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. 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  V cost of over 1km/s. SIRA Orbit Selection Trade

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

6. Earth - Moon L4 Libration Orbit

7. Distant Retrograde Orbit (DRO) Orbit Lunar orbit Mission orbit Transfer orbit Sun-Earth L1 Libration Point 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. Lunar orbit Mission orbit Transfer orbit L1 Libration Point 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 Sun-Earth L1 Libration Orbit

11. DROEarth-Moon LibSun-Earth Lib Launch C3 Energy (km 2 /s 2 )-0.52 -1.8-0.67 Mission Orbit Insertion  V (m/s)444 700~10 Orbit Maintenance  V/year (m/s) 0 55 Formation Maintenance  V/year (m/s) S - 0.22 S –15.6S – 0.63 per spacecraftL - 0.16 L – 8.28L – 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 NoneNone Angle variation between 360. 360. +/-37.0 Spacecraft-Earth and Spacecraft-Sun vectors over one orbit period (degrees) SIRA Orbit Selection Trade

12. Launch Vehicle Information Corresponds to a DRO C3 of –0.5 km 2 /s 2 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 km 2 /s 2 Mass to orbit ranges from 260 kg(Taurus) to 1585kg (Delta-II)

14. 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 SIRA Formation Analysis 3-D view SIRA spacecraft 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

17.  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 SIRA Formation U-V Plane Analysis

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  V in general is not a driver  V/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 Technology Requirements: Intermicrosat ranging (to ~3 m) “Full-sky” aperture synthesis mapping algorithm development Onboard data cross-correlation desirable (for space weather snapshots) 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 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 (~10 6 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

24. SIRA Formation Control Analysis

25.  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 16 th s/c Radial Distance from Center SIRA Formation Control Analysis