Attitude and Orbit Dynamics of High Area-to-Mass Ratio (HAMR) Objects and

Transcription

1 Attitude and Orbit Dynamics of High Area-to-Mass Ratio (HAMR) Objects and Carolin Früh National Research Council Postdoctoral Fellow, AFRL,

2 Orbital Evolution of Space Debris Objects Main orbit perturbation Luni-Solar precession of the orbital plane Progression of RA of ascending node: for GEO approx: Variation of Inclination ±15 degrees with period of 53 years. Stable eccentricity (without drag).

3 Detection of HAMR Objects Detection by Schildknecht (2004): Orbits could only be fit estimating a high area-tomass ratio (HAMR)!

4 HAMR materials Candidates for those objects are multilayer insulation (MLI) materials, used as insulation and shielding materials for space crafts, which shed off over time. Insulated propellant tank This is consistent with the estimated AMR values and also in agreement with spectral measurements (except reddening). Fermi-Bus

5 Standard Method Canon ball model assumption: Allows to neglect attitude motion Avoids 6 DoF modeling.

6 Long-term Simulations HAMR HAMR objects in near geostationary 1 m 2 orbits /kg show significantly different orbital element evolution than low area-to-mass ratio objects. Inclination rises higher values than 15 degrees with a period of significantly less than 52 years Eccentricity shows changes with a period of one nodal year. 20 m 2 /kg Orbits are highly perturbed by non-conservative forces. Direct radiation pressure is the strongest of those forces. Liou, 2005, simulation under assumption of a stable AMR value

7 Obs: AMR Variations E06321D E07194A E07308B E06293A using observations ZIMLAT, ESASDT, ISON

8 Obs: AMR Variations E07308B E06293A E06321D The values, which do not follow a general trend E07194A not always large uncertainties in AMR value. not always large differences between propagated ephemerides to further observations. using observations ZIMLAT, ESASDT, ISON

9 Orbit and Attitude Propagation Orbit and attitude propagation as a fully coupled system. Orbit: Attitude: Coupled via perturbing terms, changing attitude, which changes the direct radiation pressure force influencing the orbit: Gravitational Torque:

10 Orbit and Attitude Propagation Orbital perturbations: Earth Gravity field order/degree 6, Sun, Moon Direct radiation pressure Attitude Perturbations: Earth gravity field, first order Direct radiation pressure

11 3. Simulation of HAMR object dynamics Simulation of uniform flat-plate object PET Simulation of non-uniform objects skap, rkap Simulation of tilted objects, with selfshadowing

12 Simulation Setup: Orbit All objects have the same initial orbital elements and attitude parameters at start epoch: a = km Φ = 24.4 deg e = Ψ = 53.8 deg i = 40.0 deg RAAN = 60.0 deg arg. of per. = 9.0 deg M = deg Θ = deg ω = [0.0,0.0,0.0] T PET m 2 /kg

13 Inclination and Eccentricity: PET Eccentricity and inclinations show typical HAMR variations. Different values for ball and plate model.

14 Inclination and Eccentricity: PET Differences in eccentricity and inclination of stable plate and plate with free attitude motion. Different values for stable plate and plate with attitude motion even for uniform reflection.

15 Euler Angles and Torque: PET Different values for stable plate and plate with attitude motion even for uniform reflection.

16 Modelling of shadow passes s1: cylinder model: s2: dual cone model (Baker): s3: superposition of dual cones (Hujsak):

17 At shadow passes: F_p Torques

18 At shadow passes: F_p Torques Simple cylinder model does not pick up any torque (not physically realistic).

19 At shadow pass: Euler Angles using s1 s3-s2 using s2 Simple cylinder model s1 nearly identical to nonshadow case, differences between s2 and s3 are small.

20 Inclination and Eccentricity: PET Relative Eccentricity Relative Inclination Up to state differences of 1km per pass between s1 and the dual cone models.

21 3b. Modeling of objects skap and rkap with non-uniform reflection properties. skap 26.3 m 2 /kg rkap 19.7 m 2 /kg

22 Inclination, Eccentricity: skap rkap Eccentricity Inclination Different values for ball and plate model.ee

23 Object skap: Euler Angles Euler angles relative to initial values. Rapid attitude motion. Beat period of ~ 5h.

24 Object skap: Angular Velocity Initial angular velocity equal to zero. Rapid attitude motion. Beat period of ~ 5h.

25 Object rkap: Euler Angles Euler angles relative to initial values. Rapid attitude motion. Beat period of ~ 12h.

26 skap and rkap: an illustration Normal vector: coverage in four days

27 skap and rkap: an illustration Normal vector: coverage in four days

28 Self-Shadowing Object geometry: convex concave

29 Self-Shadowing Probability Different probability of different points:

30 Shadow Map Allows for an efficient shadow calculation Is also an average model for self-shadowing of controlled and uncontrolled objects.

31 Self-Shadow: Orbital Elements

32 Self-Shadowing: Ang. Velocity Simulations neglecting self-shadowing and averaged simulations have slower rotation rates.

33 Angular Coverage

34 Conclusions HAMR objects are very sensitive to perturbations and careful modeling is necessary Even uniform objects drift in attitude Objects do not simply spin up or end up in a uniform tumbling Self-shadowing cannot be neglected, but shadow-map can save computational time. Expansions to low Earth orbits, i.a. drag Improvements to understand nonuniformities better.

35 Thank you for your attention. Questions? Fragen? Vragen?

36 Simulation of Measurements One meter Zimmerwald Laser and Astrometry Telescope (ZIMLAT) Light curve measurements using subframe technique, sampling rates ~3 seconds Absolute magnitude errors: Mapping Series at the beginning of each light curve to determine (Tycho, USNO 2B) Relative magnitude errors: SNR source relative to background. Using Welch s and Periodiogram method, and Fourier transformation to extract periods

37 HAMR object E07337C measured simulated Simulation is smoother and covers a larger magnitude interval. Large magnitudes may be above sensor capabilities.

38 HAMR object E07047A measured simulated Simulation is smoother and covers a larger magnitude interval. Measured peak values occur regularly in the simulated light curve.

39 HAMR object E07047A measured simulated Simulation covers a larger magnitude interval. No grouping of values around 15.2 magnitudes appears in the simulation.

40 HAMR object E07047A measured simulated Simulation covers a slightly larger magnitude interval. No grouping of values around 15.6 magnitudes appears in the simulation.

41 Conclusions Attitude and orbital motion of HAMR objects is coupled via direct radiation pressure. Even objects with uniform reflection properties drift in attitude. Shadow passes alter attitude significantly and have therefore double effect on orbit. Objects with non-uniform reflection properties and/or offset in the center of mass end up in a very rapid but swaying attitude motion. Canon ball model has proven to be not a good approximation in either of the cases. Comparison with measurements without taking a physical motor for rapid attitude motion into account is not fully successful.

42 3c. Simulated light curves PET, KAP, skap, rkap Definition light curve: reflected brightness over time in the direction of an observer.

43 Simulations: Reflections Apparent magnitude: is a shape dependent function. Including Lambertian and specular reflection: Flat plate:

44 Simulated Light Curves: Uniform Difference in attitude by shadow passes are hardly detectable.

45 Simulated Light Curves: skap 12h structure visible.

46 Simulated Light Curves: rkap Double 12h structure visible.

47 Sensor Model Magnitude errors are determined via signal-tonoise ratio: The flux of the object (background sources) is determined: Count: Signal:

48 Sensor Model For the visibility the following constraints applied: Object above local horizon Civil twilight condition 10 degree halo of a full moon, linearly decreasing with the moon phases Sensor was simulated: One meter aparature Atmospheric extinction coefficient 0.25 Averaging with mean bandwidths 600nm

49 Simulated Light Curves: Uniform Sensor located in central Europe. Only canon-ball object is visible in this setup, cosine structure washed out. Long dark times of other objects makes them invisible.

50 Simulated Light Curves: skap 12h structure is not detectable any more.

51 Simulated Light Curves: rkap 12h structure is not detectable any more.

52 4. Modeling of light curves and comparison to measurements: brightness variations over time as observed by a sensor: Note: Object were simulated as having uniform reflection properties: Thus the physical motor for a rapid attitude motion is missing!

53 Outlook Non-rigid body assumption Self-shadowing, thermal reflection Enhanced integration Shape inversion, rotation axis determination for comparison with measurements

54 Thank you for your attention!