Range Of Phase Angles Research Articles

Light Scattering From High‐Porosity 3D Simulants of the Lunar Regolith at Small Phase Angles

AbstractLunar regolith consists of unconsolidated grains with high porosity, called the fairy castle structure. It is closely linked to the lunar opposition effect, which is the effect where brightness sharply increases as the phase angle approaches 0. However, owing to the Earth's gravity, it is difficult to reproduce the structure to study the physical characteristics of the lunar fairy castle structure in the laboratory. We designed a lunar fairy castle structure model for 3D printing. These models had high porosity and were simplified to tree‐like shapes. Various porous conditions of the surface were considered, represented by the number of trees, maximum trunk length, and maximum branch angle. In this study, a laboratory experiment was conducted to measure the reflectance of simulants with a fairy castle structure within a small phase angle range from 1.4 to 5.0. The result is analyzed for the sample porosity with the tangential slope of the reflectance S, which denotes the strength of the opposition effect. In addition, the results of this study were compared with lunar observation data. The porous samples exhibited a relatively large S value. The influence of branch length and attachment angle was very weak in this study. Samples with a porosity between 0.78 and 0.82 represent the similar S values to the lunar observation data, a mean porosity of lunar regolith. In conclusion, our findings suggest a potential correlation between porosity and the opposition effect in printed samples, proposing a new research approach for understanding the lunar opposition effect.

Using synthetic disk-integrated reflectance spectra to constrain direct imaging sensitivity requirements for a Mars-like exoplanet

The 2020 Decadal Survey on Astronomy and Astrophysics 11https://doi.org/10.17226/26141. recommended the prioritization of a space-based telescope capable of directly characterizing Earth-like exoplanets in reflected light. The planned suite of instruments onboard such a mission are expected to provide disk-integrated spectra with moderate spectral resolution and signal-to-noise (SNR). Although the detection and characterization of Earth-like exoplanets remains the primary focus of such a mission, land planets with limited available water, such as Mars, may be much more common. Mars-like exoplanets, therefore, are an equally significant set of targets when investigating the diverse climatologies and potential habitability of other worlds, especially if our own Solar System is any indication of planetary diversity. In this study, we constrain the direct imaging sensitivity requirements for observing and characterizing Mars-like exoplanets with the goal of informing future telescope design and mission planning. Employing an instrument noise model simulating a coronagraph-equipped, space-based telescope, spatially- and spectrally-resolved synthetic observations of Mars are produced. We evaluate the direct imaging sensitivity requirements across a range of wavelengths, from the ultraviolet (UV) to near-infrared (near-IR), to enable the spectral characterization of key atmospheric and surface features from disk-integrated reflectance spectra. Detectability at a given SNR is assessed through optical wavelength integration times for a range of phase angles, host star spectral types, and levels of atmospheric dustiness. Our results indicate that a Decadal-recommended space telescope featuring an aperture of 6-m is likely only proficient in detecting Mars-like exoplanets around K-type stars located within a 10 parsec (pc) radius from Earth. Furthermore, we demonstrate that when integrating over visible and near-IR wavelengths, required exposure times to detect such a planet are reasonable, especially near full phase angles. In the context of upcoming and proposed observatories, such as the Habitable Exoplanet Observatory (HabEx) and Large UV/Optical/IR Surveyor (LUVOIR), our findings provide valuable insights into the direct imaging capabilities and optimal observational strategies needed for detecting and studying Mars-like exoplanets.

Pre‐Flight and In‐Flight Calibration and Performance of the Terminal Tracking Cameras (TTCams) on the NASA Lucy Mission

AbstractThe Terminal Tracking Camera (TTCam) imaging system on the NASA Lucy Discovery mission consists of a pair of cameras that are being used mainly as a navigation and target acquisition system for the mission's asteroid encounters. However, a secondary science‐focused function of the TTCam system is to provide wide‐angle broadband images over a large range of phase angles around close approach during each asteroid flyby. The scientific data acquired by TTCam can be used for shape modeling and topographic and geologic analyses. This paper describes the pre‐flight and initial in‐flight calibration and characterization of the TTCams, including the development of a radiometric calibration pipeline to convert raw TTCam images into radiance and radiance factor (I/F) images, along with their uncertainties. Details are also provided here on the specific calibration algorithms, the origin and archived location of the required ancillary calibration files, and the archived sources of the raw calibration and flight data used in this analysis.

Unveiling the properties of asteroids: linking photopolarimetry to spectral classification

ABSTRACT This paper attempts to present a comprehensive analysis of the photopolarimetric properties of asteroids. In light of the limitations identified in several previously employed empirical formulae, this paper introduces a new formula that offers a reliable fit for the phase-polarization curve of asteroids. The validity of the new empirical formula is confirmed by analysing polarimetric data for lunar soil samples across a wide range of phase angles and various spectral bands. Notably, this investigation reveals a strong negative correlation between $P_{\mathrm{ max}}$ and wavelength ($\lambda$) for lunar soil samples. Furthermore, the examination of key features of the phase-polarization curve of asteroids, such as the polarization minimum ($P_{\mathrm{ min}}$), polarization maximum ($P_{\mathrm{ max}}$), and the slope (h) at the inversion angle, allows us to explore their correlations with the geometric albedo (A) of asteroids. We have investigated whether our photopolarimetric studies could corroborate the existing classification scheme for asteroids, which divides them into three major composition classes: Chondrite (C), Metallic (M), and Stony (S)-types, based on spectral analysis. Our findings have revealed a good agreement with the existing classification. Each class is characterized by a specific combination of geometric albedo (A) and polarimetric properties ($P_{\mathrm{ min}}$, $P_{\mathrm{ max}}$, and h) observed in asteroids, represented by four distinct regions. Interestingly, besides the three main types (C-, M-, and S-), we have found an overlapping region containing both M- and S-type asteroids.

Phase angle dependence of the dust cross section in a cometary coma

Context. Rosetta/OSIRIS took optical measurements of the intensity of scattered light from the coma of 67P/Churyumov-Gerasimenko over a wide range of phase angles. These data have been used to measure the phase angle dependent radiance profile of the dust coma. Aims. We want to provide information about the column area densities of the dust coma as seen from Rosetta. This information in combination with the measured OSIRIS phase function can then be used to determine the scattering phase function of the dust particles. Methods. We use a simple numerical model to calculate the dust density in the coma. For this we neglect all forces but solar gravitation and radiation pressure. As this cannot describe particles close to the surface of the comet, we assume starting conditions at a sufficient distance. We evaluate the column area density as observed from Rosetta/OSIRIS and compare the results for different spacecraft positions, dust sizes and surface activity distributions. Results. We find the phase angle dependence of the column area density to be largely independent of particle size and spacecraft positions. The determining factor is the activity distribution across the surface, especially the activity on the night side. For models with no night side activity, we find the column area density at high phase angles to be roughly two orders of magnitude larger than at low phase angles. Conclusions. The radiance profile measured from inside a cometary coma results from the combined effects of a phase angle dependent column area density and the scattering phase function. The radiance profile is therefore strongly dependent on the surface activity distribution, and - unless the dust emission is isotropic - any attempt to infer particle properties (as expressed through the scattering phase function) from such data must take into account and de-bias for this spatial variation of the dust column area density.

Imaging polarimetry of comet 67 P/Churyumov–Gerasimenko: homogeneous distribution of polarization and its implications

ABSTRACT Comet 67P/Churyumov–Gerasimenko (67P) become observable for the first time in 2021 since the Rosetta rendezvous in 2014–2016. Here, we present pre-perihelion polarimetric measurements of 67P from 2021 performed with the Very Large Telescope (VLT), as well as post-perihelion polarimetric measurements from 2015 to 2016 obtained with the VLT and the William Herschel Telescope. This new data covers a phase angle range of ∼4○−50○ and presents polarimetric measurements of unprecedentedly high S/N ratio. Complementing previous measurements, the polarimetric phase curve of 67P resembles that of other Jupiter family comets and high-polarization, dusty comets. Comparing pre- and post-perihelion data sets, we find only a marginal difference between the polarimetric phase curves. In our imaging maps, we detect various linear structures produced by the dust in the inner coma of the comet. Despite this, we find a homogeneous spread of polarization around the photocentre throughout the coma and tail, in contrast to previous studies. Finally, we explore the consequences of image misalignments on both polarimetric maps and aperture polarimetric measurements.

Simulation of Natural Convection with Sinusoidal Temperature Distribution of Heat Source at the Bottom of an Enclosed Square Cavity.

The lattice Boltzmann method is employed in the current study to simulate the heat transfer characteristics of sinusoidal-temperature-distributed heat sources at the bottom of a square cavity under various conditions, including different amplitudes, phase angles, initial positions, and angular velocities. Additionally, a machine learning-based model is developed to accurately predict the Nusselt number in such a sinusoidal temperature distribution of heat source at the bottom of a square cavity. The results indicate that (1) in the phase angle range from 0 to π, Nu basically shows a decreasing trend with an increase in phase angle. The decline in Nu at an accelerated rate is consistently observed when the phase angle reaches 4π/16. The corresponding Nu decreases as the amplitude increases at the same phase angle. (2) The initial position of the sinusoidal-temperature-distributed heat source Lc significantly impacts the convective heat transfer in the cavity. Moreover, the decline in Nu was further exacerbated when Lc reached 7/16. (3) The optimal overall heat transfer effect was achieved when the angular velocity of the non-uniform heat source reached π. As the angular velocity increases, the local Nu in the square cavity exhibits a gradual and oscillatory decline. Notably, it is observed that Nu at odd multiples of π surpasses that at even multiples of π. Furthermore, the current work integrates LBM with machine learning, enabling the development of a precise and efficient prediction model for simulating Nu under specific operational conditions. This research provides valuable insights into the application of machine learning in the field of heat transfer.

Photometry of the Didymos System across the DART Impact Apparition

On 2022 September 26, the Double Asteroid Redirection Test (DART) spacecraft impacted Dimorphos, the satellite of binary near-Earth asteroid (65803) Didymos. This demonstrated the efficacy of a kinetic impactor for planetary defense by changing the orbital period of Dimorphos by 33 minutes. Measuring the period change relied heavily on a coordinated campaign of lightcurve photometry designed to detect mutual events (occultations and eclipses) as a direct probe of the satellite’s orbital period. A total of 28 telescopes contributed 224 individual lightcurves during the impact apparition from 2022 July to 2023 February. We focus here on decomposable lightcurves, i.e., those from which mutual events could be extracted. We describe our process of lightcurve decomposition and use that to release the full data set for future analysis. We leverage these data to place constraints on the postimpact evolution of ejecta. The measured depths of mutual events relative to models showed that the ejecta became optically thin within the first ∼1 day after impact and then faded with a decay time of about 25 days. The bulk magnitude of the system showed that ejecta no longer contributed measurable brightness enhancement after about 20 days postimpact. This bulk photometric behavior was not well represented by an HG photometric model. An HG 1 G 2 model did fit the data well across a wide range of phase angles. Lastly, we note the presence of an ejecta tail through at least 2023 March. Its persistence implied ongoing escape of ejecta from the system many months after DART impact.

Pit-to-crack mechanisms of 316LN stainless steel reinforcement in alkaline solution influenced by strain induced martensite

The pit-to-crack transition of AISI 316LN stainless steel reinforcement exposed to stress corrosion cracking (SCC) in chlorides contaminated alkaline environment, was studied by a combination of slow strain rate testing (SSRT) and electrochemical impedance spectroscopy (EIS). The phase angle shift (Δφ) obtained by EIS at low frequencies was utilized to determine the pit-to-crack transition, differentiating from crack nucleation and propagation as identified by shifts in the frequency range of phase angle (θ) peaks. The pit-to-crack transition was developed once the maximum θ value shifted from the low to high frequencies. EIS analysis was corroborated by assessment of repassivation rates and pit growth, in addition to calculating {Delta G}^{{rm{gamma }}to {rm{alpha }}{rm{mbox{'}}}}. Crack nucleation at lath martensite developed transgranular SCC. Strain-induced martensitic transformation was associated with the brittle failure of AISI 316LN stainless steel, where α’–martensite phase preferentially incubated the pit, and favored crack nucleation, thus promoting pit-to-crack transition.

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.

Photometry and Polarimetry of 2010 XC15: Observational Confirmation of E-type Near-Earth Asteroid Pair

Asteroid systems such as binaries and pairs are indicative of the physical properties and dynamical histories of small solar system bodies. Although numerous observational and theoretical studies have been carried out, the formation mechanism of asteroid pairs is still unclear, especially for near-Earth asteroid (NEA) pairs. We conducted a series of optical photometric and polarimetric observations of a small NEA 2010 XC15 in 2022 December to investigate its surface properties. The rotation period of 2010 XC15 is possibly a few to several dozen hours and the color indices of 2010 XC15 are derived as g − r = 0.435 ± 0.008, r − i = 0.158 ± 0.017, and r − z = 0.186 ± 0.009 in the Pan-STARRS system. The linear polarization degrees of 2010 XC15 are a few percent at the phase angle range of 58°–114°. We found that 2010 XC15 is a rare E-type NEA on the basis of its photometric and polarimetric properties. Taking the similarity of not only physical properties but also dynamical integrals and the rarity of E-type NEAs into account, we suppose that 2010 XC15 and 1998 WT24 are of common origin (i.e., an asteroid pair). These two NEAs are the sixth NEA pair and first E-type NEA pair ever confirmed, possibly formed by rotational fission. We conjecture that the parent body of 2010 XC15 and 1998 WT24 was transported from the main belt through the ν 6 resonance or Hungaria region.

Fast detection of short circuits in low-voltage AC systems based on wavelet packet transform and current change rate

The safe and stable operation of a new low-voltage power system requires the research and application of fast detection technology of short-circuit faults. However, the existing methods are difficult to effectively realize the rapidity and reliability in case of short circuits with unclear features and various interference conditions. Therefore, the fault feature of short-circuit current in the full phase angle range is analyzed, and a new method of short-circuit detection based on wavelet packet transform and current change rate is proposed. Among them, the fast-action detection method of wavelet packet transform is used for faults with obvious features to achieve detection rapidity, and the double criteria backup detection method of wavelet packet transform and current change rate is used for faults with unclear features to ensure detection reliability. On this basis, the hardware technology realization of short-circuit fault fast detection algorithm is studied. For short circuit faults, load startup, load switching, and other situations, the real low-voltage AC system experiment is carried out to verify. Finally, the test shows that the detection method can effectively and rapidly detect short-circuit faults within 1ms in the full phase angle range, and has robustness under interference conditions.

Chasing rainbows and ocean glints: Inner working angle constraints for the Habitable Worlds Observatory

ABSTRACT NASA is engaged in planning for a Habitable Worlds Observatory (HabWorlds ), a coronagraphic space mission to detect rocky planets in habitable zones and establish their habitability. Surface liquid water is central to the definition of planetary habitability. Photometric and polarimetric phase curves of starlight reflected by an exoplanet can reveal ocean glint, rainbows, and other phenomena caused by scattering by clouds or atmospheric gas. Direct imaging missions are optimized for planets near quadrature, but HabWorlds ’ coronagraph may obscure the phase angles where such optical features are strongest. The range of accessible phase angles for a given exoplanet will depend on the planet’s orbital inclination and/or the coronagraph’s inner working angle (IWA). We use a recently created catalog relevant to HabWorlds of 164 stars to estimate the number of exo-Earths that could be searched for ocean glint, rainbows, and polarization effects due to Rayleigh scattering. We find that the polarimetric Rayleigh scattering peak is accessible in most of the exo-Earth planetary systems. The rainbow due to water clouds at phase angles of ∼20○ − 60○ would be accessible with HabWorlds for a planet with an Earth equivalent instellation in ∼46 systems, while the ocean glint signature at phase angles of ∼130○ − 170○ would be accessible in ∼16 systems, assuming an IWA = 62 mas (3λ/D). Improving the IWA = 41 mas (2λ/D) increases accessibility to rainbows and glints by factors of approximately 2 and 3, respectively. By observing these scattering features, HabWorlds could detect a surface ocean and water cycle, key indicators of habitability.

Temporal fingerprints of cortical gyrification in marmosets and humans.

Recent neuroimaging studies in humans have reported distinct temporal dynamics of gyri and sulci, which may be associated with putative functions of cortical gyrification. However, the complex folding patterns of the human cortex make it difficult to explain temporal patterns of gyrification. In this study, we used the common marmoset as a simplified model to examine the temporal characteristics and compare them with the complex gyrification of humans. Using a brain-inspired deep neural network, we obtained reliable temporal-frequency fingerprints of gyri and sulci from the awake rs-fMRI data of marmosets and humans. Notably, the temporal fingerprints of one region successfully classified the gyrus/sulcus of another region in both marmosets and humans. Additionally, the temporal-frequency fingerprints were remarkably similar in both species. We then analyzed the resulting fingerprints in several domains and adopted the Wavelet Transform Coherence approach to characterize the gyro-sulcal coupling patterns. In both humans and marmosets, sulci exhibited higher frequency bands than gyri, and the two were temporally coupled within the same range of phase angles. This study supports the notion that gyri and sulci possess unique and evolutionarily conserved features that are consistent across functional areas, and advances our understanding of the functional role of cortical gyrification.

Distance Protection for Lines Connecting Converter Interfaced Renewable Power Plants: Adaptive to Grid-end Structural Changes

Typical fault current characteristics of converter interfaced renewable power plants have significant impact on the reliability of traditional line distance protection. Large degrees of system non-homogeneity introduce substantial error in the apparent impedance calculation. In this paper, an adaptive distance relaying method for lines connected to converter-interfaced renewable power plants is proposed. A range of fault current phase angles is identified using the local and remote equivalent source impedances, which are calculated using only local measurements. Corresponding to the lower and upper bound of the identified range of fault current phase angle, two apparent impedances are calculated based on priority to dependability and security of protection operation. The trip decision is made based on the weighted sum of the first and second apparent impedances. Tuning of the dependability and security weightage factors based on the calculated remote grid-end source impedance, ensures adaptability and reliability of operation, even after structural changes in the grid. The proposed method is verified using IEEE 39 bus system and validated using field data. Comparative assessment with practically proven distance and modified distance protection method for lines connected with renewables is also provided.

Shape Models of Lucy Targets (3548) Eurybates and (21900) Orus from Disk-integrated Photometry

We use our new light curves, along with historical data, to determine the rotation state, photometric properties, and convex shape models of the targets of the Lucy mission (3548) Eurybates and (21900) Orus. We determine a retrograde spin for both targets, with sidereal rotation periods of 8.7027283 ± 0.0000029 h and 13.486190 ± 0.000017 h, respectively. The phase curves of both objects are nearly linear in the phase-angle range observable from Earth and lack a pronounced opposition effect. Unsupervised classification of these phase curves by the Penttilä et al. tool suggests that Eurybates and Orus belong to the C and D taxonomic types, respectively, thereby independently confirming past classifications based on their spectral slope. Time-resolved color-index measurements show no systematic color variations correlated with rotation for either target at the 1% level, suggesting that no variegation is present on a hemispherical scale for any of the objects. Comparison of the shape models with stellar occultation data available for the two objects from the program by Buie et al. allows us to resolve the longitude ambiguity of the orientations of the spin axes and derive unique pole solutions for both targets. Furthermore, scaling the shape models to match the occultation chords produces accurate sizes and geometric albedos for both objects. The derived surface-equivalent spherical diameters are D s = 69.3 ± 1.4 km and D s = 60.5 ± 0.9 km for Eurybates and Orus, respectively, while the geometric albedo in the H, G 1, G 2 system is p V (H, G 1, G 2) = 0.044 ± 0.003 and p V (H, G 1, G 2) = 0.040 ± 0.002 for Eurybates and Orus, respectively.

AOTF-based spectro-polarimeter for observing Earth as an exoplanet

Earth is the only known habitable planet and it serves as a testbed to benchmark the observations of temperate and more Earth-like exoplanets. It is required to observe the disk-integrated signatures of Earth for a large range of phase angles, resembling the observations of an exoplanet. In this work, an acousto-optic tunable filter (AOTF)-based experiment is designed to observe the spectro-polarimetric signatures of Earth. The results of spectroscopic and polarimetric laboratory calibration are presented here along with a brief overview of a possible instrument configuration. Based on the results of the spectro-polarimetric calibration, simulations are carried out to optimize the instrument design for the expected signal levels for various observing conditions. The usefulness of an AOTF-based spectro-polarimeter is established from this study, and it is found that, in the present configuration, the instrument can achieve a polarimetric accuracy of <0.3 % for linear polarization for an integration time of 100 ms or larger. The design configuration of the instrument and the planning of conducting such observations from Lunar orbit are discussed.

Absolute colors and phase coefficients of asteroids

Context. We use the phase curves of small bodies to measure absolute magnitudes and, together with complementary theoretical and laboratory results, to understand the micro- and macroscopic properties of their surfaces. Although we can observe asteroids up to phase angles of about 30 deg, the range of phase angles covered by outer Solar System objects usually does not go further than 7−10 deg for centaurs and 2 deg for trans-Neptunian objects, and a linear relation between magnitude and phase angle may be assumed. Aims. We aim to directly compare data taken for objects in the inner Solar System (inside the orbit of Jupiter) with data for centaurs and trans-Neptunian objects. Methods. We use the SLOAN Moving Objects Catalog (MOC) data to construct phase curves restricted to phase angles of less than or equal to 7.5 deg, which is compatible with the angles observed for the trans-Neptunian and Centaur population. We assume a linear model for the photometric behavior to obtain absolute magnitudes and phase coefficients in the ugirz, V, and R filters. Results. We obtain absolute magnitudes in seven filters for over 4000 objects. Our comparison with outer Solar System objects suggests the surfaces have a common property: intrinsically redder objects become blue with increasing phase angle, while the opposite happens for intrinsically bluer objects.

Spectrophotometry of the lunar regolith using the Chang’E-3 Panoramic Camera (PCAM)

Aims. We present a multiband photometric study of the lunar mare surface based on in situ measurements using the Panoramic Camera on board the Chang'E-3 mission. We aim to obtain photometric properties and to investigate the differences in measuring sites in various conditions. Methods. Data were collected with a vast range of phase angles from 0.5° to 160°, probing 0–5° phases to constrain the opposition effect (OE) and phases above 120° to constrain the phase function. Stray light and spectral corrections were conducted to calibrate the regolith’s bidirectional reflectance distribution function. We employed the Hapke photometric model to describe the regolith’s photometric properties. Results. Phase functions and Hapke parameters at three measuring sites were retrieved. The mare regolith at the measuring sites had a single-scattering albedo (SSA) of 0.17-0.21 for the green channel and exhibited backscattering and a strong OE. The coherent backscatter opposition effect (CBOE) represented the majority of OE, with a proportion of around 80% for pristine regolith. The phase ratio curves were arch-shaped, and the arch positions of the curves were associated with grain size.

Asteroid (3200) Phaethon: results of polarimetric, photometric, and spectral observations

ABSTRACT We present results of polarimetric, photometric, and spectral observations of the near-Earth asteroid (3200) Phaethon carried out at the 6-m BTA telescope of the Special Astrophysical Observatory and the 2.6-m and 1.25-m telescopes of the Crimean Astrophysical Observatory over a wide range of phase angles during its close approach to the Earth at the end of 2017 (α = 19°–135°) and in 2020 at α = 52.2°. Using our and other available in literature data, we found that the maximum degree of linear polarization of Phaethon in the V band is Pmax = (45 ± 1) per cent at the phase angle αmax = 124.0° ± 0.4°, whereas the inversion angle αinv = 21.4° ± 1.2° and polarimetric slope is h = (0.326 ± 0.027) per cent per degree. Using the dependence ‘polarimetric slope – albedo,’ we have found the geometric albedo of asteroid Phaethon to be pv = 0.060 ± 0.005. This value falls into the lower range of albedo values for asteroids determined by different methods. The mean colour indices U–B = 0.207 m ± 0.053 m and B–V = 0.639 m ± 0.054 m of the asteroid are derived at heliocentric and geocentric distances 1.077 au and 0.102 au, respectively, and phase angle α = 23.78°. The absolute magnitude of Phaethon is V(1,1,0) = 14.505 m ± 0.059 m. The effective diameter of Phaethon is estimated from obtained absolute magnitude and geometrical albedo, it is equal to 6.8 ± 0.3 km. The best fit to the observed polarimetric data was obtained with the Sh-matrix model of conjugated random Gaussian particles composed of Mg-rich silicate (90 per cent) and amorphous carbon (10 per cent).