## Introduction

Near-Earth object (NEO) (469219) Kamoʻoalewa (provisional designation 2016 HO3) is the most stable of the five known quasi-satellites of the Earth, with a dynamical lifetime of a few hundred years1. As a quasi-satellite, the orbit of Kamoʻoalewa is very Earth-like, with semi-major axis within 0.001 au of Earth’s, a low eccentricity of just ~0.1, and a modest inclination of about 8 degrees to the ecliptic2 and it is a frequently proposed target for spacecraft study3,4,5. As it orbits the Sun with a ~1 year orbital period, it takes a quasi-satellite path relative to Earth, that is, it makes retrograde loops around Earth with a ~1 year period but well beyond Earth’s Hill sphere6. Study of this class of objects began with the initial discovery of (164207) 2004 GU97,8,9. Physical characterization of the quasi-satellite population has been lacking due to challenging observing geometry and short residence time in near-Earth space. Uniquely, Kamoʻoalewa is favorably placed for observations once a year around April when it becomes bright enough (with visual magnitude V < 23.0mag) to be characterized by large telescopes on Earth. These regular observing windows allow for continued study, unlike temporarily captured minimoons such as 2020 CD3 that require dedicated observing campaigns during a single apparition shortly after their discovery10,11.

## Results and Discussion

We used the LBT to obtain broadband color photometry and visible spectra on UT 14 April 2017. The Multi-Object Double Spectrograph (MODS) instrument was used in imaging and long-slit spectroscopic modes12 to carry out our observations. These observations provided an initial assessment of the quasi-satellite’s taxonomic class as being consistent with S- and L-type silicate asteroids13 and rotation period, which was determined to be < 30 minutes upon the object’s discovery14.

Follow-up broadband photometry was collected on UT 18 April 2017 at LDT in the VR filter using the Large Monolithic Imager15. Exposure times varied from 200 s to 300 s. The goal of these observations was to collect high signal-to-noise ratio data, which combined with the LBT observations provided a longer baseline in time to derive the object’s rotational lightcurve and so improve the period determination.

Using established data calibration and reduction routines16, we find Kamoʻoalewa’s rotational period to be 28.3 (+1.8/−1.3) minutes (99th percentile error limits), consistent with the findings upon its discovery14. The peak-to-peak lightcurve amplitude is 1.07 ± 0.05mag based on a Fourier fit, corresponding to an axis ratio of a/b ≥ 1.5317. The lightcurve is plotted in Fig. 1, which also provides a comparison of Kamoʻoalewa’s spin period with that of known NEOs18, showing that its rotation state is typical of similarly sized NEOs. The population of NEOs with H > 21.0 mag rotate fast enough to imply internal cohesion19, illustrated by curves indicating the maximum spin speed of an object at a given size given a range of assumed object bulk densities ($${\rho }_{b}$$) and tensile strength coefficients ($$\kappa$$). Previous study of plausible shape and rotation models for Kamoʻoalewa found that Kamoʻoalewa’s surface may retain grains smaller than ~1 mm-1 cm in size20.

Our observed reflectance spectrum at visible wavelengths (0.4–0.95 µm) is consistent with many types of silicate materials which are common among near-Earth asteroids, particularly S- and L- taxonomic classes, but is not diagnostic of any single compositional category (Fig. 2, note that all spectra plot very closely at wavelengths below 0.8 µm). Follow-up spectroscopic observations in the near-infrared (1.0–1.3 µm) obtained in 2019 confirmed the presence of a 1.0-micron absorption band, due to the minerals olivine and/or pyroxene, but superimposed on a steep red continuum slope. This slope was confirmed by measuring broadband zJH photometric colors on UT 7 March 2021 with the LBT, and JK colors on UT 11 April 2021.

We used curve matching to constrain the surface composition and identify possible analog materials for Kamoʻoalewa. The spectral slope of Kamoʻoalewa is redder (higher reflectance at increasing wavelength) than typical S-type asteroid spectra as defined by the Bus-Demeo taxonomy. As an example, Fig. 2 shows the spectrum of Kamoʻoalewa with that of Sw-type asteroid (63) Ausonia21,22. Sw-types exhibit the same characteristics as S-types but have redder slopes in the infrared23. The spectral slope of Kamoʻoalewa is even redder than the slope of these objects. Reddening of spectral slope can be due to a range of factors including phase angle (Sun-Target-Observer angle), particle size of the regolith (increasing grain size causes bluer spectral slope), metal content (increasing metal causes redder spectral slope), and lunar-style space weathering (increasing space weathering causes redder spectral slope and weaker absorption bands).

Laboratory measurements of LL ordinary chondrite meteorites, which are derived from S-type asteroids, have shown maximal spectral slope changes by up to 30%/1 µm due to phase angle variations of ~120 degrees24. The NIR spectrum of Kamoʻoalewa was observed at a phase angle of 43.2° and its slope (measured by the online Bus-DeMeo taxonomy tool25) of 89%/1 µm is too steep to be explained by just phase angle effects. The grain size of the regolith also influences spectral slope and band depth. Typically for silicates, the band depth and spectral slope decrease (becoming blue-sloped) as grain size approaches millimeters to centimeters. In the case of Kamoʻoalewa, the band depth is weak, but the spectral slope is red—not blue as would be expected from grain size effects alone. Hence, grain size effects are insufficient to reconcile the observed spectral properties of Kamoʻoalewa with that of a typical S-type composition (a more neutral reflectance spectrum).

The choice of characterizing the spectral slope of Kamoʻoalewa using the standard Bus-DeMeo taxonomic tool23 was made to enable general comparisons with the NEA population. This method involves fitting a straight line to a well-sampled spectrum from 0.45 to 2.45 µm. Since our spectrum of Kamoʻoalewa is not uniformly sampled in wavelength, the calculation of the slope was performed by first linearly interpolating the spectrum. To assess the uncertainty of the slope measurement, which is dominated by the errors in the infrared reflectance, the slope measurement was repeated after varying the data at wavelengths greater than 1.0 µm uniformly by either ±1$$\sigma$$ (prior to interpolation). While this is an overestimate of the error (as it assumes the photometric errors are correlated), it provides a transparent look at the variability inherent to our unevenly sampled spectrum. This method returns a range of slope values from 76 to 101%/1 µm. Figure 3 shows the range of slopes plotted with those of near-Earth asteroids compiled by the MITHNEOS survey26. The one object with an overall spectral slope which overlaps the range for Kamoʻoalewa is (4142) Dersu-Uzala, a Mars-crossing asteroid that was originally classified as an A-type27 and whose 0.4–1.0 micron spectral slope and 1.0 micron band differs from Kamoʻoalewa.

Metal-silicate mixtures have been shown to have spectra similar to Kamoʻoalewa with steep spectral slope and a weaker olivine or pyroxene band. Such materials would be analogous to pallasite, mesosiderite, or CB chondrite meteorites. Spectral reddening has been shown to occur in mixtures where the metal content is >50%28. We compared the spectral slope and band depth of Kamoʻoalewa with metal+olivine and metal+pyroxene mixtures. To illustrate this hypothesis, reflectance measurements were collected of the iron meteorite Gibeon and mesosiderite Vaca Muerta, with a linear combination of these two endmembers plotted in Fig. 2. This approach uses only one source of meteoritic metal for comparison, but we note that the spectrum of the Gibeon sample we use is iron-rich, and  hence among the reddest possible analogs amongst meteoritic metal sources. When mixed with spectrally neutral silicates to fit the 1.0-micron band, the spectral slope becomes even less red. Therefore, we conclude generally that mixtures of meteoritic metal with unweathered silicates do not provide a suitable match to Kamoʻoalewa’s spectrum.

Lunar style space weathering has been demonstrated to reduce the albedo and band depth and increase the spectral slope of a reflectance spectrum29,30. We compared the spectrum of Kamoʻoalewa to Apollo lunar samples from the RELAB database31,32,33,34. A total of 19 available samples were used to identify the best spectral match to Kamoʻoalewa. Based on our search, the 20–45 µm grains from Apollo 14 Lunar sample #14163 provides a close match amongst surveyed materials to our reflectance measurements of Kamoʻoalewa (Fig. 2). However, a variety of slopes is present among the lunar soil sample database, including higher and lower slopes. This shows the inherent uncertainty in separating specific compositional hypotheses based on our low-resolution data. We note that spectral slope matches to fine-grained lunar materials does not necessarily imply a fine-grained regolith on the surface of Kamoʻoalewa, as recent in-situ observations by the Chang’e-4 rover of a rock >20 cm in size found it to highly reddened35. The spectrum of this rock traces closely with Apollo sample 14163 at wavelengths < 1.75 microns, but rolls over to neutral reflectance from 1.75 to 2.5 microns.

Regardless of its origin, we show via Figs. 2 and 3 that the overall spectrum of Kamoʻoalewa is inconsistent with typical near-Earth asteroid taxonomies and requires additional explanation (e.g. high metal content and/or extreme Lunar style space weathering) for its reflectance properties. We note that S-type asteroids often have higher visible albedos than the lunar samples we compared to. For example, the 20–45 µm grains of Apollo 14 sample #14163 has a visible albedo of ~0.1 (although this is dependent on grain size), while S-type asteroid Ausonia has an albedo of ~0.1636. Adopting a range of albedos from 0.10 to 0.16 provides an effective diameter for Kamoʻoalewa (H = 24.3mag) in the range from D = 58–46 m. Direct measurements of Kamoʻoalewa’s albedo (or size) coupled with knowledge of the grain size distribution of its surface would therefore play a useful role in discriminating between compositional hypotheses.

Planetary perturbations make Kamoʻoalewa’s annual retrograde loops around the Earth slightly variable in amplitude over a longer period of about 40 years. Numerical propagation of its orbit over decadal timescales in the past and in the future finds that these nearly-periodic variations remain small (its annual epicyclic path relative to Earth’s orbit remains at a geocentric distance of 10–30 $${r}_{H\oplus }$$, where $${r}_{H\oplus }$$ ≈ 1.5 × 106 km is the radius of Earth’s Hill sphere), but larger changes occur over timescales of centuries, as seen in Fig. 4. The longer-term orbit propagation finds that the quasi-satellite motion began approximately 100 years ago and will last for about 300 years in the future. Prior to a century ago (and beyond ~300 years in the future), Kamoʻoalewa’s annual epicyclic loops slowly drift away from Earth, tracking a horseshoe-shaped path in a frame co-rotating with Earth around the Sun; in this state, its semi-major axis alternately falls below and above Earth’s by about 0.005 au, and it approaches Earth closely (within ~10 $${r}_{H\oplus }$$) only every ~130 years. In Fig. 4, the quasi-satellite state is indicated by the green track, which shows the small amplitude librations of the semi-major axis about 1 au (Fig. 4a) and of the mean longitude about Earth’s mean longitude (Fig. 4b) and the small geocentric distance (Fig. 4c); the horseshoe state is indicated by the black track which shows that the semi-major axis alternately falls below and above Earth’s by about 0.005 au (Fig. 4a) and the mean longitude relative to Earth’s has large amplitude librations about 180 degrees (Fig. 4b) and the geocentric distance varies up to about 2 au (Fig. 4c). The retrograde quasi-satellite orbits, the horseshoe orbits, and transitions between these two types are known dynamical behaviors near the 1:1 mean motion resonance in the three-body problem37. The current errors in the orbital parameters grow beyond the ± 500 year timeframe, precluding confidence in its longer term orbital path. However, numerical sampling of its possible longer term orbital path has been carried out with models of various degrees of fidelity1,38,39,40,41. These studies commonly indicate that Kamoʻoalewa remains in an Earth-like orbit, exhibiting intermittent transitions between horseshoe and quasi-satellite motion, on ~105–106-year timescales, but this state is unlikely to persist over timescales comparable to the age of the Earth and of the solar system.

## Conclusions

The natural question that arises is: what is Kamo’oalewa’s origin? The answers are speculative. One possibility is that it was captured in its Earth-like orbit from the general population of NEOs. Its low eccentricity and inclination are, however, rather atypical of such captured co-orbital states found in numerical simulations42. Another possibility is that Kamo’oalewa originates from an as-yet undiscovered quasi-stable population of Earth’s Trojan asteroids orbiting near Earth’s L4 and L5 Lagrange points43,44. This hypothesis can be tested in future deeper and wider observational surveys of the Earth-Sun Trojan regions, supplemented with theoretical investigation of dynamical pathways between Earth Trojans and quasi-satellites. A third possibility is that Kamoʻoalewa originates in the Earth-Moon system, perhaps as impact ejecta from the lunar surface45 or as a fragment of a parent NEO’s tidal or rotational break up during a close encounter with Earth-Moon46. Three NEOs, 2020 PN1, 2020 PP1, and 2020 KZ2, have been identified as having orbital parameters cluster near Kamoʻoalewa’s closely enough that they may be break-up companions47. The reflectance spectrum of Kamoʻoalewa (as reported in the present work) lends support to the lunar ejecta hypothesis. An origin near or within the Earth-Moon system is further supported by the low value of the relative velocity, v ≈ 2–5 km/s, of Kamoʻoalewa during its close approaches to Earth-Moon, whereas NEOs have larger relative velocities at close approaches, with an average v ≈ 20 km/s48,49.

## Methods

Data collected using the twin MODS instrument (one per mirror) on LBT used an exposure time of 120 s for all images, which were taken using Sloan i’ and z’ filters, and exposure times of 900 s for the spectral frames. The G2V star HIP 52192 was used as the solar analog to convert raw spectral fluxes to reflectance.

The data calibration and reduction routines described in16 were applied to the visible photometric data set to determine the object’s rotational period. After the light-time correction, we performed a search for periodicity using the Lomb periodogram technique50. We find one main peak with a confidence level >99.9% located at ~102.4 cycles/day (i.e, 0.234 h) and corresponding to a single-peaked lightcurve (Fig. 5). However, the measured lightcurve presents a strong asymmetry with one minimum deeper than the other one by about 0.65 mag. Therefore, we conclude that the double-peaked lightcurve corresponds to the object’s full rotation.

Near-infrared spectra were collected as a series of 300 s exposures nodded in an AB pattern, totalling 110 min of exposure time. Data were processed, including sky subtraction and wavelength fitting, via the Flame pipeline51 using SAO 120107 as a solar analog. Extraction was performed using an optimized extraction technique52 implemented in python53. As a validation of our techniques, we observed the main-belt asteroid (26) Proserpina in August 2019 using the NASA Infrared Telescope Facility and the twin LUCI (LBT Utility Camera in the Infrared) spectrographs on LBT. We found close agreement between both measurements using the same processing on the LBT data as implemented for Kamo’oalewa (Fig. 6).

Color measurements were obtained by measuring target fluxes through standard aperture photometry, relative to the G2V solar analog star GSPC P330-E54. On UT 7 March 2021, both the target and the solar analog were observed at airmass <1.01. On UT 11 April 2021, the target was observed over an airmass range of 1.07–1.16, and the solar analog was observed at airmass <1.01. To ensure that the time variability of the target’s brightness did not affect color measurements, images were obtained in two filters (z.H., J.H., and J.K.) simultaneously to derive the reflectance ratios between each filter combination. This analysis made use of the Photutils package in Astropy55,56,57.