Solar Imaging Radio Array (SIRA) Trajectory and Formation Analysis Flight Dynamics Analysis Branch Code 595 (572) Dave

1. Solar Imaging Radio Array (SIRA) Trajectory and Formation Analysis Flight Dynamics Analysis Branch Code 595 (572) Dave Folta 6-6082 Bo Naasz 6-3819 Frank Vaughn 6-5551 January 30, 2003

2. Solar Imaging Radio Array (SIRA) Trajectory and Formation Analysis • Agenda • Mission Metrics • Orbit Trades • Formation Control • U-V Plane Stats • Summary

3. SIRA Metrics • Earth-constellation distance: • Greater than 50 Re (interference) • Less than 100 Re (link margin) • Minimize orbit insertion requirements • Avoid eclipses • 16 microsats on ~50 km diameter sphere (to achieve desired angular resolution) • Uniform distribution of u-v baselines density (spacecraft randomly positioned on surface of a sphere)  • Defunct satellites should not "interfere" excessively with operational satellites • Satellites "approximately" 3-axis stabilized 

4. SIRA Orbit Selection Trade • Reviewed orbits*: • Earth-Moon L4 Libration orbit • Earth Centered Distant Retrograde orbit (DRO) • Sun-Earth L1 Libration orbit • All orbit trades used high fidelity perturbation modeling and precision integrators • * A moon centered circular orbit at about 30,000km was also analyzed, but was eliminated due to the high insertion DV cost of over 1km/s.

5. Moon Earth Earth - Moon L4 Libration Orbit L4 Libration Point • Stable orbit in Earth - moon neighborhood • L4 location is at equal distances from Earth and moon • Requires insertion maneuver Earth Moon L2 L1 L4 SIRA Orbit Shown in Earth-Moon Rotating System

6. Earth - Moon L4 Libration Orbit

7. Lunar orbit Mission orbit Distant Retrograde Orbit (DRO) Orbit Sun-Earth L1 Libration Point Transfer orbit • Stable, heliocentric orbit with same period as Earth, and slightly altered eccentricity • Circular relative motion wrt Earth orbiting clockwise • Requires insertion maneuver • Dimensions ~ 1.7 x 2.0 Million km in ‘x’ and ‘y’ directions

8. Earth Distant Retrograde Orbit (DRO) Orbit

9. Transfer orbit Lunar orbit L1 Libration Point Mission orbit Sun-Earth L1 Libration Orbit • Standard libration orbit about the co-linear L1 point • (ISEE, SOHO, ACE) • Dimensions ~ 1.6 x 1.9 Million km in ‘x’ and ‘y’ directions

10. Sun-Earth L1 Libration Orbit

11. SIRA Orbit Selection Trade DRO Earth-Moon Lib Sun-Earth Lib Launch C3 Energy (km2/s2) -0.52 -1.8 -0.67 Mission Orbit Insertion DV (m/s) 444 700 ~10 Orbit Maintenance DV/year (m/s) 0 5 5 Formation Maintenance DV/year (m/s) S - 0.22 S –15.6 S – 0.63 per spacecraft L - 0.16 L – 8.28 L – 0.29 Strict (S) & Loose (L), Assuming 0.1mN Min / Max Distances to Earth (Re km) 266 to 313 39 to 78 188 to 266 Shadows None None None Angle variation between 360. 360. +/-37.0 Spacecraft-Earth and Spacecraft-Sun vectors over one orbit period (degrees)

12. Launch Vehicle Information • Corresponds to a DRO C3 of –0.5 km2/s2 • Mass to orbit ranges from 250 kg (Taurus) to 1510kg (Delta-II)

13. Launch Vehicle Information • Corresponds to a Earth-moon L4 orbit C3 of –1.8 km2/s2 • Mass to orbit ranges from 260 kg(Taurus) to 1585kg (Delta-II)

14. 3-D view SIRA spacecraft SIRA Formation Analysis • Apply control to maintain a 25km radius sphere • Center of sphere follows mission orbit • Simple PD controller to maintain spherical formation • Assumes shared knowledge of relative states • Constant low thrust control (0.1mN) • Allows strict and loose control efforts • Initial placement on sphere based on “igloo” placement from: • Robert Bauer's "Uniform Sampling of SO3" algorithm from 2001 Flight Mechanics Symposium"

15. SIRA Formation Control Analysis

16. SIRA Formation Control Analysis

17. SIRA Formation U-V Plane Analysis • Sample Earth/Moon L4 libration orbit formation • Spacecraft controlled to maintain only relative separations • Plots show statistic of U-V plane and relative formation positions

18. SIRA Trade Summary • Given mission metrics and assumptions, analysis shows feasibility of SIRA mission with a spherical formation • Orbit selection dependent upon mission metrics, launch mass capability, system engineering • Formation maintenance DV in general is not a driver DV/year ~ 0.16 to 15.6 (m/s) • Additional analysis required for maneuver type and system engineering aspects • U-V plane statistics provided for sphere shape formation

19. Backup

23. Solar Imaging Radio Array • Science Objectives: • Understand CME structure, propagation, and evolution from the Sun to 1 AU • Apply solar radio burst images to mapping of solar wind density structures and magnetic field topology, providing a unique tool for solar wind analysis • Enhance space weather prediction capabilities using radio images of CMEs • Observe and analyze the global response of Earth’s magnetosphere to CMEs and other space-weather-effective events from an external perspective • Image the low-frequency (< 30 MHz) radio universe at high angular resolution and catalog and understand the objects found therein • Mission Description: • Microsat constellation of 10 – 16 identical spacecraft • Crossed dipole antennas and low frequency radio receivers • Quasi-spherical constellation with <100 km diameter • Nearly circular distant retrograde orbit (~106 km from Earth) or other terrestrial radio interference limiting orbit • Individual microsat communication with ground stations • Measurement Strategies: • High spatial and temporal resolution • Frequency range from ~30 MHz to ~30 kHz • Frequency spacing and time resolution optimized for solar burst analysis • Rapid data processing for space weather prediction Two dimensional radio imaging of the CME-driven shock front and the CME density profile is critical for predicting the space weather effects of CMEs • Technology Requirements: • Intermicrosat ranging (to ~3 m) • “Full-sky” aperture synthesis mapping algorithm development • Onboard data cross-correlation desirable (for space weather snapshots)

24. SIRA Formation Control Analysis

25. SIRA Formation Control Analysis • Earth/Moon L4 Libration Orbit • Spacecraft controlled to maintain only relative separations • Plots show formation position and drift (sphere represent 25km radius) • Maneuver performed in most optimum direction based on controller ouput Impulsive Maneuver of 16th s/c Radial Distance from Center