Solar Imaging Radio Array (SIRA)

Trajectory and Formation Analysis

Flight Dynamics Analysis BranchCode 595 (572)

Dave Folta 6-6082 Bo Naasz 6-3819

Frank Vaughn 6-5551

January 30, 2003

Solar Imaging Radio Array (SIRA)Trajectory and Formation Analysis

Agenda

Mission Metrics Orbit Trades Formation Control U-V Plane Stats Summary

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 

• 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

Earth - Moon L4 Libration Orbit• Stable orbit in Earth - moon neighborhood• L4 location is at equal distances from Earth and moon• Requires insertion maneuver

L1L2

L4

EarthMoon

Shown in Earth-Moon Rotating System

SIRA Orbit

EarthMoon

L4 Libration Point

Earth - Moon L4 Libration Orbit

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

Earth Distant Retrograde Orbit (DRO) Orbit

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

Sun-Earth L1 Libration Orbit

  DRO Earth-Moon Lib Sun-Earth Lib

Launch C3 Energy (km2/s2) -0.52 -1.8 -0.67

Mission Orbit Insertion V (m/s) 444 700 ~10

Orbit Maintenance V/year (m/s) 0 5 5

Formation Maintenance V/year (m/s) S - 0.22 S –15.6 S – 0.63 per spacecraft L - 0.16 L – 8.28 L – 0.29Strict (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. +/-37.0Spacecraft-Earth and Spacecraft-Sun vectors over one orbit period (degrees)

SIRA Orbit Selection Trade

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)

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)

• 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"

SIRA Formation Control Analysis

SIRA Formation Control 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

SIRA Formation U-V Plane Analysis

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

Backup

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 (~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

SIRA Formation Control Analysis

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

FreeFlyer Plot Window4/30/2003

Km/s

A1.ElapsedDays (Days)

ImpulsiveBurn.X-Component (Km/s) ImpulsiveBurn.Y-Component (Km/s)

ImpulsiveBurn.Z-Component (Km/s)

0

5

10

15

20

25

0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175

FreeFlyer Plot Window4/30/2003

Km

A1.ElapsedDays (Days)

Formation.Range (Km) Formation.Range (Km) Formation.Range (Km) Formation.Range (Km)

Formation.Range (Km) Formation.Range (Km) Formation.Range (Km)

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

SIRA Formation Control Analysis