Flight Dynamics Frank Vaughn Michael Mesarch 30 Apr – 1 May, 2012

1. Advanced X-ray Spectroscopic Imaging Observatory(AXSIO)ReduxNOTE: Original AXSIO material through slide 16, then AXSIO Redux info Flight Dynamics Frank Vaughn Michael Mesarch 30 Apr – 1 May, 2012

2. AXSIO Mission Requirements • AXSIO will be launched by an Atlas-V variant on a direct transfer to a Sun-Earth L2 orbit • Launch Date: 2021 time frame • Lifetime: 5 years • There is no requirement for a Halo orbit … depending on launch conditions the orbit could be a Halo, a Lissajous, or a Toroidal (bounded lissajous) • Old IXO presentations had conflicting constraints relating to Y-amplitude and L2-Earth-AXSIO angle (i.e. angle off of Sun-line) • 800,000 km Y-amplitude equates to 28° (similar to JWST) • Requirements reference a 35° angle – equates to 1,000,000 km Y-amplitude • The choice of 28° vs. 35° will have an impact on launch opportunities • Is the Y-amplitude/angle constraint driven by Sun-shielding & pointing (pitch angle) or is it driven by the desire to keep AXSIO within the magnetosheath? • No eclipses (from Earth or Moon) are allowed during entire mission • No eclipses requirement during launch phase limits the Centaur coast duration and will limit the available launch opportunities

3. Libration Point Geometry • Sun-Earth libration point orbits are typically shown in Sun-Earth rotating coordinates • X-axis: Sun-Earth vector • Z-axis: Earth orbit angular momentum vector • Y-axis: forms orthogonal triad (Z x X) • The SEL2 orbit can be orientated either with the “near side” above or below the plane (see cartoons at right) • The orientation is fixed once spacecraft is launched Moon Sun Earth SEL2 Sun Moon Earth SEL2 Either SEL2 Orbit Orientation is Possible Z Z X X Y Sun Moon Earth SEL2 Y Y X Z

4. AXSIO Angles to Earth • L2 orbit Y- and Z-amplitudes are coupled • Y = 800,000 km, Z = 500,000 km • Y = 900,000 km, Z = 700,000 km • Y = 1,000,000 km, Z = 800,000 km • X-position ranges from -300,000 km to +200,000 km (relative to L2) • Maximum L2-Earth-SC angle is at max/min Y (Z = 0) • Y = 800,000 km,  = 30° • Y = 900,000 km,  = 33° • Y = 1,000,000 km,  = 35° • The L2-Earth-SC angle at max/min Z(X = -300,000, + 200,000 km ; Y = 0) • Z = 500,000 km,  = 17° (far) - 23° (near) • Z = 700,000 km,  = 23° (far) - 30° (near) • Z = 800,000 km,  = 26° (far) - 34° (near) Moon Sun Earth SEL2  Sun Moon Earth SEL2 Z  X Y Y X Z

5. L2 Mission Design Parameters • L2 mission design has several design parameters that feed into the available L2 orbit size and type • Launch Date & Time • TTILT: Transfer Trajectory Insertion Solar Local Time (typically 11:00 to 14:00) • Launch C3: Launch energy (-0.5 km2/s2 is conservative number) • Chosen to allow for zero ΔV at L2 orbit insertion • Coast Time: time in parking orbit before final firing of the Centaur (600 sec to 5400 sec) • Atlas-V launch vehicle provides a very large solution space for L2 missions • Zero eclipse constraint during launch considerably reduces solution space by limiting the Coast duration Launch Coast Sun TTI To L2

6. Eclipse Growth vs. Coast • A scan of the eclipse time during the launch phase was examined over 2021 • As the coast time increases, the available solution space decreases • This is the first constraint applied to remove launch opportunities • Constraints for L2 orbit size (or angle) and eclipses at L2 will be layered on top of this constraint Zero Eclipse Zero Eclipse Zero Eclipse Zero Eclipse

7. Full L2 Solution Space for 1 Day Coast Time TTI Local Time • L2 orbit solution space (partial is below) is very complex, subject to dynamical limitations and overlapping constraints Lissajous Orbits Halo Orbits Shadow Region

8. Sample Y-Amplitude Solution Space • Sample Y-Amplitude solution space for a single day • Launch eclipse constraint (Coast) limits minimum Y-amplitude to > 800,000 km

9. Sample Z-Amplitude Solution Space • Sample Z-Amplitude solution space for a single launch day • Launch eclipse constraint (Coast) forces Z-amplitude up to 950,000 km

10. Mission Timeline • A direct transfer to L2 has a simple timeline • Launch • Separation (dependent on Coast duration) • ELV Dispersion Correction (TTI + 24 hrs) • Mid-Course Correction #1 (TTI + 15 days) • Mid-Course Correction #2 (TTI + 60 days) • L2 Orbit Insertion (TTI +  100 days) • L2 Stationkeeping (depends on momentum unloading strategy)

11. Maneuver Directions • Typical maneuver directions are along the Sun-line • ELV Dispersion correction maneuver is more efficient if along velocity/anti-velocity (typically close to along Sun-line) • No indications that AXSIO can’t thrust towards or away from Sun • Dual direction allows for zero bias on launch vehicle energy • JWST limited to anti-Sun thrusting only due to Sun-shade • Mid-Course Corrections (MCC) and Stationkeeping are also aligned towards Sun or anti-Sun Dispersion Correction MCC SK SK

12. Stationkeeping at L2 • Stationkeeping at L2 is relatively benign – 4 m/s per year • The stationkeeping frequency is highly dependent on the frequency for momentum unloading • Since the L2 orbit is quasi-stable (saddle point), frequent momentum unloads can perturb an L2 orbiter “off the hill” • Two examples of this are • WMAP: presents a constant face to the Sun and momentum unloading is very infrequent leading to infrequent stationkeeping (≥ 3 months between maneuvers) • JWST: big Cp-Cg offset, frequent off-pointing, variable area to Sun, & anti-Sun thrusting only leads to stationkeeping maneuvers planned every 3 weeks • Careful management of AXSIO’s Cp-Cg offset will help to reduce the momentum buildup and reduce the frequency of AXSIO’s stationkeeping maneuvers • All signs point to AXSIO being able to perform stationkeeping maneuvers every 3-months • This will need to be monitored as the design matures

13. ΔV Budget • The Atlas-V DV budget for AXSIO • Launch Window 10 m/s(1) • ELV Dispersion Correction 20 m/s(2) • Mid-Course Corrections (2) 15 m/s(3) • L2 Stationkeeping (5 years) 20 m/s(4) • End of Life Disposal 1 m/s(5) • Total 66 m/s • Assumptions • Accounts for 30 minute finite daily launch window • ELV Dispersion correction assumes Atlas-V dispersions corrected at TTI + 24 hours • Atlas-V ELV Dispersion: C3 ±0.05 km2/s2 (3) [equates to  ±3 m/s at TTI] • Accommodates a neutral “mid”-biased launch • Dispersion values were obtained from KSC ELV analysts • Two MCC maneuvers to correct for execution errors (5%) on ELV correction maneuver • Budgeting 4 m/s/year • Small maneuver to ensure that observatory leaves the Earth-Moon system

14. Libration Point Orbit Accuracy (1 of 2) • Traditional orbit determination for libration point missions are based on using range and Doppler measurements … usually from the DSN • Radial (line of sight) accuracy is considerably more accurate than the accuracy in the plane of the sky • Historic orbit determination accuracies (3σ) are listed below • Data is from paper “Orbit Determination Issues for Libration Point Orbits” by Mark Beckman (GSFC) and was presented at the Libration Point Orbits and Applications conference in Girona, Spain (June, 2002) • ISEE-3: 9 km, S-band, 9 x 5 minute passes per day, 21-day arc • SOHO: 7 km, S-band DSN (26m, 34m, 70m), 5 hrs/day, 21-day arc • Analysis of SOHO data with 40 minutes/day showed accuracy of 10 km • ACE: 10 km, S-band DSN (26m,34m), 3.5 hrs/day, attitude reor every 4-14 days • WMAP: 2 km … S-band DSN (34m, 70m) 45 min/day, 14-72 day arc • WMAP benefited from excellent “knowledge” of solar pressure forces • JWST requirement is for 50 km position knowledge • JWST will be employing a sequential orbit determination method using a Kalman filter that allows the OD process to handle the frequent momentum unloading and stationkeeping maneuvers

15. Libration Point Orbit Accuracy (1 of 2) • AXSIO can expect a orbit position accuracy of 10 km (conservative) using the traditional methods of tracking • Does this work with respect to the AXSIO timing requirement? • An alternative to traditional OD methods would be to use Delta-Differential One-Way Range (DDOR) • VLBI measurement obtained by double differencing simultaneous observations of the spacecraft from two widely separated ground sites followed immediately by observations from an angularly nearby quasar • Used for Voyager, Galileo, & Magellan • Sample analysis for libration point orbiters shows improved accuracy ( 3 km) with decrease in tracking time (1 hour every 3 days, 2.5 hours per week) • Further analysis would be required

16. Issues & Concerns • Only concern is how full set of mission constraints could affect available launch opportunities • Will need to be monitored as design matures

17. AXSIO Deltas

18. Launch Dispersions • The latest dispersion data for Atlas V under the NLS-2 contract indicates that the advertised C3 dispersion for that vehicle has tripled • Previous value: C3 = ± 0.05 km2/s2 (3) [equates to ± 3 m/s at TTI] • New value: C3 = ± 0.15 km2/s2 (3) [equates to ± 7 m/s at TTI] • As a result, the DV budget for launch dispersions has increased (over AXSIO) from 20 m/s to 45 m/s

19. ΔV Budget • Mission DV budget • Launch Window 10 m/s(1) • ELV Dispersion Correction 45 m/s(2) • Mid-Course Corrections (2) 15 m/s(3) • L2 Stationkeeping (5 years) 20 m/s(4) • End of Life Disposal 1 m/s(5) • Total 91 m/s • Assumptions • Accounts for 30 minute finite daily launch window. Corrected along with launch dispersion, if necessary. • ELV Dispersion correction assumes Atlas-V dispersions corrected at TTI + 24 hours • Atlas-V ELV Dispersion: C3 ±0.15 km2/s2 (3) [equates to  ±7 m/s at TTI] • Accommodates a neutral “mid”-biased launch • Dispersion values were obtained from KSC ELV analysts • Two MCC maneuvers to correct for execution errors (5%) on ELV correction maneuver • Budgeting 4 m/s/year • Small maneuver to ensure that observatory leaves the Earth-Moon system

20. Eclipse Duration by Trajectory Phase for AXSIO Nominal Launch Date • A scan for no-eclipse constraint violations during all trajectory phases was conducted for June 15, 2022 (AXSIO) • Transfer and L2 eclipses occur in the middle to high range of coast times • The majority of no-eclipse constraint violations occur in the launch/coast phase • Most violations in the transfer and L2 phases occur for cases already violated at launch • Transfer and L2 eliminate one additional launch time for short coast durations Eclipse Duration (hrs) Eclipse Duration (hrs) Eclipse Duration (hrs) Eclipse Duration (hrs)