Yamamoto et al. Earth, Planets and Space (2020) 72:85 https://doi.org/10.1186/s40623-020-01213-2 FULL PAPER Open Access Dynamic precise orbit determination of Hayabusa2 using laser altimeter (LIDAR) and image tracking data sets Keiko Yamamoto1* , Toshimichi Otsubo2, Koji Matsumoto3,4, Hirotomo Noda3,4, Noriyuki Namiki1,4, Hiroshi Takeuchi4,5, Hitoshi Ikeda6, Makoto Yoshikawa4,5, Yukio Yamamoto4,5, Hiroki Senshu7, Takahide Mizuno5, Naru Hirata8, Ryuhei Yamada8, Yoshiaki Ishihara9,14, Hiroshi Araki1,4, Shinsuke Abe10, Fumi Yoshida7, Arika Higuchi1, Sho Sasaki11, Shoko Oshigami5, Seiitsu Tsuruta3, Kazuyoshi Asari3, Makoto Shizugami1, Naoko Ogawa5, Go Ono6, Yuya Mimasu5, Kent Yoshikawa5, Tadateru Takahashi12, Yuto Takei5, Atsushi Fujii5, Tomohiro Yamaguchi5,15, Shota Kikuchi5, Sei‑ichiro Watanabe5,13, Satoshi Tanaka4,5, Fuyuto Terui5, Satoru Nakazawa5, Takanao Saiki5 and Yuichi Tsuda4,5 Abstract The precise orbit of the Hayabusa2 spacecraft with respect to asteroid Ryugu is dynamically determined using the data sets collected by the spacecraft’s onboard laser altimeter (LIght Detection And Ranging, LIDAR) and automated image tracking (AIT). The LIDAR range data and the AIT angular data play complementary roles because LIDAR is sensitive to the line‑of‑sight direction from Hayabusa2 to Ryugu, while the AIT is sensitive to the directions perpen‑ dicular to it. Using LIDAR and AIT, all six components of the initial state vector can be derived stably, which is difcult to achieve using only LIDAR or AIT. The coefcient of solar radiation pressure (SRP) of the Hayabusa2 spacecraft and standard gravitational parameter (GM) of Ryugu can also be estimated in the orbit determination process, by combin‑ ing multiple orbit arcs at various altitudes. In the process of orbit determination, the Ryugu‑fxed coordinate of the center of the LIDAR spot is determined by ftting the range data geometrically to the topography of Ryugu using the Markov Chain Monte Carlo method. Such an approach is efective for realizing the rapid convergence of the solution. The root mean squares of the residuals of the observed minus computed values of the range and brightness‑centroid direction of the image are 1.36 m and 0.0270°, respectively. The estimated values of the GM of Ryugu and a correction factor to our initial SRP model are 29.8 0.3 m3/s2 and 1.13 0.16, respectively. ± ± Keywords: Hayabusa2, Precise orbit determination, LIDAR range data, ONC image tracking data, GM of Ryugu, Solar radiation pressure Introduction December 2015, and arrived at the target asteroid Ryugu Hayabusa2 is an asteroid-sample return mission that is in June 2018. Subsequent to its arrival at Ryugu, Haya- being conducted by Japan Aerospace Exploration Agency busa2 performed various observations and experiments, (JAXA). Te spacecraft was launched in December 2014, such as remote-sensing observations using onboard performed an Earth swing-by utilizing Earth gravity in instruments, releases of a small rover and lander, ejection of the impactor, and sample collection from the surface *Correspondence: [email protected] and subsurface of Ryugu. 1 National Astronomical Observatory of Japan, 2‑21‑1 Osawa, Mitaka, Some papers have been published on the results of Tokyo 181‑8588, Japan the remote-sensing observations of Hayabusa2. Wata- Full list of author information is available at the end of the article nabe et al. (2019) discussed the formation process and © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. Yamamoto et al. Earth, Planets and Space (2020) 72:85 Page 2 of 17 evolution of the rotation of Ryugu based on the shape range observations during the periods other than special model and the standard gravitational parameter, i.e., the operations, although the sampling frequency may vary product of the gravitational constant (G) and mass of (see “LIDAR range data” section). However, they frst Ryugu (M). Kitazato et al. (2019) analyzed the spectrum approximated the three-dimensional coordinates of the absorption in the 3-μm-wavelength band obtained from spacecraft using polynomials before the geometrical ft- the near-infrared spectrometer (NIRS3) observation ting to the topography. Owing to the use of such a non- and found that water was present in the form of hydrous dynamical approach, the velocities and other parameters, minerals on the surface of Ryugu. Sugita et al. (2019) such as the GM of Ryugu, cannot be determined using estimated the parent body of Ryugu on the basis of the this method. spectral type of Ryugu that was determined from the data In this study, we determine the orbit by dynamical obtained by the optical navigation camera (ONC) and the approach, to improve the trajectory determined by Mat- data of thermal infrared imager (TIR) and laser altimeter sumoto et al. (2020) (MCMC orbit). In order to obtain a (light detection and ranging, LIDAR). Te evolution pro- more precise orbit, in addition to the initial state vectors cess from the parent body to Ryugu was also discussed of the orbit, two parameters, i.e., the GM of Ryugu and a based on the surface topography, spectrum, and thermal correction factor of the Hayabusa2 solar radiation-pres- properties of Ryugu. sure (SRP) model, are also estimated. To estimate these In these studies, the precise orbit of the spacecraft is parameters precisely, we use the data of multiple arcs indispensable to map the acquired remote-sensing data with diferent altitudes, including the ones of the period on the surface of Ryugu. In general, the spacecraft orbit when GCP-NAV data is unavailable. We use the AIT data is initially determined using radiometric observation data as well as the LIDAR data. In principle, the AIT data are acquired at ground stations on the Earth. However, the automatically calculated onboard at all times, although precision of the orbit determination using radiometric the data availability depends on whether the telemetry data only is insufcient for mapping purpose (see “Orbit data are downlinked at that time. Our approach and soft- determination using LIDAR and AIT data sets” sec- ware are independent of those used by Watanabe et al. tion) and should be improved with respect to the target (2019), and hence, our obtained GM value of Ryugu is body. Onboard instrument data—in case of Hayabusa2, useful for validating their results. the range data from the LIDAR and image data from Tis paper is organized as follows. In “Data sets” sec- the ONC—are useful for this purpose. Watanabe et al. tion, we present the orbit arcs and details of the data sets (2019) performed a dynamic orbit determination and used in this study. Te method of orbit determination determined the GM of Ryugu using the LIDAR range, the as well as software improvement is presented in “Orbit automated image tracking (AIT) and the ground-control- determination” section. In “Results and discussion” sec- point navigation (GCP-NAV) data besides of radiometric tion, the results of the estimation of the Hayabusa2 orbit, observation data, i.e., Doppler, range, and delta-diferen- GM of Ryugu, and correction factor of the Hayabusa2 tial one-way ranging (Delta-DOR) data. AIT data are a SRP model are presented along with the corresponding time series of the coordinates of the brightness centroid discussion, and fnally, the conclusion of this study is pre- of the ONC images. GCP-NAV is an optical navigation sented in “Conclusion” section. technique used mainly during the special operations to determine the position and velocity of the spacecraft Data sets based on ONC-observed feature points on the asteroid Hayabusa2 orbit and selection of arcs surface (Terui et al. 2013). Te Hayabusa2 spacecraft is not orbiting Ryugu, but sim- Matsumoto et al. (2020) developed a simple method ply remaining around it, i.e., it is usually hovering at the to improve the Hayabusa2 trajectory for the landing-site home position (HP), which is 20 km above Ryugu and selection of the mission. Tey used LIDAR range data facing the sub-Earth direction (Tsuda et al. 2013). In the and a shape model of Ryugu that was developed using case of observations obtained at higher latitudes and low- ONC images and determined the trajectory of Haya- altitude, or special events such as a gravity measurement, busa2 using the Markov Chain Monte Carlo (MCMC) touch down, and ejection of a rover, lander, or impactor, method such that temporal variations of the range Hayabusa2 starts from the HP, changes its position, and observations geometrically ft the topographic fuctua- returns to the HP after the operation is completed. tions of Ryugu. Tey showed that the Hayabusa2 tra- In this study, we aim to determine not only the ini- jectory was greatly improved on using the LIDAR data. tial state vectors of the trajectory, but also the GM of Te advantage of this method is that the trajectory can Ryugu and a correction factor for the Hayabusa2 SRP be determined even outside the period of special opera- model. Te arcs used for the orbit determination are tions if LIDAR data is available.