Sail-Assisted End-of-Life Disposal of High-LEO Satellites

Transcription

1 4th International Symposium on Solar Sailing Kyoto, Japan, January 17-20, 2017 Sail-Assisted End-of-Life Disposal of High-LEO Satellites Sergey Trofimov Keldysh Institute of Applied Mathematics Russian Academy of Sciences Stepan Tkachev, Dmitry Roldugin Keldysh Institute of Applied Mathematics Russian Academy of Sciences

2 Space Debris in Low-Earth Orbits Kessler syndrome: a cascade of collisions of debris objects For low-earth orbits, Kessler syndrome is likely to happen by mid-century Credit: C. Wiedemann 2/22

3 Atmospheric Drag or SRP Force? 3/22

4 Apparent Sun Motion and Desired Sailcraft Orientation in Orbital RF Similar to hyperbolic Likins-Pringle relative equilibrium 4/22

5 Sailcraft Model (Nominal) 3U CubeSat: 2U is for the sail and its deployment mechanism, 1U is for the subsystems and the payload Sailcraft is axisymmetric, with the center of mass being shifted from the center of pressure along the sail normal by distance d Sailcraft s ellipsoid of inertia is an oblate spheroid I kg m m 3 kg 2 A 25 m d 13 cm 5/22

6 Sources of axisymmetry violation Manufacture/assembly errors and the partial sail deployment The FEA analysis of several deployment scenarios shows that variations in principal moments of inertia can amount to 10%. Micrometeoroids impacts and quasi-static deformations For a year of flight in a 900-km orbit, non-critical collisions with further tear propagation lead to dynamical parameters changes up to 0.01%. Quasi-static effects for a fully deployed sail are of the same order. The essentially triaxial sailcraft tensor of inertia used below: I kg m /22

7 Environmental Torques 7/22

8 Existence of Sailcraft Relative Equilibria D. Lawrence, M. Whorton (2009): Assuming the sun vector is orthogonal to the orbit plane, there are three types of relative equilibria in the presence of the three environmental torques of equal magnitude. Hyperbolic-like equilibria exist if the spin rate (the angular velocity component along the sail s normal) is equal to coseq I sgncos I n 0 2 t 0 a s eq 8/22

9 General Illumination Conditions When no control applied, actual sailcraft rotation is chaotic due to the following: The sun vector cannot be orthogonal to the orbit plane (excluding discrete moments of time) For low-earth orbits, shadowing is an important factor almost half of the orbit can be in the Earth shadow Sailcraft orbit is not exactly circular and, besides, changes over time Effective potential behavior throughout the orbital period 9/22

10 Stabilization by Ideal Damping Torque The Lyapunov exponent analysis shows that a small damping torque is enough for any illumination conditions and solar activity level: 1 U 2 cos sin 0 2 It sin sin 20 cos 1 2 U U s U g U a It0cos 0cos Corresponding torque in BF frame axes: 1 I t U k d k d effective potential T T sin sin cos k I k I ω T sin cos sin d d t d t rel 10/22

11 Parametric Stability wrt Spin Rate 11/22

12 Sail Attitude and Orbital Altitude Evolution (18h SSO, Mean SA Level) One-week evolution k d rad/s 12/22

13 Effectiveness of Proposed Technique Compared to Other Deorbiting Modes 0 rad/s Ram-facing sailcraft attitude Uncontrolled sailcraft rotations rad/s Attitude regime Deorbit time, days Uncontrolled rotations 362 Ram-facing (velocity-pointing) attitude 215 Proposed regime, ω ζ = 0 rad/s 130 Proposed regime, ω ζ = 1.1*10-4 rad/s 92 13/22

14 Damping by CubeSat Magnetorquers (axisymmetric sailcraft model) One-week evolution 1 kd It Tm m B where m 2 Td n B n 2 n ωrel B n B B 14/22

15 Mixed Magnetic Damping Control If a sailcraft is not axisymmetric, the spin rate is no longer the first integral. The spin rate keeping control is then critical for stability. Two kinds of damping: Relative angular velocity damping m k ω B 1 m rel Differential spin rate damping ˆ 2 km m n B For a set of typical CubeSat magnetorquers m=0.1 Am 2 km Nms/T If combined, we have a mixed damping control: m ˆ m ˆ m 4 1 m2, 10 rad/s 4 1, 10 rad/s 15/22

16 Sail attitude evolution for 18h SSO 16/22

17 Relative angular velocity components and the spin rate for 18h SSO 4 ˆ 210 rad/s 17/22

18 Orbit altitude evolution for 18h SSO For comparison a) ideal damping, zero spin rate: T = 130 days b) ideal damping, spin rate 1.1*10-4 rad/s: T = 92 days 18/22

19 Euler angles evolution for 16h SSO 19/22

20 Relative angular velocity components and the spin rate for 16h SSO 4 ˆ 210 rad/s 20/22

21 Orbit altitude evolution for 16h SSO For comparison a) ideal damping, zero spin rate: T = 121 days b) ideal damping, spin rate 2.2*10-4 rad/s: T = 83 days 21/22

22 Conclusions The proposed technique ensures fast and efficient end-of-life disposal for spacecraft in the most polluted near-earth region low-earth orbits with altitudes >700 km The technique works for any types of orbit and any SA level Since the dominant SRP force is effectively used at the initial stage of deorbiting, the reduction in deorbit time amounts to 200% compared to the ram-facing deorbiting mode CubeSat magnetorquers are enough to produce a torque required for establishing/restoring the desired attitude Mixed magnetic damping control can effectively counteract the attitude disturbances due to the lack of axisymmetry 22/22

23 Acknowledgments Russian Foundation for Basic Research (RFBR) Grant mol_a Thank you for your attention

24 Space Sailing: First Steps Successfully accomplished missions: IKAROS (2010) flight to Venus S/c mass 310 kg (including 2 kg for the sail membrane) Sail area 200 m 2 Credit: NASA Credit: JAXA NanoSail-D2 (2011) testing of sailassisted deorbiting technology 3U CubeSat with a total mass of 4 kg Sail area 10 m 2, orbit altitude 640 km Deorbit time 240 days 24/33

25 Space Sailing: On the Verge of New Era Several missions with similar sailcraft: 3U CubeSat with a mass of 4-6 kg equipped with a 5mx5m square sail LightSail 1 (May 2015; Planetary Society) successful Orbit: 355 km x 700 km DeorbitSail (July 2015; Surrey Space Centre) failed Orbit: sun-synchronous, circular, 650 km LightSail 2 (September 2017; Planetary Society) scheduled Gossamer-1 (ESA, Surrey Space Centre) InflateSail (ESA, Surrey Space Centre) CubeSail (Surrey Space Centre, ESA) 25/33

26 Solar Pressure Force and Torque Absorption a 0.12 r 0.83 r 0.05 s Reflection specular diffuse d f f b b f b 2 F SRP PA s n rs f rd a rd a s n n s P N/m 6 2 T d n F 1 r PAd s n s n SRP SRP s solar pressure at a distance of 1 a.u. from the Sun 26/33

27 Equations of Sailcraft Attitude Motion 2 sin sin 2 cos 0 0 sin cos I I n t 0 0 the ratio of the axial and transverse moments of inertia xcos ysin p e u e u a rotation rate of the orbital RF the spin rate (axial component of absolute angular velocity) 1 I t U e u e u e u e u 2 1 cos sin cos sin 1 x y y x 1 I t U U U g U a U s the net potential function of external torques 27/33

28 Potentials of External Torques U I I 2 2 U U Ug U 2 g 2 gsin cos sin, gsin sin cos Ua g 2 g, e n sin 2 sin 2, 3 2 g X g 0 n t v a a 2 rel a, ey n ey n cos cos sin, a D 2 Ua a cos sin sin, a cos cos sin cos U s s cos coss sin sins cos s sin sins sin s C Ad 2 2 s s,, t s n s n cos cos sin sin cos s 0 s s s cos coss sin sins cos s, s s0 0, s 1 s t r PAd U s s cos coss sin sins cos s sin coss cos sinscos s 28/33

29 Sun-Synchronous Orbits Sun-synchronous orbits (SSOs) are illuminated at approximately constant level over time Due to the symmetry of motion equations, it is enough to consider several SSOs with a mean local time of the ascending node (MLTAN) from 12 h (the sun vector lies almost in the orbit plane) to 18 h (the sun vector is almost orthogonal to the orbit plane) The following 900-km SSOs are considered: LTAN= 12 h («noon-midnight») LTAN= 14 h LTAN= 16 h LTAN= 18 h («dusk-dawn») Credit: ESA 29/33

30 Numerical Study of Damped Rotations The coupled orbit-attitude sailcraft motion is studied by numerical simulation under the following assumptions: Among the perturbing forces, the Earth s oblateness (J2) and the drag are taken into account CIRA-2012 atmospheric density model is used. The cases of low, mean, and high solar activity (SA) are considered Cylindrical model of the Earth s shadow is used At initial moment of time, the sail s orientation corresponds to one of hyperbolic relative equilibria 30/33

31 SRP Force Efficiency as a Function of Average Nutation Angle 31/33

32 Sensitivity to Initial Conditions In all figures, one-week evolution of Euler angles is shown for a 16h SSO at mean solar activity level k d rad/s /33

33 Sensitivity to Sailcraft Parameters Nominal values rs 0.8 rs 0.73 In all figures, one-week evolution of Euler angles is shown for a 16h SSO at mean solar activity level k d rad/s d 15 sm 33/33