Article Content
Abstract
The Chelyabinsk meteor entered Earth’s atmosphere on 15 February 2013, producing a shock wave that injured about 1500 people and damaged thousands of buildings. Despite its relatively large size (∼20 m), the progenitor asteroid approached Earth undetected. Its apparent radiant was too close to the Sun for standard ground-based near-Earth asteroid (NEA) surveys operating in the visible light. In addition, it would have been very faint due to an observing geometry at a large phase angle, and very fast moving. We examine the potential for early detection with current and upcoming infrared (IR) space telescopes, such as NASA’s upcoming NEOSurveyor mission and ESA’s planned NEOMIR mission. We use the 20-m Chelyabinsk progenitor to demonstrate detection possibilities and limitations of an object on a day-side trajectory before impact. IR observations from space offer key advantages like an enhanced Sun-asteroid contrast (compared to visible wavelengths). The small, fast-rotating objects are (nearly) isothermal which make IR detections at high phase angles easier compared to visible-light ones, and allow for radiometric size estimation. The latter is crucial for immediate assessment of the impact risk. The Chelyabinsk asteroid would have entered the field-of-regard about 39 h (NEO Surveyor) or 54 h (NEOMIR) before impact. However, we find that a 20-m object on a Chelyabinsk progenitor orbit could be detected theoretically with a 0.5-m telescope in space (located at the Lagrangian point L1), at mid-IR wavelengths, with a lead time of 5–12 days. The large uncertainty in the calculation of the detection lead-time is mainly related to uncertainties in the flux predictions for small, possibly fast-rotating asteroids seen under very extreme phase angles. However, technical challenges, including detector operations at high sky background due to the low solar elongation, telescope straylight problems for observations close to the Sun, near real-time application of synthetic tracking techniques, and fast orbit determination also must be overcome to achieve reliable early warning capabilities.
1. Introduction
The Chelyabinsk impact event during the morning hours on February 15, 2013, underscored the risks posed by small near-Earth objects (NEOs) [1, 2]. A ∼20-m asteroid entered Earth’s atmosphere undetected, producing a bright flash and a powerful explosion. The resulting blast wave, arriving 2-3 min after the meteor became visible, shattered windows and injured about 1500 people, primarily from glass debris. This event highlights the urgent need for improved detection of small asteroids before impact to issue timely warnings and take preventive actions, such as staying away from windows or evacuating specific regions.
Fireballs and bolides are currently detected using various instruments, including fisheye camera networks, global infrasound detectors, or lightning mapping instruments aboard weather satellites. Notable examples include the European Fireball Network [3] (ESA’s NEOCC Fireball Database: https://neo.ssa.esa.int/search-for-fireballs), fireballs reports from U.S. Government Sensors (NASA’s CNEOS Fireball Database: https://cneos.jpl.nasa.gov/fireballs/), and bolides observed by the Geostationary Lightning Mapper (GLM) on the GOES East and West satellites (NEO Bolide Data: https://neo-bolide.ndc.nasa.gov/ [4]). Efforts are also underway to search for small NEOs inside Earth’s orbit during twilight, as demonstrated by dedicated projects [5–9]. However, detecting meter-to decameter-scale objects before impact remains a significant challenge. To date, only 11 such objects have been observed prior to entering Earth’s atmosphere (ESA’s Past Impactors: https://neo.ssa.esa.int/past-impactors or https://en.wikipedia.org/wiki/Asteroid_impact_prediction). These objects were discovered in the night sky and their sizes ranged from 0.5 to 8 m, with detection-to-impact times between 2 and 21 h, leading to extremely short warning times. Despite these limitations, even alerts with just a few minutes of lead time could help mitigate injuries during high-energy events like the Chelyabinsk impact. However, meaningful alerts always require hours of observations of the target beforehand for a reliable trajectory prediction.
The progenitor object of the Chelyabinsk bolide had about 20 m in size [1]. The impact is very well documented and it caused substantial damages to modern civilization. It can therefore be considered as a good reference case for a feasibility study. However, it was not detected by any ground- or space-based monitoring programs, as it approached from a near-Sun direction, a challenging area for observations [1, 10]. The situation will improve in the near-term future when the NEO Surveyor [11] and the NEOMIR [12] infrared (IR) survey missions are in operations. This study examines the possibilities and limitations of detecting such an object well before impact, from a theoretical point of view and also in the light of the two upcoming complementary missions. In Section 2, we explore the optimal locations and wavelength regimes for deploying a small telescope capable of detecting a ∼20-m object on a Chelyabinsk-like trajectory. Section 3 examines the limitations imposed by sky background brightness, while Section 4 focuses on estimating the object’s apparent brightness. Section 5 provides detailed signal-to-noise ratio (SNR) calculations to assess detectability. In Section 6, we discuss our findings, and in Section 7, we present our conclusions.
2. Telescope Location and Wavelength Regime
Based on the orbit of the Chelyabinsk progenitor [1], we calculated the solar elongation (Sun-Observer-Target S-O-T angle), apparent motion, and phase angle (Sun-Target-Observer S-T-O angle) as observed from Earth and from four different Sun-Earth/Moon Barycenter (Sun-EMB) Lagrangian points: L1, L2, L4, and L5. The L3 point, being on the opposite side of the Sun relative to Earth, is not operationally meaningful for satellite deployment and was excluded from this analysis. L1 is located approximately 1.5 million kilometers (0.01 au) from Earth, in the direction of the Sun; L2 is at the same distance from Earth as L1, but lies in the anti-Sun direction. L4 and L5 are positioned 60° ahead and 60° behind Earth in its orbit, respectively. These points are about 1 au from both the Sun and Earth, roughly 100 times farther than the distance from Earth to L1 or L2.
Figures 1 and 2 present calculations for a 20-m-diameter object (H = 26.4, G = 0.15) on the Chelyabinsk progenitor orbit, as observed from five different locations: Earth (black), Sun-EMB L1 (red), L2 (blue), L4 (light blue), and L5 (green). For this analysis, we considered the object’s apparent magnitude, the solar elongation shown in Figure 1, the phase angle, and the object’s apparent motion (in arcsec/min), shown in Figure 2.

Figure 1

Figure 2 (a)

Figure 2 (b)
As observed from Earth at visible wavelengths, the 20 m body passed the V∼28-magnitude detection threshold only about 17 h before impact. Additionally, it crossed the 20° solar elongation limit only around 8 h prior to impact. At that point, the object had an extremely high phase angle (S-T-O > 150°) and a very rapid apparent motion (≫ 10 arcsec/min) that further hindered first detections at visible wavelengths from the ground during the pre-impact hours. These factors would have posed significant challenges even for dedicated long-integration observations from ground-based telescopes.
The L4 and L5 locations are more favorable for observing a Chelyabinsk-type object during the last 15 days before impact. From these positions, the object would have a solar elongation greater than 50°, a phase angle less than 60°, and an apparent motion below 5 arcsec/min. However, the object’s apparent magnitudes would still be fainter than V∼28 mag (or well below 10 μJy at mid-IR wavelengths), making it undetectable with typical existing or planned survey telescopes in space.
In contrast, the L2 location, while widely used for space observatories, is poorly suited for detecting objects on Chelyabinsk-type trajectories. From L2, such objects would appear extremely faint, with apparent magnitudes below 30, very close to the Sun, with solar elongation < 20° (having then also the Earth and the Moon close to or even inside the survey area), and under very high phase angles (S-T-O > 150°). These factors make L2 an unsuitable choice for searching for decameter-scale Earth-impacting objects.
After excluding Earth, L2, L4, and L5 as viable locations for an NEO survey telescope, the remaining option is L1. Note that both currently planned IR survey projects, NEO Surveyor [11, 13, 14] and NEOMIR [12, 15] consider L1 as the best operational option. From this position, the object would be brighter than V∼28 mag for approximately 3.5 days before impact, it would always appear at a solar elongation of more than 20°, and the phase angle would undergo a rapid transition, decreasing from about 150° to nearly 0° shortly before impact. However, one significant challenge remains: the object’s large apparent motion, which reaches several tens of arcsec per minute and can escalate to extreme values of a few hundred arcsec per minute approximately one day before impact. This high motion complicates detection (elongated streaks), and astrometric and photometric efforts.
The choice between a visible or (thermal) IR telescope is straightforward: about 80%-90% of the incoming solar radiation is re-emitted in the IR (see also [11], Figure 2). Additionally, the risk of source confusion (e.g., with background stars or galaxies) is approximately two orders of magnitude lower at mid-IR (mid-IR) wavelengths compared to visible wavelengths. This high IR-to-visible flux ratio and the reduced confusion risk are particularly advantageous for observing NEOs, which are often seen close to the Sun and under large phase angles. At large phase angles, the illuminated part of the surface visible in reflected light (e.g., like a crescent moon) is very small. In contrast, at IR wavelengths, we detect the thermal emission from the warm surface of the body, which is much larger in extent. For rapidly rotating small objects, which could be nearly isothermal, the thermal signal originates from most of the surface, making the mid-IR signal, to a first approximation, directly proportional to the square of the asteroid’s diameter.
3. Sky Background
IR astronomical observations from space can be influenced by a high sky background, which strongly limit the detectability of the signal of a given source. These background signals depend on several factors, including the wavelength of observation, the position on the sky (in R.A. and Dec., or in ecliptic longitude and latitude), and, the solar elongation. In the mid-IR (5–30 μm), the zodiacal light (ZL) is the dominant source of sky background at low solar elongations < 90°.
The above is due to dust particles in the inner solar system (Interplanetary Dust Cloud-IDC) thermally re-radiating the absorbed Sun-light. The maximum of the relevant grain size distribution is in the range between 10 and 100 μm [16]. This IDC has a flattened, lenticular shape with an axial ratio of about 1:7, extending out to about 3 au [17], and with an inclination of about 3° with respect to the ecliptic plane caused by the influence of Venus, Mars and/or the interaction with solar wind [18–20]. Despite the short lifetime of individual dust particles of 104–105 years (due to the Poynting-Robertson effect), the IDC harbors about 1016–1017 kg of dust, comparable to the mass of a larger comet, and has a low density of about 10−19 kg·m−3 [21]. The density of the dust changes with 1/rhelio, the flux with 1/r2 [21]. The IDC is constantly replenished by cometary activity and the destruction of asteroids.
Reference [22] found a subpercentage smoothness of the ZL brightness at arcminute scale. However, at low level, there are structures noticeable at thermal IR wavelengths, mainly asteroid bands (connected to asteroid families) and cometary trails (connected to previously active individual comets). ISOPHOT-S spectra of the ZL in the 5-12 μm range revealed blackbody-like spectral shapes (T ≈ 260…300 K) with no obvious spectral features.
Despite many different ZL studies and model attempts presented in literature [18, 21, 23–30], there are very few measurements in the mid-IR range and at elongations below 60°.
For our studies (see Figure 3), we used the IRSA/IPAC background model (version 4) at: https://irsa.ipac.caltech.edu/applications/BackgroundModel/.

Figure 3
It allows to calculate the IR background as seen from the Earth’s orbit and from the Earth-Sun L2 region. As the intended L1 location is not available, we used the Earth’s orbit as observing location for the background calculations.
The online tool requires the input of coordinates, wavelength, and specific epochs (relevant for the calculation of the elongation-dependent ZL emission). The background model allows to calculate different background contributions:
- ✓The ZL: the zodiacal dust model is based on the model by Wright [30] which was fitted to the COBE/DIRBE data, with updated COBE/DIRBE fitting parameters by [31]
- ✓The diffuse interstellar medium of our galaxy: based on a combined analysis by [32–35].
- ✓Stars: the stellar brightness calculations are based on the galactic model by [36]
- ✓The extragalactic background light, see ([37], and references therein).
The ZL is clearly the dominating background contribution, reaching values up to approximately 130, 280, and 400 MJy/sr at 6, 8, and 10 μm, respectively (within the ecliptic plane and at 30° away from the Sun). The ZL background in the thermal IR shows a nearly exponential decrease between 30° and 180° solar elongation [24]. This rapid drop in background is also visible in Figure 3 between days 11 and 14 when the object undergoes a large change in solar elongation. The faint, low-level structure in the ZL (caused by asteroid families and cometary trails) is not included in these calculations.
The ISM contribution varies considerably over the sky (independently of the Sun’s position). At 8 μm, this contribution ranges from well below 0.1 MJy/sr up to about 35 MJy/sr (and much smaller values at 6 or 10 μm), with the highest values connected to the galactic plane.
The stellar background is negligible in most parts of the sky; in addition, it decreases with increasing wavelength. However, at specific locations it can still reach a few MJy/sr (up to 7, 5, and 4 MJy/sr at 6, 8, and 10 μm, respectively).
The extragalactic background is well below 0.01 MJy/sr and constant over the sky.
4. Thermal Models for Small Asteroids
We applied a range of widely used and validated thermal models to predict the IR fluxes of the 20-m Chelyabinsk progenitor object. These models calculate the surface temperature distribution based on the object’s distance from the Sun, albedo, spin state, and thermal properties. The resulting temperature distribution, when combined with surface emissivity characteristics, determines the amount of IR radiation emitted at specific wavelengths, as observed under a given phase angle.
4.1. The Standard Thermal Model (STM) and the Near-Earth Asteroid TM (NEATM)
Both models assume a spherical shape and instantaneous equilibrium between insolation and thermal emission. The total absorbed solar radiation is given by: Sabs = π (D2/4) S(1 − A), where D is the diameter, S the solar flux at the asteroid, and A the bolometric Bond albedo (ratio of total scattered solar energy in all directions and at all wavelengths to the incident energy). Since the Sun’s spectral energy distribution peaks in the visible wavelength range, we can assume that A = AV = q pV, where q is the phase integral, and pV is the visible geometric albedo. The phase integral q is given by q = 0.29 + 0.684 G (with G being the slope parameter in the H-G system, see [ [38]]). The absolute magnitude H, geometric albedo pV, and the object’s effective diameter Deff are connected via: log pV = 6.259 − 2 logDeff − 0.4H.
The STM [39, 40] calculates the object’s temperature via T (φ) = Tss cos1/4φ, where φ is the angular distance from the subsolar point, and Tss is determined from Tss = [(1-A) S/(ηεσ)]1/4 (ε emissivity, σ Stefan-Boltzmann constant, η beaming parameter), with the temperature on the nightside (φ > 90°) assumed to be zero. The beaming parameter η accounts for the observed enhancement of thermal emission at small solar phase angles, mainly due to surface roughness effects [41], and references therein], it is assumed to be 0.756 in the STM. In case an asteroid is observed under a non-zero phase angle, the surface integrated flux (from an integration over all surface elements with the given temperatures T) is corrected with an empirical thermal-IR phase coefficient of 0.01 mag/deg which is based on observations of main-belt asteroids.
The NEATM [42] is very similar to the STM but uses the beaming parameter either as a free parameter (determined from a fit to multiband measurements), a fixed value for specific object types, or as a phase-angle dependent parameter. And, instead of taking a fixed IR phase coefficient, the NEATM calculates numerically the actual thermal flux from all surface elements visible to the observer and illuminated by the Sun, i.e., as seen under the given phase angle. The NEATM assumes that there is no thermal emission from the non-illuminated hemisphere of the asteroid.
4.2. The Fast Rotating Model (FRM)
The FRM [43], also called iso-latitude thermal model (ILM), was aiming for a better characterization of small, irregularly shaped, fast-rotating objects, which possibly also lack a dusty insulating regolith and have a high thermal inertia. Here, the temperature T only changes with latitude β, and half of the thermal emission originates from the night side: T (β) = Tss cos1/4β and Tss = [(1-A) S/(πεσ)]1/4 (beaming parameter η has the value of π). For a wide phase angle range, the STM and NEATM fluxes are higher than FRM fluxes, only at very large angles (larger than about 100°) the FRM fluxes exceed the NEATM fluxes, but still stay below the STM predictions. However, none of these models has been validated at these large phase angles.
4.3. Thermophysical Model (TPM)
The different TPMs [44] and references therein] typically allow to take the object’s spin and shape into account. They consider the true illumination and observing geometry, 1-D heat conduction into the surface, self-heating and shadowing effects, wavelength- and directional-dependent emissivity characteristics, and model surface roughness effects. TPM concepts are often used in the context of space mission targets, e.g., [45]. The TPM predictions are more realistic, but also require a detailed knowledge of the objects physical and thermal properties. Testing and validation of the TPM concepts have been conducted for objects down to the sub-kilometer size range (e.g., for the OSIRIS-REx and Hayabusa2 mission targets, Bennu and Ryugu, respectively). However, the decameter-size regime and the viewing geometries under extreme phase angles have not yet been fully verified.
4.4. Thermal Parameter
The dimensionless thermal parameter Θ characterizes the thermal behavior of an asteroid’s surface under solar radiation [40]. It is defined as: Θ = Γ√(ω)/(ϵσT3) where Γ is the thermal inertia (Jm−2K−1s−1/2), ω the angular frequency of the asteroid’s rotation (2π/P), with P being the rotation period, ϵ the emissivity of the surface, σ the Stefan-Boltzmann constant (5.67 × 10−8 Wm−2K−4), and T the subsolar temperature. The Moon temperature is very close to being in equilibrium with Sun-light and has Θ = 0.025, a fast-rotating, high-inertia object might be close to the isothermal-latitude model (with Θ ⟶ ∞), most asteroids are probably somewhere in between and require TPM considerations when predicting their IR brightness. As small asteroids tend to rotate faster [46], a high thermal parameter seems to be very likely for decameter-scale objects. However, the authors in [47–49] found low thermal inertia values for small, fast-rotating asteroids which would lower the thermal parameter again.
4.5. Flux Predictions
Without knowing the specific details of a given 20-m asteroid, it is essential to consider the extreme flux predictions. At opposition and for small phase angles, the highest fluxes are observed if the object is dark (low albedo), with a very rough surface, and viewed nearly pole-on. In this scenario, the thermal inertia or rotation period have minimal influence. In contrast, the lowest fluxes occur for a bright (high albedo), fast-rotating, high thermal inertia object seen equator-on, as described by the fast-rotating or isothermal-latitude model. At high phase angles (greater than approximately 90°), the situation becomes much more complex, and factors like surface roughness, thermal inertia, spin rate, and spin-axis orientation play significant roles. Furthermore, even the most sophisticated TPM are not fully validated, as reference measurements are lacking. In our study, we consider the following cases: (i) FRM (in red), (ii) NEATM with η = 1.0 (blue) and η = 1.5 (green), (iii) TPM predictions for a different spin-pole orientations (β = 45°, 60°, 90°), rotation periods of 6, 60, and 600 min, thermal inertia values of 10, 300, and 1000 Jm−2·K−1·s−1/2, and different levels of surface roughness. As a reference model for the Chelyabinsk progenitor object, we take our TPM solution for a spin-pole at β = 45°, a rotation period of 6 min, a thermal inertia of 300 Jm−2·K−1·s−1/2, and an intermediate level of surface roughness (r.m.s. of surface slopes around 20°).
The model predictions for a 20 m asteroid, observed under these extreme phase angles (see Figure 2(a), red line), vary by about two orders of magnitude, depending on the model concept and input parameters. The lowest fluxes (e.g., NEATM with η = 1.5, TPM with a low thermal inertia of 10 Jm−2K−1s−1/2) appear to be the most unrealistic, as they would imply a low-conductivity layer of dust (or a very porous regolith) on the surface of such a small object. Depending on the model predictions, the detection threshold of 100 μJy at 8 μm is crossed between 27 days and less than 3 days before impact. At shorter wavelengths, the detection lead times would decrease, while at longer wavelengths, they would slightly increase. According to our reference model (purple dashed line in Figure 4), the object exceeds the 100-μJy threshold at 8 μm approximately 10 days before impact, while still being fainter than magnitude 30 in the visible (as observed both from Earth and from L1).

Figure 4
5. SNR Calculations
For SNR calculations, we set up a telescope, detector, filter design based on the mission details provided in [12]. The system consists of a small survey telescope with an effective aperture of 50 cm and an f/4 focal ratio, located at the Sun-Earth/Moon Barycenter L1. The telescope has a field of view (FOV) of 1.7° x 7°, with no restriction regarding solar elongation at this stage (note that the NEO Surveyor mission is limited to a longitudinal range between 45° and 120° from the Sun and a maximum ecliptic latitude of 40° [11], while NEOMIR is planned to operate within a solar elongation range of 30° to 70° [12]). The telescope and payload are passively cooled to < 60 K to achieve sky-background-limited performance by minimizing telescope self-emission. The NEOMIR baseline concept uses a 2k × 2k HgCdTe detector, cooled down to 40 K, with an on-sky pixel scale of 3 arcsec (corresponding to a solid angle of 2.115 × 10−10 sr). The array has 100% filling factor, meaning no gaps between pixels. A single wide-band filter covers the 6–10 μm range, assuming 100% transmission within this range and no transmission outside. The optics and filter throughput is 75%.
The detection system assumes a dark current of 200 e−/s, a read-out noise RMS of 30 e−, and a quantum efficiency of 60%. The thermal self-emission and the straylight are both assumed to be 10% of the (sky + source) signal, independent of wavelength and solar elongation.
A point-source observed by the 50-cm telescope and projected onto the detector at 8 μm will have a Full Width at Half Maximum (FWHM) of the Point-Spread-Function (PSF) of about 3.4 arcsec. The Airy disk, which contains 84% of the point-source energy, has an angular radius of 4.0 arcsec and covers approximately 5.6 pixels on the detector. With a pixel size of 3 arcsec, the system is undersampled. To achieve Nyquist sampling, the pixel size should be half the FWHM, or about 1.69 arcsec in width. In order to reach the full spatial resolution, avoiding aliasing, and ensure accurate astrometric and photometric measurements, a dithering scheme or de-focusing strategy might be needed to improve the sampling of the PSF.
The SNR calculation is based on (a) the asteroid signal: calculated asteroid e−/s within the Airy disk multiplied by the effective exposure time texposure(s); (b) the noise signal: square-root of all e− contributions inside the Airy disk and integrated over the effective exposure time, including (i) sky background e−/s; (ii) calculated asteroid e−/s; (iii) dark signal e−/s; (iv) straylight e−/s (here, 10% of the sky background + asteroid e−/s is assumed); (v) thermal emission e−/s (here, 10% of the sky background + asteroid e−/s is assumed); (vi) (readout noise RMS e−/readout)2 within the Airy disk for the N readouts within the total exposure time.
The baseline concept from [12] envisions capturing images every 10 s, with at least 16 exposures per visit (alternatively, 16 exposures with 15 s each or 24 exposures with 10 s each). This strategy helps avoid trailing effects and allows for stacking and synthetic tracking techniques in the postprocessing phase. In our SNR calculation, we use 10 s as the readout time (which could actually be shorter, but then followed by an onboard averaging of a few frames) and 16 × 10 s as the total exposure time. Due to the proximity to the Sun, the very bright ZL significantly limits detection capabilities. However, during the last 2 days before impact, the background light drops by over one magnitude as the object moves away from the Sun. Additionally, the asteroid flux increases dramatically when approaching the L1-Earth region. Both the high zodiacal background near the Sun and the increasing asteroid brightness in the telescope’s FOV are critical factors that could lead to pixel saturation. Depending on the pixel well capacity, physical pixel size, and readout mode (such as single-correlated double sampling, Fowler sampling, or up-the-ramp sampling), the detector readout times must be kept short (on the order of a few seconds) to avoid saturation. During the peak flux (about one day before impact, see Figure 4), the 10-s exposure time would cause streaking effects. At that time, the Chelyabinsk progenitor moved at over 400”/min on the sky, corresponding to an on-detector path of more than 60” during a 10-s exposure. While the flux distribution across multiple pixels reduces the risk of detector saturation, it poses significant challenges for accurate photometry and astrometry [50]. Shorter exposure times (less than 10 s) would therefore be advisable. In this baseline concept, we have assumed 16 exposures of 10 s each, without accounting for any saturation limits or streaking effects.
Figure 5 shows the calculated SNRs as a function of time during the 15 days before impact. We define a SNR = 5 as the detection threshold. Under the specified conditions (total integration time 160 s), the 20 m Chelyabinsk progenitor object would have been detected with an SNR > 5 approximately 5-12 days before impact. The range in lead time is related to different assumptions for the aspect angle (angle between the object’s spin pole and the direction to the observer). The asteroid had an 8 μm model flux of about 220 μJy when it reached the SNR = 5 detection limit. At that time, it was moving on a very high zodiacal background and, as observed from L1, was only 21° away from the Sun. The largest uncertainty in these calculations stems from the model flux prediction when the asteroid is seen under such extreme phase angles (between 150° and 160°). For an isothermal object (small, fast-rotating, with high thermal inertia), a theoretical SNR > 5 detection would be possible more than 15 days before impact. Conversely, for an object seen equator-on in nearly instantaneous thermal equilibrium (slow rotator, low-conductivity surface), the object would only be detected 2-3 days before impact.

Figure 5
It is important to note that small objects observed at very large phase angles well beyond 100° are extremely faint at visible wavelengths. This is due to two main factors: (1) only about 10% of the incoming solar radiation is reflected by the object’s surface; and (2) only a small, thin illuminated crescent of the object is visible. In contrast, thermal IR observations capture the ∼90% of solar energy that is first absorbed by the surfaces and then re-emitted in the mid-IR. Owing to the typically fast rotation of very small asteroids [46], these objects tend to be nearly isothermal [43]. As a result, we observe the full disk emitting at its equilibrium temperature, with minimal dependence on phase angle. Mid-IR observations of such small objects at large phase angles can therefore achieve significantly higher SNRs compared to even much larger telescope observations at visible wavelengths.
6. Discussion
Our calculations assume that near-Sun observations are feasible. However, solar elongations below about 30° might be very challenging for different reasons. Thermal stability of the detector (or the entire satellite) might be a problem. Also, our assumption of the thermal noise contribution and, even more, the possible straylight contributions could be too optimistic when pointing very close to the Sun. Another topic is the very high background which leads to rapid detector saturation and requires short readout times, possibly followed by onboard averaging of frame sequences. Shorter exposure times help for the application of synthetic tracking techniques and minimize PSF elongation or streaking effects but create higher data rates in the satellite-Earth communication, possibly exceeding current L1 data rate limits.
One obvious problem in our calculations is related to the big uncertainties in the asteroid IR brightness calculation. Thermal models are not tested or validated for large phase angles beyond approximately 90°. Small objects also tend to rotate faster [46]. Are they covered by a low-conductivity fine-grain regolith? Are they composed of high-porosity boulders or do they resemble bare monolithic rocks? The corresponding surface temperature distributions would be very different; hence the IR fluxes differ considerably for these different cases. In addition, none of the available thermal models are tested at large phase angles. Typical NEA observations published in literature rarely exceed phase angles of 90°. Higher phase angles usually require observations at high airmass and/or during twilight (see e.g., [51]) which degrades the photometric quality considerably.
The FRM would apply in cases of short rotation periods (well below 1 h), combined with high thermal inertias (as expected for a bare-rock surface). But not all small bodies are fast rotators. In addition, a WISE-based thermal study [52] found beaming parameters between 1.0 and 1.5 for about 50 NEOs in the size range between 8 and about 100 m, far away from the FRM beaming parameter of 3.14 [47–49] studied the Yarkovsky semimajor axis drift rate of a rapidly rotating small asteroids. They used the Yarkovsky drift rate to constrain the thermal inertia and found unexpectedly low thermal inertias, indicative of a highly porous or cracked surface. All studies show no indications that fast-rotating decameter objects are predominantly isothermal and thus support the use of the NEATM over the FRM. However, neither the FRM nor the NEATM concepts have been tested or validated in the phase angle range beyond ∼90°. The TPM calculations incorporate physical and thermal properties, making the simulations appear more reliable. However, spin properties, surface roughness, and thermal inertia values are poorly constrained for these very small bodies. First validation steps were achieved by temperature measurements on the asteroid Ryugu with MARA onboard MASCOT lander which was released by the Hayabusa2 mission [53] and with OSIRIS-REx-OTES measurements of night-time temperatures on Bennu’s surface, which showed good agreement with TPM predictions [54, 55]. However, the disk-integrated mid-IR signal from an object observed under extreme phase angles is dominated by the small, warm crescent. It remains uncertain whether TPM disk-integrated predictions for such extreme phase angles and rough surfaces are still accurate.
Our calculations also assume that the Chelyabinsk progenitor is directly detected when the SNR exceeds 5, but this would require a constant monitoring of the entire available sky or at least a very short survey cadence to minimize the chances of missing such objects. The NEOMIR survey cadence could be as short as 10 h [12], in comparison to the NEO Surveyor survey cadence [11] that spans more than 10 days for the majority of the objects.
We also tried to find the best wavelength for such detections. The calculated SNRs increase slightly with wavelength and reach a maximum in the 10–13 μm range. But at the longer wavelength the telescope self-emission starts to degrade the quality of measurements and our assumptions of 10% thermal noise contribution become unrealistic. Also telescope and detector cooling requirements might not be sufficient for operating at longer wavelengths. With increasing wavelength, it is also more and more problematic to obtain high-quality astrometry as background stars disappear along the Rayleigh-Jeans tail of their spectral energy distribution.
We also investigated the theoretical detection capabilities of NEO Surveyor and NEOMIR for the Chelyabinsk progenitor. For the 6–10 μm band, our flux and SNR predictions remain valid, as both missions are expected to use a 0.5 m telescope. However, the very high sky background presents a critical challenge and must be addressed in the detector readout scheme to avoid saturation issues.
The limiting factor for both missions, at least in the context of the Chelyabinsk progenitor, lies in their currently planned fields of regard for sky surveys. The object would enter the 45–125° elongation range of NEO Surveyor (combined with an ecliptic latitude range of ±40°) approximately 38 h before impact. For NEOMIR, the lower elongation limit of 30° allows it to detect the object about 15 h earlier. However, would these 38 and 53 h for NEO Surveyor and NEOMIR, respectively, be sufficient to determine the object’s orbit, calculate an accurate impact trajectory, and issue a warning to the Chelyabinsk region?
These tasks would be highly challenging for such a fast-moving object, particularly against a sky background that decreases by more than an order of magnitude while the object itself increases in brightness by over two orders of magnitude during the availability window. The data processing system would need to handle detections with dramatically varying brightnesses, SNRs, and apparent motions, combining them into a single orbit calculation. Expanding the observing windows closer to the Sun (down to elongations of about 21°) would significantly ease these challenges, providing longer lead times, slower apparent motions, and more stable object and sky background fluxes.
7. Conclusions
The Chelyabinsk progenitor, approximately 20 m in size, approached Earth from a near-Sun direction, making it undetectable prior to impact by current survey projects. Our analysis demonstrates that a 50 cm telescope optimized for mid-IR observations and positioned at the Sun-Earth/Moon Barycenter Lagrangian point L1 could potentially detect such an object 5–12 days before impact. This is based on a realistic telescope and detector configuration, featuring a wide FOV, 10-s integration time, and a total of 160 s per field. However, this study assumes that observations at small solar elongations, as close as 20° to the Sun, are technically feasible. Overcoming challenges such as detector saturation and managing high data rates would be critical for the success of such a mission. The longer lead times, as compared to the 1.6 and 2.2 days for NEO Surveyor and NEOMIR, respectively, would facilitate an accurate orbit determination considerably, and possibly allow to issue warnings on time. The largest source of uncertainty in our calculations arises from estimating the IR brightness of objects observed under extreme phase angles exceeding 100° or even 150°, where surface properties and details of the thermal emission significantly affect detectability.
Conflicts of Interest
The authors declare no conflicts of interest.
Funding
This research was supported by the Agencia Estatal de Investigacion del Ministerio de Ciencia e Innovacion (AEI-MICINN), PID2020-120464GB-100; Research Council of Finland, 336546 and 359893. Open Access funding enabled and organized by Projekt DEAL.
Acknowledgments
J.L. acknowledges support from the Agencia Estatal de Investigacion del Ministerio de Ciencia e Innovacion (AEI-MICINN) under grant “Hydrated Minerals and Organic Compounds in Primitive Asteroids” with reference PID2020-120464GB-100. Research by K.M. was supported by the Research Council of Finland grants 336546 and 359893.