# Presentation: 831226

## External Occulter Trajectory Study

**Martin Lo**
**TPF Coronagraph Subsystem**
**29 September 2006**

## Agenda

**Background**
**Trajectory Options**
**Assumptions**
**Study 1: 50 Random Stars**
**Study 2: 100 Random Stars**
**Study 3: Simulation of 40 TPF Star Observation Sequence**
**Conclusions**
**References**
**Acknowledgements**
**JPL Engineering Support: Fernando Tolivar**
**NGST Technical Discussions: Jon Arenberg, Amy Lo, Richard Malmstrom**
**JPL Supercomputer Project : Chris Cathersoo, Dirk Runge**
**Temporary License for Matlab Distributed Computing Toolbox: Brian Lallensack**

## Background

**TPF Architecture Study Considered Occulters for Planet Finding**
**TRW Study: Starkman’s Concept, Precursor Mission with JWST**
- Identified Two Tall Tent Poles: Orbital Dynamics, Occulter Fabrication
**Ball Aerospace Study [2000]**
***CONCLUSION THEN*****: *****OCCULTER***** *****OPTICS NOT READY***
**W. Cash, Nature [7/2/2006] Showed *****TECNOLOGY NOW READY***
**Solved Apodization Problem**
**Mentioned Again Occulter Mission with JWST as Telescope**
**TPF Project Taking a New Look at Occulter Concept **
**This Talk Addresses Orbital Dynamics Issues Only**

## Assumptions for Study

**Two Free Flying Spacecraft: Telescope & Occulter**
**Separation 10,000 to 50,000 km**
**Observation Duration 24 Hours / Star**
**Orbits in Sun-Earth/Moon Restricted Three Body Problem **
** ********=3.04042e-06**
**~JWST L****2**** Lissajous Orbit (187,000 ****x**** 750,000 km Az, Ay Amplitudes)**
**Earth Leading Orbit**
**Model Adequate to Size Hydrazine Propulsion & Show Feasibility**
**Study 1: Monte Carlo Analysis Observing 50 Random Stars**
**Study 2: Monte Carlo Analysis Observing 100 Random Stars**
**Study 3: Simulation for Observing 40 Stars from TPF List**

## Observation Geometry Assumptions

**Telescope Always Sun-Pointed**
**Using JWST as Model (Gardner et al. 2006)**
**SKM (Station Keeping Maneuver) Every 22 Days**
**Area: 19.4 x 16.4 [m^2]**
**Occulter Always 90****°**** to Sun-Occulter-Line**
**Area: 25 m Radius Circle (W. Case 2006)**
**Assume No SRP**
**Telescope FOV 15****°**** from **
**	****Plane ******** Sun-Telescope Line**
**Retargeting Angle:**
**	******** ****15****°****  Study 1**
**	****= 15****°****  Study 2**
**	******** ****30****°****  Study 3**

## L2 Halo Orbit (Rotating Coord)

## Earth Leading Heliocentric Orbit

## L2 Orbits for Occulter & Telescope

## Typical Halo Orbit Mission V

- Study 1 Assumptions
- 50 Repointings Between Random Stars 15° Apart
- Except Case 50,000a*, random angle between stars  15°
- Fixed 20 Days Retargeting
- 1 Day Observation
- 3Year Mission

| Occulter Separation | V |
| --- | --- |
| 50,000 km | 1629.4 m/s |
| 50,000a km | 1517.2 m/s |
| 25,000 km |  816.2 m/s |
| 10,000 km |  309.0 m/s |

## Random Stars 

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Mean Retargeting V in Halo Orbit

**Total ********V ****=**** ********V1**** ****+**** ********V2**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Mean Retarget V in Halo Orbit

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## 1 Day Observation V in Halo Orbit

**Occulter Observation ********V [m/s] ****50,000 km Separation **

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Observation Thrust Accel. Profile

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Gravity ~ 10 x Thrust in Halo Orbit 

**GRAVITY  ~ 0.1 mm/sec****2**

**THRUST ~ 0.01 mm/sec****2**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Assumptions for Study 2: 100 Random Stars

**Two Free Flying Spacecraft: Telescope & Occulter**
**Separation 25,000 & 50,000 km**
**Observation Duration 24 Hours / Star**
**Orbits in Sun-Earth/Moon Restricted Three Body Problem**
**Near JWST L****2**** Lissajous Orbit (187,000 ****x**** 750,000 km Az, Ay Amplitudes)**
**Earth Leading Orbit**
**Model Adequate to Size Hydrazine Propulsion & Show Feasibility**
**Averaged Over Halo Orbit Phase and Sun-Earth Phase**
**100 Random Stars**
**Retarageting Angle ******** 15****°**
**In Hemisphere 90****°**** Away from Sun**
**Optimized Retargeting Time**

## V More Expensive in Halo Orbits

**Observation ********V 6 ****x**** More Expensive in L****2**** Orbit Than Heliocentric Orbit**
**Repointing ********V 2.6 ****x**** More Expensive in L****2**** Orbit **
**Optimum Transfer Time: 30 to 40 Days in Heliocentric Orbit**
**                                             ****10 to 15 Days in L****2**** Orbit**
**Coasting**

| Observation V (1 Day) | 50,000 km Separation | 25,000 km Separation |
| --- | --- | --- |
| L2 Orbit | 1.2 m/s | 0.6 m/s |
| Helio. Orbit | 0.2 m/s | 0.1 m/s |
| Repointing DV |  |  |
| L2 Orbit | 19 m/s | 9.5 m/s |
| Helio. Orbit | 7.1 m/s | 3.6 m/s |

## V Budget

**Assuming Observation 100 Random Stars Once**

| OBSERVATION V | 50,000 km SEPARATION | 25,000 km SEPARATION |
| --- | --- | --- |
| L2 Orbit | 120 m/s | 60 m/s |
| Helio. Orbit |   20 m/s | 10 m/s |
| REPOINTING V |  |  |
| L2 Orbit | 1900 m/s | 950 m/s |
| Helio. Orbit |   710 m/s | 360 m/s |
| TOTAL V |  |  |
| L2 Orbit | 2020 m/s | 1010 m/s |
| Helio. Orbit | 730 m/s | 370 m/s |

## Mass Budget

**Assume 3000 kg Dry Spacecraft Without Propulsion**
**Add Hydrazine System**
**Need to Add Low Thrust System for Observation Control for More Accurate Estimates**
**Current Estimate Sufficient for Feasibility Study**

| Final Wet Mass | 50,000 km Separation | 25,000 km Separation |
| --- | --- | --- |
| L2 Orbit |   14330 kg |    5887 kg |
| Helio. Orbit |     4819 kg |    3788 kg |

## Mission Duration

**Transfer: 90 Days for L2 Orbit, 30 Days for Helio. Orbit**

- 4 Years
- 10 Years

| OBSERVATION DURATION | 50,000 km SEPARATION | 25,000 km SEPARATION |
| --- | --- | --- |
| L2 Orbit | 100 Days | 100 Days |
| Helio. Orbit | 100 Days | 100 Days |
| REPOINTING |  |  |
| L2 Orbit | 1250 Days | 1250 Days |
| Helio. Orbit | 3500 Days | 3500 Days |
| TOTAL |  |  |
| L2 Orbit | 1440 Days | 1440 Days |
| Helio. Orbit | 3630 Days | 3630 Days |

## Assumptions for Study 3: 40 TPF Star Simulations

**Two Free Flying Spacecraft: Telescope & Occulter**
**Separation 50,000 km**
**Observation Duration 24 Hours / Star**
**Retarageting: 3 weeks, 6 weeks depending on the star**
**Earth Leading Orbit in Sun-Earth/Moon Restricted Three Body Problem**
**40 TPF Star Simulation Sequence: Shaklan & Hunyadi**
**Stars ≥ 75° Away from Sun**
**Retargeting Angle ******** 30****°**
**Case 1: Partial Optimization**
**Fixed Retargeting Time (********T****R****) of 3 or 6 Weeks Depending on Star**
**Case 2: More Optimization**
**Variable Retargeting Time (********T****R****) With Upper Bound of 3 or 6 Weeks Depending on Star**

## Performance in Earth Leading Orbit (Fixed TR)

**Total ********V = 1095.7 m/s**
**Spacecraft Mass [kg]:**

| DRY | RCS | FUEL | WET |
| --- | --- | --- | --- |
| 1000 | 1092 | 863 | 2092 |
| 2000 | 2184 | 1726 | 4184 |
| 3000 | 3275 | 2589 | 6275 |
| 4000 | 4367 | 3452 | 8367 |
| 5000 | 5459 | 4315 | 10459 |

## Performance in Earth Leading Orbit (Variable TR)

**Total ********V = 758.9 m/s**
**Spacecraft Mass [kg]:**

| DRY | RCS | FUEL | WET |
| --- | --- | --- | --- |
| 1000 | 639 | 506 | 1639 |
| 2000 | 1279 | 1011 | 3279 |
| 3000 | 1917 | 1516 | 4917 |
| 4000 | 2557 | 2021 | 6557 |
| 5000 | 3196 | 2526 | 8196 |

## Conclusions

**An Occulter Mission Seems Feasible for Heliocentric Orbits, But Not for *****LARGE***** L****2**** Orbits (750,000 km Y-Amplitude)**
**Occulter with JWST **
**Suitable For Finding Jupiter Planets ( ******** 25,000 km separation)**
**Not Suitable For Finding *****TERRESTRIAL***** Planets Due to Large ********V Requirements ( ≥ 50,000 km separation)**
**Occulter Concept for a TPF Mission Is Feasible from Mission Design Point of View in Heliocentric Orbit**
**NGST NWO Study Shows Smaller Halos Orbits Work  with SEP**
**For Y-Amplitude ******** 600,000 km**
**Occulter Must Be Controlled During Observation**
**Uncontrolled Drift in 1 Day**
- ~ 0.1 km in heliocentric orbit
- ~10 km in halo orbit

## Technical Points

**Observation ********V Computed Using Simple Inverse Dynamics**
**Control Issue Needs To Be Addressed**
**Uncontrolled Observation With Start/Stop Maneuvers Drifts Too Far from Observation Orbit**
**Hundreds of meters in Heliocentric Orbit**
**~10 km in L****2**** Orbit**
**Multiple Maneuvers For Retargeting Do Not Reduce the ********V**

## References

- Cash, W., Detection of Earth-like planets around nearby stars using a petal-shaped occulter, Nature Vol 442, 6 July 2006.
- Vanderbei, R. et al., Circularly symmetric apodization via star-shaped masks, Astrophysics Journal, 599, 2003.
- Starkman, G., *Occulter*, TRW	Space & Electronics Group, date?
- TRW TPF Architectural Phase 1 Study, Phase 2 Final Report, date?
- Ball Aerospace, TPF Architectural Study Final Report, March 29, 2002.
- Gardner, J., J. Mather, et al., *The James Webb Space Telescope*, Space Sciences Reviews (in press 2006)