Ephemeris and Lambert Algorithms:
Test Cases
ASEN 5519 – Interplanetary Mission Design
Fall, 2006
Introduction
Later in the semester, you will be constructing many porkchop plots to construct interplanetary mission designs to the outer planets. The fundamental building block of a porkchop plot is the solution to Lambert’s Problem. Hence, to be a successful interplanetary mission designer, your Lambert code must be a strong foundation to stand on! The algorithms also require good ephemeris code and good JD converters. This document will provide some test cases to test out your code.
Assumptions!!!
1 AU / 149,597,870 km (Vallado)Solar Gravitational Parameter / 1.327 124 28 x 1011 km3/(solar sec)2 (Vallado)
1 Day / 86400 seconds
Date to JD Conversion
Date = Nov. 25th, 1978; 4h 30m 0s
JD = 2443837.6875
Date = Sept. 15th, 2006; 10h 00m 20s
JD = 2453993.9169
Date = Jan. 1st, 2007; 0h 00m 00s
JD = 2454101.5
Ephemeris and Lambert Checks:
Planet 1: Earth Planet 2: Mars
Departure JD: 2454367.90000 Arrival JD: 2454577.90000
Transfer Duration: 210.00000 days (1.81440000e+007 seconds)
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Earth's Position at JD1: [150064539.403983 2267759.896369 -276.754311] km wrt the Sun
Earth's Velocity at JD1: [-0.935067 29.673807 -0.000519] km/s wrt the Sun
Mars' Position at JD2: [-207818935.305987 136713926.487051 7968576.434594] km wrt the Sun
Mars' Velocity at JD2: [-12.404508 -18.175755 -0.076153] km/s wrt the Sun
Spacecraft Velocity at JD1: [-0.075289 33.476420 1.907380] km/s wrt the Sun
Spacecraft Velocity at JD2: [-14.189471 -14.839340 -0.833227] km/s wrt the Sun
Spacecraft V-inf out: [0.859778 3.802612 1.907899] km/s wrt Earth
Spacecraft V-inf in: [-1.784964 3.336414 -0.757073] km/s wrt Mars
C3 at Launch: 18.839158 km^2/s^2 |V-inf| at Arrival: 3.858875 km/s
Planet 1: Earth Planet 2: Venus
Departure JD: 2454367.90000 Arrival JD: 2454577.90000
Transfer Duration: 210.00000 days (1.81440000e+007 seconds)
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Earth's Position at JD1: [150064539.403983 2267759.896369 -276.754311] km wrt the Sun
Earth's Velocity at JD1: [-0.935067 29.673807 -0.000519] km/s wrt the Sun
Venus' Position at JD2: [108502685.373919 981095.895427 -6248799.806056] km wrt the Sun
Venus' Velocity at JD2: [-0.465174 34.859502 0.504045] km/s wrt the Sun
Spacecraft Velocity at JD1: [23.041751 0.806102 4.344444] km/s wrt the Sun
Spacecraft Velocity at JD2: [34.742706 0.947442 4.007763] km/s wrt the Sun
Spacecraft V-inf out: [23.976818 -28.867706 4.344962] km/s wrt Earth
Spacecraft V-inf in: [35.207880 -33.912060 3.503718] km/s wrt Venus
C3 at Launch: 1427.110960 km^2/s^2 |V-inf| at Arrival: 49.009169 km/s
Planet 1: Earth Planet 2: Venus
Departure JD: 2454257.00000 Arrival JD: 2454402.00000
Transfer Duration: 145.00000 days (1.25280000e+007 seconds)
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Earth's Position at JD1: [-40907159.776698 -146166176.029225 2524.752269] km wrt the Sun
Earth's Velocity at JD1: [28.201602 -8.140052 0.000094] km/s wrt the Sun
Venus' Position at JD2: [21214945.229277 105654723.068676 221755.525408] km wrt the Sun
Venus' Velocity at JD2: [-34.453939 6.720951 2.080517] km/s wrt the Sun
Spacecraft Velocity at JD1: [26.151206 -6.439026 -0.747977] km/s wrt the Sun
Spacecraft Velocity at JD2: [-36.925365 8.695987 1.053181] km/s wrt the Sun
Spacecraft V-inf out: [-2.050396 1.701026 -0.748071] km/s wrt Earth
Spacecraft V-inf in: [-2.471426 1.975036 -1.027336] km/s wrt Venus
C3 at Launch: 7.657223 km^2/s^2 |V-inf| at Arrival: 3.326279 km/s
Planet 1: Earth Planet 2: Jupiter
Departure JD: 2454208.00000 Arrival JD: 2455648.00000
Transfer Duration: 1440.00000 days (1.24416000e+008 seconds)
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Earth's Position at JD1: [-133790709.833879 -68187957.669580 1327.392275] km wrt the Sun
Earth's Velocity at JD1: [13.041750 -26.652198 0.000422] km/s wrt the Sun
Jupiter's Position at JD2: [713873801.986079 196242257.471874 -16779211.940408] km wrt the Sun
Jupiter's Velocity at JD2: [-3.622026 13.220510 0.026292] km/s wrt the Sun
Spacecraft Velocity at JD1: [9.811753 -37.136284 -4.217053] km/s wrt the Sun
Spacecraft Velocity at JD2: [-6.852424 6.013385 0.951383] km/s wrt the Sun
Spacecraft V-inf out: [-3.229997 -10.484087 -4.217474] km/s wrt Earth
Spacecraft V-inf in: [-3.230398 -7.207125 0.925092] km/s wrt Jupiter
C3 at Launch: 138.136042 km^2/s^2 |V-inf| at Arrival: 7.951975 km/s
Planet 1: Earth Planet 2: Saturn
Departure JD: 2454400.00000 Arrival JD: 2456850.00000
Transfer Duration: 2450.00000 days (2.11680000e+008 seconds)
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Earth's Position at JD1: [125312162.328009 80094189.561700 -1620.778825] km wrt the Sun
Earth's Velocity at JD1: [-16.527724 24.988254 -0.000417] km/s wrt the Sun
Saturn's Position at JD2: [-916332981.031387 -1169747308.621389 56877707.789551] km wrt the Sun
Saturn's Velocity at JD2: [7.056768 -5.985045 -0.176776] km/s wrt the Sun
Spacecraft Velocity at JD1: [-26.139293 30.300255 -4.576393] km/s wrt the Sun
Spacecraft Velocity at JD2: [3.406155 -2.080308 0.414463] km/s wrt the Sun
Spacecraft V-inf out: [-9.611569 5.312002 -4.575976] km/s wrt Earth
Spacecraft V-inf in: [-3.650613 3.904737 0.591239] km/s wrt Saturn
C3 at Launch: 141.539187 km^2/s^2 |V-inf| at Arrival: 5.378058 km/s