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Deployment Optimization for Various Gravitational Wave Missions

Deployment Optimization for Various Gravitational Wave Missions. An-Ming Wu (amwu@nspo.narl.org.tw) National Space Organization, Hsinchu City, Taiwan Wei-Tou Ni (weitou@gmail.com) National Tsing Hua University, Hsinchu City, Taiwan Gang Wang (gwanggw@gmail.com)

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Deployment Optimization for Various Gravitational Wave Missions

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  1. Deployment Optimization forVarious Gravitational Wave Missions An-Ming Wu (amwu@nspo.narl.org.tw) National Space Organization, Hsinchu City, Taiwan Wei-Tou Ni (weitou@gmail.com) National Tsing Hua University, Hsinchu City, Taiwan Gang Wang (gwanggw@gmail.com) Gran Sasso Science Institute (INFN), L’Aquila, Italy 2017.5.23

  2. Outline • Introduction • Deployment of ASTROD-GW Formation • Deployment of LISA Formation • Conclusion

  3. Introduction • Space Gravitational Wave (GW) mission proposals often use constellation or formation of Earthlike orbits around the Sun. • LISA has three spacecraft in a nearly equilateral triangle formation with 2.5 Mkm arms, inclined with respect to the ecliptic by 60˚, and trailing Earth by 20˚. • TAIJI is proposed to have 3 Mkm arm-length LISA-like orbits. • ASTROD-GW has 3 spacecraft near Lagrange points with arm length about 260 Mkm. • Since the formation deployment is related to the spacecraft mass and trransfer time, it is critical for the mission cost.

  4. ASTROD-GW Orbit Configurationwith Inclination

  5. ASTROD-GW Mission Orbit Parameters

  6. Delta-Vsto escape from GEO and to enter mission orbit

  7. Spacecraft 1 d ai Reference Object ae Spacecraft 2 60 Spacecraft 3 LISA-Like Formations

  8. Orbit Parameters of LISA-Like FormationArmlength = 6 Mkm

  9. Orbit Maneuvers • Eccentricity change at periapsis or apoapsis • Inclination change at the ascending or descending nodes • Combination of changes at nodes • Escape from Earth and along the track

  10. Compact Finite-Difference Method for Orbit Equation • LHS • Acceleration • Compact Finite Differencing • Accurate with 4th Order • RHS • Forces • Implicit Newton Method • Robust with Incresing Diagonal Dominance

  11. Transfer Orbitsof 3 LISA-like Spacecraft from LEO to Mission Orbits with Transfer Time of 180 day

  12. Delta-Vsfor LISA-like spacecraft with arm length of 6 Mkm

  13. Mean Delta-Vs

  14. New LISA Mission • LISA is proposed to be launched around 2028-30 with transfer time of 400 day to arrive mission orbits. • Assume that LISA will be launched on 2030.12.18.

  15. LISA Animation

  16. LISA Animation

  17. LISA Animation

  18. LISA Formation

  19. SC1 Deployment Initial Earth Final SC1 Initial SC1 Middle of Ascending and Final Descending Ascending Middle of Initial and Ascending Periapsis

  20. SC2 Deployment Initial Earth Final SC1 Initial SC1 Middle of Initial and Ascending Ascending Periapsis Descending Middle of Ascending and Final

  21. SC3 Deployment Descending Initial Earth Final SC1 Initial SC1 Periapsis Middle of Initial and Ascending Middle of Ascending and Final Ascending

  22. Delta-Vs in LISA Proposal Transfer Time = 400 day

  23. Delta-Vs of Presented Calculation

  24. Conclusion • We use a stable 4th-order compact finite-difference method to calculate the delta-Vs for the deployment of various LISA-like formations for fixed travel time transfer from LEO. • For quick deployment, the delta-Vs of three spacecraft are different, the mean delta-V is nearly constant for different configurations of the formation, and linearly related to the arm length. • To minimize delta-Vs, the orbit maneuver for combination of eccentricity and inclination is studied.

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