Lord of the (sub-)Rings : Mapping the surface reflectance and spin-axis of Ajisai

TL;DR

This work demonstrates that high-cadence streak photometry from modest ground-based hardware can recover the spin-state of fast-spinning, non-cooperative LEO objects like Ajisai by mapping surface reflectivity in the body-fixed frame and aligning it to known mirror positions via an MCMC fit. The method uses TLE-derived directions to define the Phase Angle Bisector in the inertial frame, transforms it into the satellite's body frame with a rotation matrix conditioned on spin parameters, and yields 2D brightness maps that reproduce the observed glint pattern without relying on detailed BRDF models. Across four August 2019 observations, the inferred spin-pole coordinates and rotation periods are consistent with empirical models within small residuals, and brightness maps reveal the triplet mirror structure, validating the approach and its potential scalability to ADR/ Rendezvous operations with improved instrumentation. The results support broader adoption of streak photometry for SDA tasks and motivate future upgrades (e.g., STING) to enhance multi-band, high-temporal-resolution reflectivity mapping of tumbling satellites.

Abstract

Active debris removal techniques are posed to become an important tool in maintaining the safety of the near-Earth space environment. These techniques rely on a clear understanding of the rotational motion of the debris targets, which is challenging to constrain from unresolved imaging. The Ajisai satellite provides an ideal test case for developing and demonstrating these techniques due to its simple geometry and well constrained spin behaviour. We present four observations of the Ajisai satellite taken with SuperWASP in August of 2019, where high cadence photometry was extracted from streaked images as a part of a larger survey of Low Earth Orbit. We develop an MCMC-driven method to determine the spin-state of Ajisai by comparing the alignment between a map of modelled mirror positions and a novel derived map of surface reflectivity. We generally find good agreement within the expectation and uncertainties set by empirical models and our determined spin-state solutions align the surface reflectivity map and modelled mirror location well. Our results show that streak photometry can be used to recover the spin-axis and rotation period of fast-spinning objects such as Ajisai using modest ground-based instrumentation, making it readily scalable to a wider range of targets and observatories.

Figures (13)

• Figure 1: The Ajisai satellite with mirror panels and CCRs (corner cube reflectors) covering its spherical surface labelled on the figure. This figure is taken from 2000ITGRS..38.1417O
• Figure 2: Propagation of the empirical model 2016AdSpR..57..983K for the orientation and period of Ajisai's spin axis. The red segment corresponds to the extent of the dates in which Ajisai was observed with SuperWASP. The empirical model defines $\delta_{emp}$ as being measured relative to the south celestial pole, with a clockwise spin relative to this axis.
• Figure 3: SuperWASP North at the Roque de los Muchachos Observatory in August 2019.
• Figure 4: Left: The custom Raspberry Pi control system. Right: A high-level schematic of the modified system operations, with new components shaded in blue and the original SWASP control system shaded grey. See text for more details.
• Figure 5: A schematic illustration of the LEO observation procedure using SuperWASP. Left: The pass of the target across the sky is divided into a series of fields that account for the visibility limits of the telescope, shadow cone of the Earth, separation from the Moon, and dead time while the telescope slews and cameras read out. Right: The footprint of a single pointing (shown as a mosaic of the 6 cameras) captures a tumbling RSO as it streaks across the field. Photometry is extracted from the streak with an effective time resolution set by the speed of the target across the CCDs. Figure reproduced from Chote2019.