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Analysis of Trans-Lunar Spiral Trajectory

February 12, 2009. Analysis of Trans-Lunar Spiral Trajectory. 1. Spiral Transfer. Equations of Motion (EOM)s :. r: distance from central body to spacecraft (s/c) μ : Gravitational parameter (G*M) θ : Angle of rotation T: Thrust from engine m: Mass of spacecraft. Assumes:

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Analysis of Trans-Lunar Spiral Trajectory

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  1. February 12, 2009 [Levi Brown] [Mission Ops] Analysis of Trans-Lunar Spiral Trajectory 1

  2. Spiral Transfer Equations of Motion (EOM)s : r: distance from central body to spacecraft (s/c) μ: Gravitational parameter (G*M) θ: Angle of rotation T: Thrust from engine m: Mass of spacecraft • Assumes: • Two body problem • Point mass central body/spacecraft • Coplanar Transfer to Moon • Thrust is in • Force of gravity in the • Circular lunar orbit • Constant thrust • Created Code: • Input s/c mass, thrust levels, time of flight (TOF) • Integrate EOMs for spiral outward to • moon’s sphere of influence (r ≈ 3.2 x 105 km) • “Turn off” Earth’s gravity and “turn on” Moon • Determine velocity and position relative to • moon (integrate with a “braking” thrust) • Output history of s/c position and velocity [Levi Brown] [Mission Ops] 2

  3. Results Limiting Case: 1 Year TOF Inputs: mo = 595.4 kg (Latest OTV Mass) TOFout = 356 days TOFin≈7 days (Keep low spiral time) Results: Required Tout = 109.5 mN Required Tin= 93.5 mN Perilune Altitude ≈ 8.0 km Perilune Velocity = 2.3 km/s • Note: • Code uses physics to determine s/c motion and is independent of engine properties • Can we produce this much thrust for this amount of time with a s/c of this mass? • ΔV is dependent on engine characteristics because of low thrust • Will use this code iteratively with propulsion to determine if mission can be completed • for a given system [Levi Brown] [Mission Ops] 3

  4. [Levi Brown] [Mission Ops] Back-up Slides 4

  5. Case 1 Spiral Out [Levi Brown] [Mission Ops] 5

  6. Case 1 Spiral In [Levi Brown] [Mission Ops] 6

  7. Spacecraft Radius for Lunar Spiral [Levi Brown] [Mission Ops] 7

  8. Other Future Work: • Work with descent group • Many possibilities for altitude and velocity for descent • What works best? • Should we try to circularize orbit more first? • Look at effects of varying departure orbit (higher LEO, GTO) • Add in 3rd body effect • Have both Earth and Moon gravity in both integrations • More efficient thrusting • Is it more efficient to thrust in velocity direction? [Levi Brown] [Mission Ops] 4

  9. Notes on iteration with propulsion: • DeltaV is caused by 2 factors (gravity and thrust) • For impulse type maneuvers, it is assumed that the thrusting is instantaneous • This means that the deltaV between two points on a trajectory is only caused by gravity • Because code indicates an initial mass, a constant thrust, and a TOF, it was determined • that the best method of calculating deltaV was through the equations for the engine • The current mass was based off of our initial deltaV assumption of 8 km/s • The sizing equations take a deltaVand various specifications for a particular engine • Using the deltaV and specifications, parameters such as TOF, propellant mass, • mass flow rate, initial mass, and thrust are produced. • If we fix a TOF, we can vary deltaV until the TOF match and then find the mass and • thrust required for that engine • Then use the trajectory code to determine if we can reach the moon • If not, vary the deltaV and do it again [Levi Brown] [Mission Ops] 4

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