Multicolor Photometry of Tiny Near-Earth Asteroid 2015 RN35 across a Wide Range of Phase Angles: Possible Mission-accessible A-type Asteroid

Studying small near-Earth asteroids is important in order to understand their dynamical histories and origins as well as to mitigate the damage caused by asteroid impacts on Earth. We report the results of multicolor photometry of the tiny near-Earth asteroid 2015 RN35 using the 3.8 m Seimei telescope in Japan and the TRAPPIST-South telescope in Chile over 17 nights in 2022 December and 2023 January. We observed 2015 RN35 across a wide range of phase angles from 2° to 30° in the g, r, i, and z bands in the Pan-STARRS system. These lightcurves show that 2015 RN35 is in a nonprincipal axis spin state with two characteristic periods of 1149.7 ± 0.3 s and 896.01 ± 0.01 s. We found that the slope of the visible spectrum of 2015 RN35 is as red as asteroid (269) Justitia, one of the very red objects in the main belt, which indicates that 2015 RN35 can be classified as an A- or Z-type asteroid. In conjunction with the shallow slope of the phase curve, we suppose that 2015 RN35 is a high-albedo A-type asteroid. We demonstrated that surface properties of tiny asteroids could be well constrained by intensive observations across a wide range of phase angles. 2015 RN35 is a possible mission-accessible A-type near-Earth asteroid with a small Δv of 11.801 km s−1 in the launch window between 2030 and 2035.


INTRODUCTION
It is now well established that the first stage of the planetary formation process is the accretion of the so-called planetesimals from the solids in our protoplanetary disk.Theoretical and observational studies have shown that the planetesimals were formed at large sizes, diameters (D) larger than 50 to 100 km (Delbo' et al. 2017).The small bodies of our solar system are remnants of that era.However, not all the current asteroids are survivors from primordial times.Collisions between this original planetesimal population produced clusters of fragments of smaller sizes, the so-called asteroid families.A nongravitational effect-the Yarkovsky effect-slowly changes the orbital semimajor axis a of asteroids at a rate da/dt proportional to 1/D (Vokrouhlický 1998).Asteroids in prograde rotation have da/dt > 0 and migrate towards larger heliocentric distances, whereas those in retrograde rotation with da/dt < 0 migrate towards the Sun.Another effect that is also caused by the solar radiation, the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect (Rubincam 2000), can change the spin state of asteroids affecting the rate of the drift due to Yarkovsky.Both the Yarkovsky and YORP effects depend on the surface properties of the asteroids and their internal structure.The migration of small main belt asteroids can lead the smaller ones to reach the dynamical routes (resonances with planets) that can bring them to the near-Earth space, hence sampling several regions (as well as asteroid families) of the main belt.Studying near-Earth asteroids (NEAs) is therefore crucial to understand the material transportation from the main belt to the near-Earth space as well as to mitigate the hazard of an asteroid impact to the Earth.Tiny asteroids having diameters less than 100 m could be characterized during their close approaches to the Earth using ground-based and space-borne telescopes.Comprehensive studies of large asteroids have been conducted, whereas only few studies focus on tiny asteroids due to observational difficulties caused by limited visibilities and large apparent motions of asteroids during their close approaches.
Using the Infrared Array Camera (IRAC) on the Spitzer Space Telescope, Mommert et al. (2014a,b) conducted infrared observations of tiny NEAs 2009 BD (D ≤ 5 m) and 2011 MD (D ∼ 10 m).According to these observations, asteroid 2009 BD has inconclusive surface nature which could be either covered by fine regolith or composed of a collection of bare rocks, while the bulk density of 2011 MD is estimated to be 1.1 +0.7  −0.5 × 10 3 kg m −3 , indicating a rubble-pile origin.Recently, Fenucci et al. (2021Fenucci et al. ( , 2023) ) found that the tiny superfast rotators (499998) 2011 PT (D ∼ 35 m and rotation period P ∼ 10 minutes) and 2016 GE 1 (D ∼ 12 m and P ∼ 34 s) have small thermal conductivities of K ≤ 0.1 W m −1 K −1 and K ≤ 100 W m −1 K −1 , respectively.Such small conductivities imply that these two tiny asteroids are covered with fine regolith or highly porous rocks (Avdellidou et al. 2020;Cambioni et al. 2021).On the other hand, a bunch of fast rotators are discovered in video observations using a CMOS camera (Beniyama et al. 2022).Some of them need to have strength similar to the typical tensile strength of meteorites to keep their fast rotations.It is unclear that such fast rotators could have fine regolith on its surface.Thus, it is still in debate whether tiny asteroids are monolithic or rubble-pile, and with or without fine regolith on their surface.Reddy et al. (2016) conducted radar, lightcurve, and spectroscopic observations of the tiny E-type NEA 2015 TC 25 (D ∼ 2 m).They concluded that 2015 TC 25 is a fragment possibly ejected from the E-type main belt asteroid (44) Nysa.One of the interesting properties of 2015 TC 25 is its bluer spectrum compared to a typical E-type.They explained the bluer slope of 2015 TC 25 in the visible wavelength with a lack of fine regolith on the surface due to a combination of weak gravity and fast rotation.Recently, Licandro et al. (2023) found that a visible spectrum of the tiny fast-rotating asteroid 2022 AB (D ∼ 65 m and P ∼ 3 minutes) shows an upturn over the 0.4 to 0.6 µm, which does not fit with any known asteroid spectrum 1 .
The phase angle dependence of an asteroid brightness, the so-called phase curve, informs about the surface properties of the asteroid (see, e.g.; Bowell et al. 1989;Belskaya & Shevchenko 2000).High-albedo asteroids have shallower slope in their phase curves since the contribution of the shadowhiding decreases as albedo increases (Belskaya & Shevchenko 2000), whereas low-albedo asteroids have steeper slopes.Apart from the albedo, other properties are related to the phase curve such as the surface grain size and roughness.An important consideration to study phase curves of asteroids is the rotation correction (see, e.g.; Harris & Lupishko 1989).Homogeneous sets of the typical brightness such as maximum and mean of the lightcurves at certain phase angles are necessary to accurately derive the related quantities, otherwise, the brightness variation caused by the rotation leads to misunderstanding of observational results.Thus, the tiny asteroids, which are often fast-rotating (Thirouin et al. 2016(Thirouin et al. , 2018;;Beniyama et al. 2022) and do not require a long time to obtain a mean brightness across a rotation phase, are appropriate targets to investigate phase curves.
Well-sampled phase curves of small asteroids are less commonly obtained since their observation opportunities are limited.Reddy et al. (2015) characterized the small NEA 2004 BL 86 (D ∼300 m) at a wide phase angle range from 1.5 • to 49.6 • .The visible geometric albedo of about 0.4 derived from the slope of the phase curve is consistent with the near-infrared spectrum of 2004 BL 86 , which implies that 2004 BL 86 is a typical high-albedo V-type asteroid.Recently, several dozens of phase curves of NEAs are studied in the framework of the IMPACTON project (Rondón et al. 2019(Rondón et al. , 2022;;Ieva et al. 2022;Arcoverde et al. 2023).They made a database with phase curves of 30 NEAs using three 1 m-class telescopes in Brazil and Italy (Arcoverde et al. 2023).Their sample include only one tiny NEA, 2017 DC 38 , with the absolute magnitude H of 24.22, that was successfully observed at a very small phase angle of 1.1 • .However, its rotation period was not obtained and thus no rotation correction has been performed in the analysis of the phase curve of 2017 DC 38 .
In this paper, we present the results of multicolor photometry of the tiny NEA 2015 RN 35 over 17 nights in Japan and Chile.The target asteroid 2015 RN 35 was discovered by the Pan-STARRS 1 survey (Chambers et al. 2016) on 2015 September 9. 2015 RN 35 is an Apollo-class NEA, and its absolute magnitude in the V band is 23.24 in NASA JPL Small-Body DataBase (SBDB)2 .The trajectories of 2015 RN 35 were well studied and possible collisions with Earth were discussed (Petrov et al. 2018).2015 RN 35 had a close approach in 2022 December.2015 RN 35 was observable at phase angles from 30 • to 0.6 • from 2022 December to 2023 January, which is a quite rare opportunity to obtain a well-sampled phase curve of a tiny asteroid.The paper is organized as follows.In section 2, we summarize our observations and data reduction.The physical properties of 2015 RN 35 are summarized in Section 3. The surface properties of the tiny asteroid 2015 RN 35 and possible exploration by spacecraft mission are discussed in Section 4.

OBSERVATIONS AND DATA REDUCTION
We conducted photometric observations at two observatories in Japan and Chile.The observing conditions are summarized in Table 1.The predicted V band magnitudes, phase angles, distances between 2015 RN 35 and observer, and distances between 2015 RN 35 and the Sun in Table 1 were obtained from NASA JPL HORIZONS3 using the Python package astroquery (Ginsburg et al. 2019).

Seimei telescope
We obtained 12 lightcurves of 2015 RN 35 using TriColor CMOS Camera and Spectrograph (TriCCS) on the 3.8 m Seimei telescope (Kurita et al. 2020) from 2022 December 23 to 2023 January 21.We simultaneously took three-band images in the Pan-STARRS (g, r, i) and (g, r, z) filter (Chambers et al. 2016).The field of view is 12.6 ′ × 7.5 ′ with a pixel scale of 0.350 arcsec/pixel.
Nonsidereal tracking was performed during the observations of 2015 RN 35 .The exposure times were 5 or 60 s according to the brightness of 2015 RN 35 .The signal-to-noise ratios of 2015 RN 35 in the data taken in 2023 January are too low to detect 2015 RN 35 in a single exposure.We took multiple images with short exposures rather than a single image with long exposures in our observations in order to avoid having elongated photometric reference stars and also to eliminate the cosmic rays.
We performed standard image reduction including bias subtraction, dark subtraction, and flatfielding.The astrometry of reference sources from the Gaia Data Release 2 was performed using the astrometry.netsoftware (Lang et al. 2010).For the data taken in 2023 January, we performed stacking of images before photometry to avoid the elongations of the images of 2015 RN 35 as shown in the upper panels of Figure 1 (hereinafter referred to as the nonsidereally stacked image).We stacked 20 successive images with exposure times of 60 s.Since a typical readout time of the CMOS sensors on TriCCS is 0.4 milliseconds, the total integration time is about 1200 s, which corresponds to one of the characteristic periods of 2015 RN 35 (see Section 3.1).We also stacked images using the World Coordinate System (WCS) of images corrected with the surrounding sources to suppress the elongations of the images of reference stars as shown in the lower panels of Figure 1 (hereinafter referred to as the sidereally stacked image).
We derived colors and magnitudes of 2015 RN 35 following the same procedure described in Beniyama et al. (2023a,b).Cosmic rays were removed with the Python package astroscrappy (McCully et al. 2018) using the Pieter van Dokkum's L. A.Cosmic algorithm (van Dokkum 2001).The circular aperture photometry was performed for 2015 RN 35 and the reference stars using the SExtractorbased Python package sep (Bertin & Arnouts 1996;Barbary et al. 2017).The aperture radii were set to twice as large as the full width at half maximums (FWHMs) of the point spread functions (PSFs) of the reference stars in the sidereally stacked images.The photometric results of 2015 RN 35 and reference stars were obtained from the nonsidereal and sidereal stacked images, respectively.

TRAPPIST-South telescope
We obtained five lightcurves of 2015 RN 35 using the robotic telescope TRAPPIST-South (the Minor Planet Center code I40; Jehin et al. 2011) of the University of Liège between 2022 December 19 and 26.TRAPPIST-South is a 0.6-m Ritchey-Chrétien telescope operating at f/8 and equipped with a CCD camera FLI ProLine 3041-BB.The field of view is 22 ′ × 22 ′ with an un-binned pixel scale of 0.64 arcsec/pixel.
We obtained images in the sidereal tracking mode with the wide Exo-filter, whose wavelength coverage roughly corresponds to the r to y bands in the Pan-STARRS system (Jehin et al. 2011).We set exposure time to 40 s on December 19, 20, 21, and 22 using the 2 × 2 binning mode, and to 120 s on December 26 while using no binning.
The raw images were processed using standard bias, dark and flat fields frames.The photometry was performed using the PHOTOMETRYPIPELINE (Mommert 2017) to derive the r band magnitudes in the Pan-STARRS system.This pipeline allows zero-point calibration by matching field stars with online catalogs.Typically 100 stars with solar-like colors (i.e.stars with g − r and r − i colors closer than 0.2 magnitudes to that of the Sun) were used in each image for the magnitude calibration.Aperture radii were set to 4 pixels for the binned observations and to 8 pixels for the un-binned mode.

Lightcurves and rotation period
The light-travel time was corrected to obtain the time-series colors and magnitudes of 2015 RN 35 (Harris & Lupishko 1989).The eight lightcurves of 2015 RN 35 taken on 2022 December are shown in Figure 2. Brightness variation of about 0.7 mag is seen in each lightcurve.The lightcurves show non-perfect periodic signals, implying that 2015 RN 35 is a non-principal axis rotator in a complex rotation state (i.e., a tumbler; Pravec et al. 2005).
We performed the periodic analysis using the Lomb-Scargle technique (Lomb 1976;Scargle 1982; VanderPlas 2018) with three long lightcurves obtained with the TRAPPIST-South telescope on 2022 December 19, 22, and 26.The Lomb-Scargle periodograms with a period range between 500 to 2000 s are shown in Figure 3, where four peak frequencies, f a , f b , f c , and f d , are indicated.We focused on the two strongest frequencies, f b and f d , based on the powers of periodograms.The f d appears to be the first overtone of f b : 2f b ≒ f d .We regarded that f b corresponds to a period of 2015 RN 35 , P 1 , since folded lightcurves with f −1 b are typical double-peaked lightcurves.The uncertainty of P 1 was estimated with the Monte Carlo technique following the previous work (Beniyama et al. 2022).We obtained 1000 lightcurves by randomly resampling the data assuming each observed data-point follows a normal distribution whose standard deviation is a photometric error.We calculated the 1000 periods corresponding to P 1 and derived it with the uncertainty each night as 1149.7 ± 0.4 s (Dec.19), 1149.6 ± 0.5 s (Dec.22), and 1149.9 ± 0.5 s (Dec.26).We adopted the error-weighted average of these three periods, 1149.7 ± 0.3, as P 1 .
Figure 4 shows the eight r band lightcurves of 2015 RN 35 folded with the period of 1149.7 s.The folded lightcurves seem to be double-peaked but not perfectly overlapped each other in rotation phase, probably due to the non-principal axis rotation.The model curve with the period of 1149.7 s is also shown in Figure 4.The root mean square of residual (RMS) is calculated as follows: where n obs is the number of observation data, t i is the observation time of the i-th sample, y obs (t i ) is i-th observed brightness at t i , and y model (t i ) is the model brightness at t i .The RMS is calculated as 0.104.2023) appear as not double-peaked unlike others, the rotation period of ∼ 1150 is highly likely.
We continue the periodic analysis for the three lightcurves obtained with the TRAPPIST-South telescope on 2022 December 19, 22, and 26 following procedures in previous studies (Pravec et al. 2005(Pravec et al. , 2014;;Lee et al. 2017Lee et al. , 2022)).The purpose of successive analysis is to derive the other period P 2 characterizing the non-principal axis rotation of 2015 RN 35 .Searching for the P 2 is performed against the all five lightcurves obtained with the TRAPPIST-South telescope.We fit the lightcurves with two-dimensional Fourier series keeping P 1 fixed: where t is time, m is the order of Fourier series, C 0 , C jk and S jk are the Fourier coefficients.We set P 2 and Fourier coefficients as free parameters and searched P 2 from 100 s to 10000 s with a step of 1 s.The RMS residual between observed and model lightcurves of 2015 RN 35 is calculated in each step.The results of the search of P 2 are shown in Figure 5.We plotted results of grid search of P 2 in cases with m of 3 and 4. Five periods with smaller RMSs in the two cases, P a = 896 s, P b = 1603 s, P c = 2688 s, P d = 4062 s, and P e = 8123 s, are indicated in Figure 5.The five periods might be linear combinations of the two basic periods.These appear to be related to each other: and P e ≒ 2P d .Thus, we regard the shortest period P a as P 2 , which is a period independent from P 1 .This P 2 corresponds to the third strongest peak, f c , in Figure 3.We also estimated the uncertainty of P 2 with the Monte Carlo technique as that of P 1 .We derived P 2 as 896.01 ± 0.01 s with randomly resampled 1000 lightcurves.
The model curves with P 1 of 1149.7 s and P 2 of 896.01 s are shown in Figure 6 with the observed lightcurves.The RMS is calculated as 0.069.The model and observed lightcurves are well overlapped each other, which indicates that P 1 and P 2 are periods characterizing the rotation state of 2015 RN 35 .We note that P 1 and P 2 may not necessarily correspond to rotation and precession (or precession and rotation) periods, respectively.Determination of the rotation and precession periods need detailed physical modeling, which is out of the scope of this paper.

Colors and reflectance spectrum
The time-series of colors of 2015 RN 35 in 2022 December are shown in Figure 7.The errorweighted averages of those colors are derived as g − r =0.714 ± 0.008, r − i =0.245 ± 0.009, and r − z =0.255 ± 0.020.The systematic errors in color determination with TriCCS are considered as in Beniyama et al. (2023a).The error-weighted average colors corresponds each other within the measurement errors when we consider the results on 2023 January (see panel (b) of Figure 9).
The reflectance spectrum of 2015 RN 35 in Figure 8 was calculated with the derived colors and the solar colors with the same method in Beniyama et al. (2023b).The reflectances at the central wavelength of the r, i, and z bands, R r , R i , and R z , were calculated as: (2) where (r − g) RN 35 , (i − g) RN 35 , and (z − g) RN 35 are the colors of 2015 RN 35 , whereas (r − g) ⊙ , (i − g) ⊙ , and (z − g) ⊙ are the colors of the Sun in the Pan-STARRS system.We referred to the absolute magnitude of the Sun in the Pan-STARRS system as g = 5.03, r = 4.64, i = 4.52, and z = 4.51 (Willmer 2018).We set the uncertainties of the magnitudes of the Sun as 0.02.filter bandwidths.The reflectance spectra except 2015 RN 35 are originally normalized at 0.55 µm.
We renormalize those spectra at 0.481 µm as follows: where R ′ (λ) is a renormalized reflectance at a wavelength of λ, R(λ) is an original reflectance at a wavelength of λ, and R(0.481 µm) is an original reflectance at a wavelength of 0.481 µm.

Phase curves
We observed 2015 RN 35 across a wide range of phase angles from 2 • to 30 • , which provides us a well-sampled phase curve as shown in Figure 9.We converted the g and r band magnitudes in the  Pan-STARRS system to the V band magnitude in the Johnson system using the equations in Tonry et al. (2012).We stacked 20 images obtained in 2023 January to make a decent detection of 2015  is compatible to one of the characteristic period of 2015 RN 35 , P 1 of 1149.7 s.Thus, the rotation effects have been corrected in the phase curves of 2015 RN 35 .
We derived an absolute magnitude in the V band, H, and slope parameters, G 1 and G 2 , with the H-G 1 -G 2 model (Muinonen et al. 2010): where V red (α) is a reduced magnitude in the V band at a phase angle of α.The Φ 1 , Φ 2 , and Φ 3 are phase functions written as follows: The uncertainty of H, G 1 , and G 2 were estimated with the Monte Carlo technique.We made 1000 phase curves by randomly resampling the data assuming each observed data follows a normal distribution whose standard deviation is a standard error of weighted mean magnitude.We derived H of 23.9±0.2,G 1 of −0.10±0.08,and G 2 of 0.8±0.1.The absolute magnitude and slope parameters in the g, r, and i bands are also derived in Figure 9 for convenience.The visible spectrum of 2015 RN 35 suggests that 2015 RN 35 is a very red object (VRO) in the near-Earth region.We compare the spectrum with the class templates from Mahlke et al. (2022) in Figure 8.We also show the spectra of the A-type MBA (246) Asporina and the VRO in the main belt (269) Justitia.These two spectra were obtained with SpeX (Rayner et al. 2003) on the NASA Infrared Telescope Facility (IRTF).We obtained the two spectra via the M4AST online tool (Modeling for Asteroids; Popescu et al. 2012).Justitia is known to have a very red slope like the trans-Neptunian objects (TNOs; Hasegawa et al. 2021), and is classified as Z-type in the latest Mahlke taxonomy (Mahlke et al. 2022).We note that the spectrum of Justitia seems to be out of the range of the Ztype template in the visible wavelength in Figure 8.This is because Justitia is classified as Z-type in Mahlke et al. (2022) using both visible and near-infrared spectra.Thus, Justitia is a bit redder than the typical Z-types.The Z-types have featureless and extremely redder spectra than the D-types.
We evaluate the goodness-of-fit between the spectrum of 2015 RN 35 and templates using the following quantity: where N is the number of reflectance values, R obs,j is a reflectance of 2015 RN 35 at jth wavelength, and R model,j is a reflectance of a template spectrum at the wavelength.We found that the spectrum of 2015 RN 35 seems like those of A-types (δ 2 = 0.008) and Z-types (δ 2 = 0.018), whereas the spectrum does not fit well with S-types (δ 2 = 0.034) and D-types (δ 2 = 0.033).We note that only visible colors are often not enough to determine the spectral types of asteroids.For instance, half of all objects classified as A-types based on spectra in the visible wavelength are not A-types in the near-infrared (DeMeo et al. 2019).
We classified 2015 RN 35 as an A-or Z-type in this study, where both types represent rare populations (Mahlke et al. 2022).The A-type asteroids are olivine-rich asteroids and have similar spectra to those of silicate mineral olivine and are thought to be a piece of differentiated planetesimal (DeMeo et al. 2019), while other studies propose that some A-types may originate from the mantle of the Mars (Polishook et al. 2017).Thus, the A-types may have an important role to investigate formation  et al. (2022).The Z-types might have primitive organic materials on the surface as D-types (Barucci et al. 2018).Justitia is selected as the rendezvous target of the Emirates Mission to Explore the Asteroid Belt (Alhameli et al. 2023).
It is known that the slope parameters G 1 and G 2 have a tight correlation with the geometric albedo (Muinonen et al. 2010;Shevchenko et al. 2016).We show typical G 1 and G 2 values of A-, E-, S-, C-and D-types in Figure 10 ( Shevchenko et al. 2016;Mahlke et al. 2021).We also plot the G 1 and G 2 of the A-type MBA (246) Asporina derived using the sparse photometric observations from Gaia Data Release 2 (Martikainen et al. 2021).The smaller G 1 and larger G 2 , by definition, mean that the slope of the phase curve is shallower.The slopes of high-albedo asteroid are shallower since the contribution of the shadow-hiding effect decreases as albedo increases (e.g.; Belskaya & Shevchenko 2000), whereas those of low-albedo asteroids are steeper on the contrary.Thus, the small G 1 and large G 2 of 2015 RN 35 are indicative of a high geometric albedo.
The G 1 and G 2 of 2015 RN 35 seems a bit far from the typical values of A-types on Figure 10.But, the typical values are slightly different from each other of about 0.1-0.2 on G 1 -G 2 plane depending on the references.Thus, the discrepancy between the slope parameters of 2015 RN 35 and typical values does not necessarily indicate that 2015 RN 35 is an outlier.Therefore we concluded that 2015 RN 35 is an A-type asteroid in conjunction with the colors and slope parameters in the visible wavelength.We demonstrated that only photometry in the visible wavelength is sufficient to determine the spectral type of asteroids, if it is across a wide range of phase angles.
Finally, we discuss other interpretations of the shallow phase slope of 2015 RN 35 .The environments such as self-gravity and rotation period are different between small and large asteroids.Small asteroids may have different surface properties compared with large asteroids.Terai et al. (2013) observed a tiny L-type NEA (367943) Duende (a.k.a., 2012 DA 14 ) across a wide phase angle range from 19 • to 42 • .They derived the slope parameter in the H-G model, G, as 0.44 +0.06 −0.08 , which is larger than the typical value of L-types.The tiny asteroid Duende has a shallow slope in the phase curve.They interpreted the large slope parameter or shallow slope with the difference of surface environment due to the lack of the fine regolith or high geometric albedo.Small gravity on tiny asteroids might lead to the lack of the fine regolith on its surface.The shadow-hiding effect is weak when the fine regolith is deficient and the slope of the phase curve would be shallow.As for 2015 RN 35 , in addition to the small gravity, the fast rotation of about 20 minutes also supports the hypothesis of the lack of fine regolith.Other recent studies showed that there is almost no correlation between albedo and slope parameters using the phase curves obtained in the frame work of the IMPACTON project and the ATLAS survey (Rondón et al. 2019;Arcoverde et al. 2023).They interpreted this is due to the difference of diameters between NEAs and MBAs.The trend is not clear since the number of samples are limited due to the observational difficulties.A comprehensive research of phase parameters are desired to reach a conclusion.
Various observations such as near-infrared spectroscopy and polarimetry are crucial in forthcoming approaches of 2015 RN 35 to put an end to the spectral type.The next two opportunities are in 2031 September and 2056 December, where 2015 RN 35 will be brightened up to 21 mag and 16 mag in the V band, respectively.

Diameter estimation of tiny asteroids
Estimation of asteroid sizes is important not only to evaluate a risk of impact to the Earth but also to plan exploration missions.However, small NEAs are often observed only at a few apparitions at relatively large phase angles compared to MBAs and TNOs.Thus, the absolute magnitude of the asteroid is often not well constrained.The absolute magnitude could be uncertain by ∼ 0.3 depending on whether the opposition surge exists (see, e.g.; Belskaya et al. 2003).Jurić et al. (2002) and Pravec et al. (2012) independently estimated that there is a systematic uncertainty of H of about 0.4.In addition to the uncertainty of H, the geometric albedo is not well estimated for small bodies since observing opportunities are limited to only a short period, as this study.We estimated the absolute magnitude of 2015 RN 35 with high accuracy as 23.9±0.2 through observations across a wide range of phase angles down to 2 • .The surface colors as well as the slope of the phase curve indicate that 2015 RN 35 is a very red asteroid, probably classified as an A-type asteroid.The typical geometric albedo of A-types is estimated as 0.282 ± 0.101 and 0.28 ± 0.09 in Usui et al. (2013) andDeMeo et al. (2019), respectively.We assume the geometric albedo of 2015 RN 35 as p V of 0.28 ± 0.10.The diameter of an asteroid can be estimated with H and p V using the following equation (Fowler & Chillemi 1992;Pravec & Harris 2007): The diameter of 2015 RN 35 is estimated to be 41 ± 8 m.We updated absolute magnitude of 2015 RN 35 by about 0.7 compared to H of 23.24 in JPL SBDB.Our study demonstrated that it is crucial to observe the asteroid in multibands at multi-epochs including where the phase angles are low to derive H and D accurately.Observations at very low phase angles are not possible for all NEAs.Detailed planning of observations is crucial for the diameter estimation of tiny asteroids.

Mission accessibility
One of the important parameters to plan the spacecraft mission is the delta-v (∆v), which is the required impulse per unit of spacecraft mass to change the status of the spacecraft.We refer to the total ∆v4 as the sum of (i) the maneuver required to depart a notional 400 km altitude circular Earth parking orbit, (ii) the ∆v required to match the NEA's velocity at arrival, (iii) the ∆v required to depart the NEA, and (iv) the ∆v (if any) required to control atmospheric entry speed at Earth return.We queried the ∆v of NEAs for the Near-Earth Object Human Space Flight Accessible Targets Study (NHATS; Abell et al. 2012) 5 .The ∆v of 2015 RN 35 is estimated as 11.801 km s −1 in the launch window between 2030 and 2035, which is smaller than the limit of NHATS, 12 km s −1 .In terms of the engineering aspect, 2015 RN 35 is a good candidate for a future spacecraft mission.From a scientific point of view, 2015 RN 35 , either it is an A-or a Z-type NEA, is a great candidate for a future mission.Specifically, there are no planned future spacecraft missions to A-type asteroids.

CONCLUSIONS
We conducted multicolor photometry of the tiny NEA 2015 RN 35 over 17 nights in 2022 December and 2023 January.We observed 2015 RN 35 across a wide range of phase angles from 2 • to 30 • in the g, r, i, and z bands in the Pan-STARRS system.We found that 2015 RN 35 is in a non-principal axis spin state with two characteristic periods of 1149.7 ± 0.3 s and 896.01 ± 0.01 s.The visible spectrum of 2015 RN 35 is as red as (269) Justitia, one of the VROs in the main belt, which indicates that 2015 RN 35 can be classified as an A-or Z-type asteroid.Together with the shallow slope of the phase curve, we suppose 2015 RN 35 is a high-albedo A-type asteroid.
Various observations such as near-infrared spectroscopy and polarimetry are encouraged during the forthcoming approaches of 2015 RN 35 .The next opportunity is in September 2031, where 2015 RN 35 will be brightened up to 21 mag.Though additional follow-up observations are required to reach a conclusion, 2015 RN 35 is a possible mission accessible A-type NEA with small ∆v of 11.801 km s −1 in a launch window between 2030 and 2035.

Figure 1 .
Figure 1.Stacked images of 2015 RN 35 in g, r, and i bands with a total integration time of 1200 s in 2023 January 16.Nonsidereally stacked images (top) and sidereally stacked images (bottom) are shown.Horizontal and vertical bars indicate 2015 RN 35 .Field of view covers 1.75 ′ × 1.75 ′ .North is to the top and East is to the left.

Franco
et al. (2023) derived the rotation period of 2015 RN 35 to be 0.3193 ± 0.0001 hr ∼ 1149 s using lightcurves obtained on 2022 December 18 and 19.Koleńczuk et al. (2023) found the rotation period of 19.1692 ± 0.0069 minutes ∼ 1150 s from the intensive observation campaign during 2022 December.These reported periods are close to P 1 and corresponding to f b in Figure 3. On the other hand, Colazo et al. (2023) derived the rotation period of 2015 RN 35 to be 0.478 ± 0.008 hr ∼ 1721 s using lightcurves obtained on 2022 December 16, which corresponds to f a in Figure 3. Since the phased lightcurves in Colazo et al. (

Figure 2 .Figure 3 .
Figure 2. Lightcurves of 2015 RN 35 .The reduced g, r, i, and z bands magnitudes are presented as circles, triangles, squares, and diamonds, respectively.Bars indicate the 1σ uncertainties.Error-weighted average of magnitude in each lightcurve is presented with a dashed line.Shaded areas indicate the standard errors of the weighted averaged magnitudes.

Figure 4 .
Figure 4. Phased lightcurves of 2015 RN 35 .All lightcurves in reduced r magnitude are folded with a period of 1149.7 s.Phase zero is set to 2459932.5 JD.Bars indicate the 1σ uncertainties of measurements.Model curve fitted to lightcurves is shown by dashed line.

Figure 5 .
Figure 5. RMS residuals between observed and model lightcurves of 2015 RN 35 fixing P 1 of 1149.7 s.Residuals using two-dimensional Fourier series with m of 3 and m of 4 are shown by solid and dashed lines, respectively.Five periods with smaller RMS in either case are indicated.

Figure 7 .
Figure 7. Time-series colors of 2015 RN 35 .The g − r, r − i, and i − z colors are shown by circles, triangles, and squares, respectively.Binning of 60 s are performed for all colors.Bars indicate the 1σ uncertainties.Weighted mean and its error are indicated by dashed lines and shaded areas, respectively.
Possible classification of 2015 RN 35

Figure 9 .
Figure 9. Phase angle dependence of magnitude and colors of 2015 RN 35 .(a) Mean reduced g, r, i, z, and V band magnitudes are presented as circles, triangles, squares, diamonds, and hexagons, respectively.Bars indicate the 1σ uncertainties.Median (50th percentile) of fitting model curves with the H-G 1 -G 2 model are presented by solid lines.Uncertainty envelopes representing the 95 % highest density inverval (HDI) values are shown by dashed lines.(b) Weighted mean g − r, r − i, and r − z colors and their errors in each day are presented as circles, triangles, and squares, respectively.Bars indicate the 1σ uncertainties.Global weighted mean colors and their standard errors are indicated by dashed lines and shaded areas, respectively although they are small and hard to see due to scale effects.

Figure 10 .
Figure 10.G 1 and G 2 of 2015 RN 35 in the V band (star).Bars indicate the 1σ uncertainties.G 1 and G 2 of the A-type asteroid (246) Asporina is shown by hexagon (Martikainen et al. 2021).Typical G 1 and G 2 values of A-, E-, S-, C-, and D-types are shown by diamonds, squares, circles, triangles, and inverted triangles, respectively.Markers are enclosed by solid lines (Shevchenko et al. 2016), dashed lines (cyan band; Mahlke et al. 2021), and dotted lines (orange band; Mahlke et al. 2021).Isochrone for G 1 + G 2 = 1 is plotted by the dashed line for convenience.

Table 1 .
Summary of the observations Note-Observation time in UT in midtime of exposure (Obs.Date), telescope (Tel.), filters (Filters), total exposure time per frame (t exp ), the number of images (N img ), and weather condition (Weather) are listed.Predicted V band apparent magnitude (V), phase angle (α), distance between 2015 RN 35 and observer (∆), and distance between 2015 RN 35 and Sun (r h ) at the observation starting time are referred to NASA Jet Propulsion Laboratory (JPL) HORIZONS as of 2023 August (UTC).Elevations of 2015 RN 35 to calculate air mass range (Air Mass) are also referred to NASA JPL HORIZONS.
Phased lightcurves of 2015 RN 35 with two-dimensional Fourier series.All lightcurves in reduced r magnitude are folded with P 1 of 1149.7 s and P 2 of 896.01 s.Phase zero is set to 2459932.5 JD.Bars indicate the 1σ uncertainties.Model curves fitted to lightcurves are shown by dashed lines.