X-ray Wide Field Imager

X-ray Wide Field Imager Flight Dynamics Frank Vaughn 16 – 20 April, 2012

Subsystem Block Diagram 800,000 km Y-amplitude L2 Orbit w/ 180 day period L2 Maximum Earth-Sun angle: 28º (for 800,000 km Y-amplitude) Lunar Orbit L2 Transfer Trajectory E Earth- L2 Distance 1.5 x 106 km Max Range 1.8 x 106 km To Sun Courtesy - JWST

Subsystem Summary (1 of 2) • Direct launch on Atlas V-411 to Sun-Earth L2 • Nominal Launch Date: January 1, 2021 • L2 Orbit Y-amplitude ≥ 800,000 km • Mission Lifetime: 3 years required, 5 years desired • No eclipse requirement from launch to end-of-life • The DV budget is 91 m/s • 20 m/s for stationkeeping at L2 for 5 years (4 m/s per year) • 1 m/s for end-of-life disposal • The remainder is allocated to trajectory corrections related to launch uncertainties • Stationkeeping maneuvers required approximately every 3 months • Nominally at every L2 X-Z plane crossing (near Sun line) • Spacecraft thruster complement can maneuver in Sun, anti-Sun directions at the nominal Sun-pointing attitude • Frequency of stationkeeping maneuvers could increase if frequent momentum unloads are required • OD accuracy requirements • Timing requirement of ≤ 1 ms equates to range error of ≤ 150 km • The timing error budget OD allocation is currently unknown

Subsystem Summary (2 of 2) • The trajectory design for this study is identical to that developed for AXSIO by Michael Mesarch of Code 595 • More information is needed to determine if the 21-day tracking arc carried over from the AXSIO study could be reduced • It is unknown if the 21-day OD tracking arc is sufficient to meet the AXSIO requirement. If it was, then, given the reduction in timing accuracy (1 ms) from AXSIO (100 ms), it is likely that the length of the tracking arc could be reduced. • The portion of the error budget allocated to range knowledge is required to make a determination. • Reducing the length of the tracking arc could also have a negative effect on the stationkeeping DV budget

Mission Requirements • Launched by Atlas V-411 on a direct transfer to a Sun-Earth L2 orbit • Launch Date: January 1, 2021 • Lifetime: 3 years required, 5 years desired • 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-S/C angle (i.e. angle off of Sun-line) • 800,000 km Y-amplitude equates to 28° (similar to JWST) • Requirements (AXSIO) reference a 34° angle – equates to 1,000,000 km Y-amplitude • The Y-amplitude/angle constraint will have an impact on launch opportunities • All geometries cannot be reached on all launch days • No eclipses (from Earth or Moon) are allowed during entire mission • Requirement for no eclipse during launch phase limits the launch vehicle coast duration and will limit the available launch opportunities • Requirement for no eclipse during mission phase also limits available launch opportunities. Initial Y- and Z-amplitude and phasing of Lissajous orbits must be selected to avoid eclipses at L2

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

Spacecraft 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,  = 28° • Y = 900,000 km,  = 31° • Y = 1,000,000 km,  = 34° • 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

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 large solution space for L2 missions • No eclipse constraint during launch considerably reduces solution space by limiting the Coast duration Launch Coast Sun TTI To L2

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

Eclipse Duration by Trajectory Phase for Gratings Nominal Launch Date • A scan for no-eclipse constraint violations during all trajectory phases was conducted for June 11, 2021 (Gratings) • The majority of no-eclipse constraint violations occur in the launch/coast phase • Transfer and L2 eclipses occur in the upper range of coast times • Most violations in the transfer and L2 phases occur for cases already violated at launch • Transfer and L2 eliminate three additional launch times for short coast durations Eclipse Duration (hrs) Eclipse Duration (hrs) Eclipse Duration (hrs) Eclipse Duration (hrs)

Eclipse Duration by Trajectory Phase for WFI Nominal Launch Date • A scan for no-eclipse constraint violations during all trajectory phases was conducted for January 1, 2021 (WFI) • This run was shorter than the Gratings run due to time constraints • Transfer and L2 eclipses occur in the lower to middle 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)

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

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

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

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)

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) • Thruster complement allows for thrusting 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

Stationkeeping at L2 • The DV for stationkeeping at L2 is 4 m/s per year • The stationkeeping frequency is highly dependent on the frequency of 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 • X-Ray WFI falls somewhere in between • More frequent than WMAP since it is off-pointing to targets • Less frequent than JWST since it can thrust in Sun and anti-Sun directions and Cp-Cg offset is being “minimized” by design • Careful management of spacecraft Cp-Cg offset will help to reduce the momentum buildup and reduce the frequency of stationkeeping maneuvers • All signs point to stationkeeping maneuvers approximately every 3 months • This will need to be monitored as the design matures

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 from the NLS-1 contract • 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

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

Open Items & Future Work • How does the full set of mission constraints affect launch opportunities? • Analysis for AXSIO characterized the limiting effect of the no eclipse constraint during the launch phase on acceptable launch, coast, and injection time combinations • Other constraints must be layered on to determine their combined effect on launch opportunities • Preliminary analysis of no eclipse constraint violation during the transfer and L2 phases indicate that very few additional violation cases are added to those that occur during the launch and coast phases • Requirements for coverage of critical launch events (e.g., TTI) and Moon avoidance on the outbound trajectory could possibly eliminate additional launch opportunities • Will need to be monitored as design matures • What is the driving requirement for range knowledge? • Affects tracking/OD requirements • Could place constraints on the frequency of momentum unloads and stationkeeping maneuvers • Relaxed OD accuracy and frequent momentum unloads could result in an increase in stationkeepingDV

Backup

Libration Point Orbit Accuracy (1 of 3) • 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 • X-Ray WFI tracking and OD requirements will depend on: • What portion of the timing error budget is allocated to range knowledge • Frequency of momentum unloads and stationkeeping maneuvers • A relaxed timing requirement (1 ms) compared to AXSIO (100 ms) suggests that the 21-day tracking arc presumed for AXSIO could be reduced • It is unknown if the 21-day tracking data arc is sufficient to meet the AXSIO requirement • If the entire timing error budget was allocated to range knowledge, then the range knowledge would have to be ≤ 150 km • Detailed analysis would be required to determine how much reduction could be tolerated, as relaxed OD requirements would also tend to increase the stationkeepingDV

Libration Point Orbit Accuracy (2 of 3) • Orbit position accuracy of 6-10 km (conservative) can be expected using the traditional methods of tracking • Does this work with respect to the timing requirement of 1 ms? • 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

Libration Point Orbit Accuracy (3 of 3) • The question of reducing the 21-day OD tracking arc was put to knowledgeable navigation analysts in the Navigation and Mission Design branch. The following comments are from Greg Marr and Mark Beckman of Code 595: • Greg Marr • Relaxing the 21-day uninterrupted tracking data arc between thrust perturbations is not unheard of, but it can result in significant challenges for OD • A 150 km OD requirement is a loose requirement, even for a librationpoint mission • Based on prior analysis of Triana and other librationpoint missions, with an approximate 21-day tracking data arc and a reasonable tracking schedule, the position errors would be approximately 6 km. Adding thrust perturbations over the arc and decreasing the tracking schedule will increase the errors. The 21-day tracking data arc is typical because of the poor dynamics of these orbits. • The degradation of OD accuracy as a result of thrust perturbations will probably have far more effect on the increase in stationkeepingDV than the thrust perturbations themselves. It is very important to be able to measure the thrust perturbations as accurately as possible to include those perturbations in the OD solutions if necessary. • Mark Beckman • 150 km is not accurate enough for stationkeeping. Even with sparse tracking, say every 3 days or so, you'll get less than 20 km accuracy anyway. • Reducing the tracking data arc to less than 21 days is possible, but you cannot predict that solution long, which means you'll have to do more frequent stationkeeping. The stationkeepingDVwill go up because you are bouncing around a wide deadband. Frequent momentum unloads can be handled with a sequential filter with a 21-day tracking data arc. But frequent momentum unloads will also drive up stationkeepingDV costs.

X-ray Wide Field Imager