Goddard Space Flight Center Stationkeeping in and Design of Transfer Between Earth-Moon L1,2 Orbits: ARTEMIS Mission Results Future In-Space Operations (FISO) Dave Folta Goddard Space Flight Center February, 23, 2011 Agenda Goddard Space Flight Center • General Libration Orbit Background • Stationkeeping Methods • The ARTEMIS Mission Results and Operations • Stationkeeping Observations • Comparison to Other Lunar Orbits • Summary Libration Orbit Dynamics Goddard Space Flight Center Where Are They? What Are They?? Collinear Points: L1, L2, L3 (unstable) Equilibrium or libration points represent Triangular Points: L4, L5 (stable) singularities in the equations of motion where velocity and acceleration components are zero and the forces are balanced Viewed in the rotating frame: centrifugal L4 (Coriolis-Type) force balances with gravitational forces of the two primaries 1 a.u. 1 a.u. Libration points are in plane with no Z component. Orbits are mapped to a rotating L3 Sun L1 L2 frame where there are no time dependent forces 0.01 a.u. A system of interest involves the Sun (m1), Earth/Moon System the Earth-Moon system (m2) and the spacecraft m3 L1 and L2 At a distance of 1.5 million km L5 L4 and L5 At a distance of 150. million km Solar Rotating Coordinates Ecliptic Plane Projection Rotating Coordinate Frames Goddard Space Flight Center Sun-Earth & Earth-Moon • X is towards smaller body (sun to Earth) • Y is along smaller body velocity • Z is out of Ecliptic plane • Co-linear Unstable locations at L1, L2, and ‘L3’ • Stable locations at L4 and L5 L4 L2 L Sun - Earth 1 Sun - Earth Moon’s Orbit L1 L2 150 million km L Sun 5 L3 1.5 million km 1.5 million km General Background and ARTEMIS Goddard Space Flight Center • Vicinity of the Earth-Moon collinear libration points as promising locations for scientific data collection and/or communications options • Orbits near the collinear locations, including quasi-periodic Lissajous trajectories, are inherently unstable and must be controlled • A variety of stationkeeping strategies have previously been investigated, most notably for applications in the Sun-Earth system; fewer studies have considered trajectories near the Earth-Moon libration points • A true four-body problem - Earth-Moon orbit maintenance is more challenging than Sun-Earth system Shorter time scales (~14 days vs. ~6 months for 1 rev) Larger orbital eccentricity of the secondary (lunar eccentricity ~0.055) Sun acts as a significant perturbing body both in terms of the gravitational force as well as solar radiation pressure • ARTEMIS Implications Baseline trajectory is defined only to design a feasible mission No reference motion that is required Minimize cost in terms of fuel is the highest priority 5 Spacecraft constraints (spinning with limited DV direction) General Background and ARTEMIS Goddard Space Flight Center • Only recently has anyone exploited the regions near the Earth-Moon libration points • ARTEMIS (Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun) is the first Earth-Moon libration mission • Two spacecraft entered into Earth-Moon L1 and L2 orbits in August and October of 2010 • Stationkeeping strategies implemented for ARTEMIS support A traditional baseline orbit-targeting approach A global optimum search scheme A balancing approach as part of an orbit continuation scheme • To support ARTEMIS, orbit maintenance costs were compared for periodic and non-periodic orbits in different dynamical models; Circular Restricted Three-Body (CRTB) as well as Moon-Earth-Sun ephemeris models using high-fidelity modeling that incorporates all perturbations. 6 ARTEMIS Goddard Space Flight Center • The ARTEMIS mission is an extension to the Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission. • The ARTEMIS mission moved two (of five) spacecraft in the outer-most elliptical Earth orbits and, with lunar gravity assists, re-directing to both the L1 and L2 via transfer trajectories that exploit the multi-body dynamical environment. • Once the Earth-Moon libration point orbits are achieved and maintained for several months, both spacecraft will be inserted into elliptical lunar orbits. • The P1 spacecraft entered Earth-Moon Lissajous orbits August 25th 2010 and P2 followed in October 2010. Artemis provides comprehensive Earth-lunar environment analysis using particles and fields instruments. P2 Transfer Trajectory P1 Transfer Trajectory 7 ARTEMIS P1 In Earth-Moon L2 Lissajous orbit Goddard Space Flight Center Earth-moon Libration Orbit • P1 captures into L2 Orbit • Transfer to L1 Orbit • Transfer to Lunar Orbit ARTEMIS-P1 Spacecraft’s Orbit – Side View Towards Earth ARTEMIS- Moon P1 Here on August L1 25th L2 ARTEMIS L1 Orbit ARTEMIS L2 Orbit ARTEMIS P2 to Enter Earth-Moon L1 Orbit October 23 Goddard Space Flight Center ARTEMIS L1 Orbit Earth-Moon Libration L2 to L1 Transfer Orbit Orbit Direction • P2 captures into L1 to Earth Orbit via L2 • Transfer to Lunar Orbit Moon Sample of Unstable Mode Directions using STM of and EML Orbit Goddard Space Flight Center 2 • System dynamics show six modes, 4 oscillating, one converging, one diverging • Stable or Unstable directions can be used to maintain orbit balance Sample of stable and unstable modes for the EML2 early orbit Earth-Moon L1 and L2 Stability Goddard Space Flight Center • Application of a 0.1cm/s DV in the +/- velocity direction at 1 day interval locations about a sample orbit L2 Departures -DV applied +DV applied Along Unstable Modes -Dv Returns to Lunar Region +Dv Departs Toward L2 Moon L2 Sun/Earth Libration Points L 1 -DV applied +DV applied Departures Along Unstable Modes +Dv Returns to Lunar Region -Dv Departs L1 Moon L1 Toward Stationkeeping Strategies (1 of 2) Goddard Space Flight Center Stationkeeping strategies must satisfy the following self-imposed conditions: o Full ephemeris with high-fidelity models o Globally optimized solutions were possible o Methods that can be applied for any Earth-Moon orbital requirements at L1 or L2 Standard approaches cannot be employed for various reasons, o Reference orbit is required which is not necessarily available nor desired o Strategy is based on the CRTB model only o Proposed approach cannot accommodate the ARTEMIS spacecraft constraints Strategy Goal(s) Advantage Disadvantage Selection Criteria 1 Target x-axis Velocity at -Validated in Sun-Earth - Overly constraining -Operationally constraining and larger crossing, parallel to operations - Can lead to increased DVs DV budget crossing with x- x-axis, is zero - Can use a DC or optimization - Dynamics may not result in - Sensitivity issues in computing axis velocity process to target a single reaching subsequent x-axis maneuvers to achieve targets can require parameter crossings high recovery DVs constraint - May not meet operational - Not selected for this ARTEMIS constraints 2 Unstable mode Cancel unstable - Simple design based on - Requires the use of STMs based - Reference orbit not available component of the dynamical properties of the on reference orbit or the EM - Sensitivity to mode calculation due to cancellation error libration point orbit libration point lunar eccentricity + solar gravity - Multiple algorithms available - Intensive and iterative - Not selected for this application to apply DV calculations 3 Continuous Converge onto a - Possibly less sensitive to - Requires a reference orbit - Requires a reference orbit reference orbit navigation and execution errors - Uses near continuous thrusting - Does not apply to ARTEMIS spacecraft Controllers - Maintains orbit within user- (may be discretized) operationally (near continuous control) defined small torus -Requires computation of gain - Not selected for this application from an STM that is based on the libration point or actual orbit -Linear approximations for control feedback 12 Stationkeeping Strategies (2 of 2) Goddard Space Flight Center • Baseline orbit control-point targeting approach: employs a DC to maintain the vehicle near a nominal trajectory, determined a priori. • Global optimum search method: a strategy that can be applied to any trajectory designed within a higher-fidelity environment • Continuation: Balance the orbit by meeting goals several revolutions downstream, thereby ensuring a continuous orbit without near-term requirements or the reliance on specific orbit specifications. … Use Velocity or Energy to define goals … Employs a Boxed environment for divergence control Strategy Goal(s) Advantage Disadvantage Selection Criteria 4 Baseline Orbit Target multiple points - Rigorous method with -Selection of control points results - Reference points computed as a along orbit guaranteed results in the computation of a reference first guess from an available baseline Control-Point - Based in ephemeris model orbit - Used only as first guess utility for Targeting - Possibly larger DVs ARTEMIS 5 Boxed Define constraints in - Always converges if box - Current implementation algorithms - Used in this application only to terms of distance from size and targeting scheme are limited identify and re-direct solutions that Environment x-axis and combined properly - Logic required in s/w to check for are not converging y-axis trajectories that depart the system 6 Orbit Velocity (or energy) is - Guarantees a minimal DV - Needs accurate integration and full - Analyzed with intent to apply to determined to deliver to achieve orbit continuation ephemeris modeling ARTEMIS Continuation s/c several revs - Several control constraints