(3):
-97.7579049517824
890.6147177047887
-22.10024628653403
julia> insertion_orb = arrival_orbit(target_orb, v̄_insertion, endtime)[1]
Orbit above Duna:
semi-major axis: -381152.85373850045 m
eccentricity: 2.1019197583378046
inclination: 1.605586783222423°
RA of ascending node: 214.6218218467353°
argument of periapsis: 180.05673308987429°
mean anomaly at epoch: -0.037260288183548824°
epoch: 1.0732725844524838e7 sObtain all ejection, insertion, and transfer orbits for a ballistic transfer between any two orbits within a star system:
julia> tfer = Transfer(parking_orb, target_orb, starttime, endtime)
Transfer from orbit around Kerbin to orbit around Duna
departure time: 5.091522e6 s
arrival time: 1.067976e7 s
Δv: 1692.0562845940308 m/s
julia> tfer.transfer_orbits
1-element Vector{Orbit}:
Orbit above Kerbol:
semi-major axis: 1.6833240192579033e10 m
eccentricity: 0.1926164653078007
inclination: 0.1434866354451145°
RA of ascending node: 19.065485668978525°
argument of periapsis: 354.82322931318316°
mean anomaly at epoch: 3.4404814375472044°
epoch: 5.091522e6 s
julia> tfer.ejection_orbits
1-element Vector{Orbit}:
Orbit above Kerbin:
semi-major axis: -5.322430914063159e6 m
eccentricity: 1.1315005119137438
inclination: 3.4432174905445865°
RA of ascending node: 308.4387644550581°
argument of periapsis: 358.686708883049°
mean anomaly at epoch: 0.04289926269835575°
epoch: 5.004695828269423e6 s
julia> tfer.insertion_orbits
1-element Vector{Orbit}:
Orbit above Duna:
semi-major axis: -381152.85373850045 m
eccentricity: 2.1019197583378046
inclination: 1.605586783222423°
RA of ascending node: 214.6218218467353°
argument of periapsis: 180.05673308987429°
mean anomaly at epoch: -0.037260288183548824°
epoch:
julia> tfer.burns
2-element Vector{Burn}:
Instantaneous burn in orbit above Kerbin:
UT: 5.004695828269423e6 s
total Δv: 1046.4726500752242 m/s
prograde: 1026.9996921227305 m/s
normal: 196.93801584416403 m/s
radial: 39.90059712139015 m/s
Instantaneous burn in orbit above Duna:
UT: 1.0732725844524838e7 s
total Δv: 645.5836345188064 m/s
prograde: -644.2281248462269 m/s
normal: 41.80131947390173 m/s
radial: 1.001002430789867 m/s