Conor Benson, University of Colorado Boulder; Daniel Scheeres, University of Colorado Boulder; William Ryan, New Mexico Tech/MRO; Eileen Ryan, New Mexico Tech/MRO
Keywords: GEO debris, YORP effect, tumbling, light curves
Abstract:
With the growing value of GEO for communications and observation, understanding and predicting the motion of GEO debris becomes increasingly important. Defunct satellites constitute a large fraction of the GEO debris population. The orbital evolution of these satellites has been studied extensively, but little is known about their rotational dynamics. However, many defunct GEO satellites have evolving spin states. Albuja et al. show that the observed spin period evolution of several defunct GOES weather satellites can be explained by solar radiation torques generated through the Yarkovsky-OKeefe-Radzievskii-Paddack (YORP) effect [1]. YORP is known to alter the spin states of small asteroids [2,3]. Albuja et al. also hypothesize that YORP and kinetic energy dissipation from structural flexibility and residual fuel slosh may cause some satellites to cycle between uniform and complex rotation (i.e. non-principal axis tumbling). As a satellites uniform spin rate decreases due to YORP, it loses spin stability. At some small non-zero spin rate, YORP then preferentially spins up the long axis, the most easily accelerated by external torques. Such behavior was observed by Albuja et al. in dynamical simulations. During tumbling spin up, they predict that energy dissipation will eventually overpower YORP, driving the satellite back towards uniform rotation. We further explore this cyclic hypothesis by extracting rotation states from recent GOES light curves. Better knowledge of defunct satellite spin state evolution stands to improve attitude dependent SRP modeling for long-term orbit prediction and aid on-orbit debris mitigation and servicing efforts where rotation state information is crucial for grappling and docking.
The five defunct GOES 8-12 weather satellites are ideal for testing this cyclic evolution hypothesis. Nearly identical and sequentially retired between 2004 and 2013, their significant asymmetry and long appendages make these satellites highly susceptible to YORP torques and energy dissipation. In addition, their end of life mass distributions, geometry, and pre-launch material properties are well documented, greatly assisting light curve inversion and dynamical modeling. Consequently, these satellites have been observed periodically at the Maui Research and Technology Center, Naval Observatory Flagstaff Station (NOFS), as well as Magdalena Ridge and Lowell Observatories since 2013. GOES 8 is particularly intriguing, with its uniform spin period steadily increasing from 16.48 s to 75.66 s between February and July 2014 [4,5]. By September 2014, NOFS observations revealed a ~40 min spin period. Subsequent observations obtained from late 2014 early 2018 show continuously evolving, potentially complex rotation with spin periods of roughly 5-20 minutes.
To better understand GOES 8s ongoing evolution, plausible tumbling rotation states were extracted from each light curve. Assuming torque-free rigid body rotation over each 30 120 min light curve, two constant fundamental periods define the satellites motion. The first period corresponds to rotation of the satellites long (minimum inertia) axis about itself and the second to precession of this axis about the inertially fixed rotational angular momentum vector. To aid in analysis, ray traced simulated light curves were generated using a high fidelity GOES shape model and the physically-based Ashikhmin-Shirley microfacet BRDF. Simulated light curve surveys with inertially fixed lighting and viewing directions showed that the dominant light curve power spectrum frequencies are integer linear combinations of the two fundamental tumbling frequencies. For simulated light curves under realistic GEO observing conditions, the slowly varying phase angle and viewing geometry created slight differences between the true (sidereal) and observed (synodic) fundamental frequencies and sometimes introduced low frequency aliases. The simulated light curve surveys also showed that for the majority of anticipated (relatively relaxed) tumbling states, multiples of the long axis precession frequency dominated the power spectra, followed by other frequency combinations. Applying insights from the light curve surveys in combination with Fourier analysis, candidate fundamental period pairs were extracted from each observed light curve. Torque-free dynamical constraints and the satellites known moments of inertia were then leveraged to eliminate non-physical solutions. Finally, the candidate rotation states were compared to the observations using simulated light curves and Nelder-Mead simplex optimization to find the best-fitting solutions.
Following the well documented deceleration from February – July 2014, the best-fitting solutions trace out a path in which GOES 8s spin period continued to increase until early September 2014, reaching a maximum of at least 40 min. Subsequent observations exhibited complex rotation with the satellites long axis precession period appearing to decrease, reaching a minimum of ~10 min in mid-2016. From the second half of 2016 through late 2017, the satellite appeared to spin back down with a zero spin rate intercept near the end of 2017. The April 2018 observations strongly indicate complex rotation with a precession period of 5-10 min, suggesting significant spin up in early 2018. This proposed evolution outlines a roughly three year span between significant spin up/down transitions and suggests the satellite is currently spinning up again. The tumbling GOES 8 light curves seem to confirm Albuja et al.s first proposed phase of evolution, that YORP can drive satellites from uniform to complex rotation given sufficient deceleration. While there is no conclusive observational evidence that GOES 8 returned to uniform rotation during this three year span, it is definitely a possibility. A return in the near future is not ruled out either. Additional observations and dynamical modeling with YORP and energy dissipation are needed to better understand this proposed transition back towards uniform rotation.
[1] Albuja A. A., Scheeres, D. J., Cognion, R. L., Ryan, W., Ryan, E. V., The YORP effect on the GOES 8 and GOES 10 satellites: A case study, Advances in Space Research, Vol. 61, pp. 122-144, 2018.
[2] Rubincam, D., Radiative spin-up and spin-down of small asteroids, Icarus, Vol. 148, pp. 2-11, 2000.
[3] Lowry, S., et al., Direct detection of the asteroidal YORP effect, Science, Vol. 316, pp. 272-274, 2007.
[4] Cognion, R. L., Rotation rates of inactive satellites near geosynchronous earth orbit, Proceedings of AMOS 2014.
[5] Ryan, W. H., Ryan, E. V., Photometric Studies of Rapidly Spinning Decommissioned GEO Satellites, Proceedings of AMOS 2015.
Date of Conference: September 11-14, 2018
Track: Non-Resolved Object Characterization