Establishing Earth's Minimoon Population through Characterization of Asteroid 2020 CD₃

An overview of all instruments used in this analysis is provided in Table 1. 2020 CD₃ was discovered on 2020 February 15.51 UT by the Catalina Sky Survey (CSS; Christensen et al. 2018) 1.5 m telescope on Mt. Lemmon (MPC observatory code G96). Upon discovery, the object was favorably placed near the ecliptic plane ∼45° east of opposition. The discovery image sequence consisted of four 30 s exposures, with ∼7 minute separation between each successive image, that were inspected soon after the final image by two observers and submitted to the MPC as a new NEO candidate. After the object was placed on the MPC's NEO Confirmation Page, additional same-night follow-up observations were performed with the same telescope that was used to discover 2020 CD₃.

Table 1. Telescopes Used in This Work and Their Purpose

Telescope	Aperture (m)	Astrometry	Photometry	Lightcurve
CSS Mt. Lemmon	1.5	$\checkmark$
Calar Alto Schmidt	0.8	$\checkmark$
Nordic Optical Telescope	2.5	$\checkmark$
Gemini North	8.1		$\checkmark$
Canada–France–Hawai'i Telescope	3.6	$\checkmark$
Lowell Discovery Telescope	4.3	$\checkmark$		$\checkmark$
U. of Hawai'i 2.2 m	2.2	$\checkmark$

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Multiple broadband photometric imaging was performed on 2020 February 24 with the 8.1 m Frederick C. Gillett Gemini North Telescope located on Maunakea, Hawai'i, USA. The Gemini Multi-Object Spectrograph (GMOS; Hook et al. 2004) observations consisted of three $r^{\prime} g^{\prime} i^{\prime}$ sequences with the G0301, G0303, and G0302 filters, taken in photometric conditions with Image Quality 85 (105 full zenith corrected seeing) or better seeing. The telescope was tracked nonsidereally at 2020 CD₃'s rate of motion, thereby maintaining its stellar point-spread function (PSF) for photometry but elongating the reference field stars. We also obtained sidereally tracked images in the three filters immediately before and after the nonsidereal tracking of 2020 CD₃ in order to perform absolute photometry.

To obtain 2020 CD₃'s photometric lightcurve, we employed the Large Monolithic Imager (LMI) on the 4.3 m Lowell Discovery Telescope (LDT, G37) for approximately 1 hr on 2020 February 27 UTC. Exposures were taken with 30 s integrations using a broadband VR filter that provides high throughput between approximately 500 and 700 nm. LMI was binned 3 × 3 for an effective plate scale of 036 pixel⁻¹ and the telescope was tracked at the nonsidereal rates of the target. On several later occasions, we used LDT/LMI to obtain astrometry with a similar technique but without any filters.

The 3.6 m Canada–France–Hawaii Telescope (CFHT, 568) on Maunakea, Hawai'i, USA, was used to obtain astrometry using nonsidereal tracking with exposures of up to 120 s in gri-band MegaCam images with no pixel binning. MegaCam has 0187 pixels allowing for precise astrometric measurements under good seeing conditions.

Astrometric observations were also made with the Alhambra Faint Object Spectrograph and Camera (ALFOSC) at the 2.5 m Nordic Optical Telescope (NOT, Z23) at the Roque de los Muchachos Observatory, La Palma, Canary islands, Spain. The exposures were tracked nonsidereally on 2020 CD₃. Each image's exposure time was set equal to the time it would take for 2020 CD₃ to move at most one stellar FWHM on the sky. Most of the 2020 CD₃ detections had signal-to-noise ratio (S/N) ≥ 15, but the last observations reached only S/N ∼ 5 as the target reached the detection threshold. The observations were performed without any filters with 4 × 4 pixel binning.

The University of Hawaii 2.2 m (UH 2.2, 568) telescope was used for astrometric observations with nonsidereal tracking at 2020 CD₃'s apparent rates of motion in unfiltered 300 s exposures. Additional astrometric observations were extracted from dedicated early observations obtained with the Calar Alto Schmidt telescope (Z84) in Spain. The detections were obtained from a set of short sidereally tracked frames, stacked with respect to the known motion of the object.

The image archives for several survey telescopes were searched for prediscovery observations of 2020 CD₃ by generating an ephemeris for each exposure and visually examining any potential matches. The 1.8 m Pan-STARRS1 telescope (F51) has an extensive archive dating back to 2010 (Chambers et al. 2016) and is sensitive to V ∼ 23, but no detections were found. The Zwicky Transient Facility (ZTF, I41) is an ongoing wide-field optical survey using the 1.2 m Palomar Oschin Schmidt telescope and has been in operation since 2018 (Bellm et al. 2019; Graham et al. 2019; Masci et al. 2019). No detections were found in its Data Release 3 (DR3) archive that extends from 2018 March to the end of 2019 December. The Chinese NEO Survey Telescope (CNEOST, D29; Zhao et al. 2007) is a 1.0 m Schmidt telescope at Xuyi, Jiangsu, China, equipped with a 3° × 3° camera. We searched images taken between 2018 January and 2019 May (when the telescope went offline for hardware upgrades) but did not find any matching fields. Lastly, we checked all of the telescopes used by the Catalina Sky Survey for prediscovery opportunities and found only two suitable fields imaged by the Mt. Lemmon telescope (G96) on 2019 November 9 and 2019 January 24, close to times when the object was expected to be at perigee and therefore relatively bright. Significant trailing losses, the spreading of the light from the target over many pixels due to its motion during an exposure, combined with nonoptimal sky conditions, prevented a detection in both images. In summary, the signals in the possible images were mostly smeared by trailing losses, and no detections were found from any of the mentioned surveys.

Due to the different observing strategies and capabilities of each instrument/telescope combination, each image set was astrometrically analyzed with different techniques. In some cases, a direct measurement on individual frames was possible by fitting 2020 CD₃'s detection to a stellar PSF or trail. In other cases, especially later in the apparition, we stacked multiple frames at 2020 CD₃'s (often rapidly changing) rates of motion to achieve sufficient S/N for a measurable detection. We carefully estimated our formal astrometric uncertainty by taking into account contributions from the object's S/N (often dominant) and also from the astrometric solution, now typically negligible thanks to the Gaia DR2 catalog (Gaia Collaboration et al. 2016, 2018; Lindegren et al. 2018), to which all the astrometry was calibrated. For all instruments used in the analysis, an assessment of the timing accuracy was also included. In most cases, a conservative timing uncertainty of 1 s was assumed. When timing biases were suspected, we only included the cross-track component of the astrometric position in the astrometric fit and deweighted the along-track direction. All acquired and remeasured astrometry is provided in Table 2.

The peculiarities of 2020 CD₃'s outgoing trajectory and, in particular, its low relative velocity with respect to Earth, kept the object at small geocentric distances for many weeks after discovery. As a result, most of the astrometric coverage was obtained when topocentric parallax was significant, and it is essential to know the precise and accurate location of the observing telescope, ideally to within a few meters in the Gaia catalog era. We therefore dedicated significant effort to obtain accurate coordinates and/or codes for all telescopes we used to extract observations of 2020 CD₃.

The raw GMOS-N data frames were reduced using standard techniques with the Gemini DRAGONS Python package (Data Reduction for Astronomy from Gemini Observatory North and South, AURA Gemini Observatory-Science User Support Department 2018). Nightly bias frames and twilight flats from the several nights surrounding the observations were used to create the master bias and flat fields. The DAOPHOT software package (Stetson 1987), embedded in the Image Reduction and Analysis Facility (IRAF; Tody 1986, 1993), was used to perform aperture photometry for all GMOS images. The photometry was calibrated to the Sloan Digital Sky Survey (SDSS) photometric system ($g^{\prime}$, $r^{\prime}$, and $i^{\prime}$, Fukugita et al. 1996) with the SDSS Data Release catalog 12 (Alam et al. 2015), accessed through the SkyServer platform. The resulting individual measurements and errors of GMOS photometry are provided in Table 3. The resulting magnitudes in each filter are mean values of individual measurements with respective filters. That way we diminish the effect of the brightness variations induced by the rotation of the asteroid.

Table 3. Gemini North Photometry of 2020 CD₃

Obs. id	Filter	Mag.	σINST	σZP
1	r'	22.399	0.037	0.048
2	i'	22.269	0.039	0.054
3	$r^{\prime}$	22.413	0.035	0.048
4	$g^{\prime}$	23.111	0.049	0.033
5	$i^{\prime}$	22.267	0.050	0.054
6	$r^{\prime}$	22.389	0.040	0.048
7	$g^{\prime}$	23.265	0.056	0.033
8	$i^{\prime}$	22.340	0.053	0.054

Note. The columns are, from left to right: sequential number of observation; filter; derived magnitude; instrumental error; zero-point error.

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The set of images obtained with LDT/LMI for the lightcurve were reduced using standard bias subtraction and flat-field correction from facility dome flats. 2020 CD₃'s photometry was measured using the Photometry Pipeline (Mommert 2017). This pipeline extracted sources with SourceExtractor using a 3 pixel (108) aperture (Bertin & Arnouts 1996), astrometrically registered the images based on the Gaia DR2 catalog (Gaia Collaboration et al. 2018), and then determined the zero-point calibration for each image by referencing to approximately 50 field stars from the Pan-STARRS DR1 catalog (Flewelling et al. 2020). The photometric calibration was performed by tying the VR images to the Pan-STARRS1 r_P1 band. This technique introduces errors in the absolute photometric calibration as the bands are not identical but they are significantly smaller than the typical uncertainty (∼0.1–0.2 mag) on the individual measurements. All data points for the lightcurve are provided in Table 4.

Table 4. Lightcurve Photometric Data for 2020 CD₃ Obtained with the LDT Translated to the ${r}_{{\rm{P}}1}$ Filter

Date (MJD)	Mag(${r}_{{\rm{P}}1}$)	${\sigma }_{\mathrm{ZP}}$	${\sigma }_{\mathrm{INST}}$
58906.4881610	22.7116	0.0228	0.1087
58906.4889677	22.6461	0.0215	0.1050
58906.4894715	22.8355	0.0224	0.1289
58906.4899752	22.6235	0.0227	0.1126
58906.4905406	22.9247	0.0216	0.1407
58906.4910444	22.8095	0.0227	0.1270
58906.4915481	23.0082	0.0226	0.1508
58906.4923176	22.8036	0.0218	0.1241
58906.4928214	22.9557	0.0227	0.1618
58906.4933251	22.6341	0.0213	0.1121
58906.4938292	23.1323	0.0232	0.1768
58906.4943329	22.8583	0.0225	0.1346
58906.4953404	22.7895	0.0231	0.1333
58906.4963479	22.8472	0.0229	0.1373
58906.4968516	23.1161	0.0243	0.1807
58906.4973554	23.1744	0.0229	0.1949
58906.5013856	22.9624	0.0229	0.1503
58906.5018894	22.9546	0.0232	0.1508
58906.5029427	22.8884	0.0239	0.1488
58906.5034464	22.6851	0.0234	0.1236
58906.5039502	22.9444	0.0226	0.1473
58906.5049578	23.1792	0.0225	0.1871
58906.5054615	23.0686	0.0220	0.1513
58906.5059652	22.9580	0.0224	0.1486
58906.5074792	22.7658	0.0227	0.1207
58906.5079829	22.9301	0.0223	0.1403
58906.5089904	22.9475	0.0224	0.1535
58906.5094942	22.6765	0.0228	0.1160
58906.5099979	22.8687	0.0225	0.1325
58906.5105017	23.0201	0.0225	0.1490
58906.5110060	22.6124	0.0221	0.1041
58906.5120135	22.6595	0.0231	0.1040
58906.5126895	23.1251	0.0223	0.1675
58906.5131933	22.6779	0.0220	0.1112
58906.5136970	22.9829	0.0231	0.1546
58906.5142007	22.6173	0.0221	0.1030
58906.5147052	22.9908	0.0232	0.1551
58906.5152090	22.6400	0.0225	0.1069
58906.5157131	23.0546	0.0228	0.1527
58906.5162168	22.6199	0.0219	0.1141
58906.5167207	22.6704	0.0226	0.1151
58906.5172244	23.1026	0.0226	0.1690
58906.5177281	22.6366	0.0217	0.1102
58906.5182319	22.8375	0.0225	0.1326
58906.5187356	22.8540	0.0232	0.1375
58906.5192395	22.8399	0.0220	0.1317
58906.5197432	22.6965	0.0221	0.1144
58906.5202471	23.0981	0.0220	0.1653
58906.5207509	22.7457	0.0214	0.1193
58906.5212546	22.8318	0.0218	0.1292
58906.5217587	23.0903	0.0221	0.1685
58906.5222624	22.7996	0.0216	0.1359
58906.5228400	22.6896	0.0227	0.1138
58906.5233449	22.9262	0.0230	0.1470
58906.5238487	23.1095	0.0217	0.1704
58906.5243527	22.7774	0.0224	0.1202
58906.5248564	22.7482	0.0228	0.1234
58906.5253602	22.7669	0.0222	0.1259
58906.5258639	22.9694	0.0228	0.1472
58906.5263677	22.7342	0.0225	0.1164
58906.5283826	23.1254	0.0226	0.1831
58906.5288865	22.8278	0.0224	0.1341
58906.5293902	22.7815	0.0221	0.1421
58906.5298940	22.7310	0.0239	0.1272
58906.5319088	22.7927	0.0230	0.1459

Note. The columns are, from left to right: observation date; measured magnitude; zero-point error; instrumental error.

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The astrometric data show that the motion of 2020 CD₃ is significantly affected by solar radiation pressure. Establishing its signature with a 3σ detection in about three weeks is two to three times faster than similar analyses in the past. The evolution of the development of the radiation pressure as a function of time is presented in Figure 1. This improvement is due to the enhanced precision and accuracy of the astrometry enabled by the Gaia DR2 catalog (Gaia Collaboration et al. 2018; Lindegren et al. 2018), which permits measuring individual ground-based positions with 005 accuracy.

In what follows, we interpret the nongravitational acceleration as a result of solar radiation pressure. Following Farnocchia et al. (2015b), we modeled solar radiation pressure perturbation as a purely radial acceleration A₁/r², where r is the heliocentric distance. The off-radial components, A₂ and A₃, of the Marsden nongravitational force model (Marsden 1969; Marsden et al. 1973) do not play a significant role in the albedo-density modeling, unlike for the orbital evolution. The A₁ parameter is proportional to the area-to-mass ratio A/m and therefore can provide useful constraints on the physical properties of the object and discern between a natural and artificial origin. For a spherical object,

$$\begin{eqnarray}&&{A}_{1}=A/m\left(1+\displaystyle \frac{4}{9}A\right)\displaystyle \frac{{G}_{S}}{c}\ ,\ A/m=\displaystyle \frac{3}{2D\rho },\end{eqnarray} \tag{ 1 }$$

where A is the Bond albedo, G_S is the solar constant, c is the speed of light, D the effective diameter, and ρ the density (Vokrouhlický & Milani 2000; Mommert et al. 2014b). We note that this formulation does not take into account the Yarkovsky effect (see Vokrouhlický 1998), which could contribute to 10%–20% of the total radial nongravitational acceleration (e.g., Chesley et al. 2014). Therefore, our calculation is an upper bound estimate of A/m.

The effective diameter D, absolute magnitude H, and geometric albedo p are related as (Pravec & Harris 2007)

$$\begin{eqnarray*}&&D=1329\ \mathrm{km}\displaystyle \frac{{10}^{-0.2H}}{\sqrt{p}},\end{eqnarray*}$$

while the Bond albedo A is the product of the geometric albedo p and the phase integral q,

$$\begin{eqnarray*}&&A=p\,q=p\,(0.009082+0.4061{G}_{1}+0.8092{G}_{2}),\end{eqnarray*}$$

where we have expressed the phase integral q in terms of the G₁, and G₂ photometric parameters (Muinonen et al. 2010).

We used a Monte Carlo approach to analyze 2020 CD₃'s past trajectory. We generated 1000 synthetic sets of orbital elements and area-to-mass ratios by sampling the uncertainty region as calculated from the fit to the astrometry. We modeled the solar radiation perturbation using all three coefficients (A₁, A₂, A₃) of the Marsden nongravitational model (Marsden 1969; Marsden et al. 1973). Given the size of 2020 CD₃ and its unknown shape, unlike for the calculation of the area-to-mass ratio, for orbit computation the off-radial components of the solar radiation pressure signature are significant on the timescale of the capture duration. We integrated each synthetic object backwards from 2020 until the object had been captured into the Earth–Moon system. The date of the first perigee within 1 lunar distance (LD) after the insertion into the Earth–Moon system is used as a proxy for the capture date.

Several synthetic objects's orbits were consistent with a lunar origin and their distribution at launch from the Moon's surface is provided in the Appendix assuming that the Moon is a sphere of radius 1737 km. In order to trace the possible origin of 2020 CD₃ from the Moon, we mapped the outbound trajectories of the samples originating from the Moon on the lunar surface. We computed the state vectors of the samples when leaving the Moon's surface and transformed them into the lunar mean Earth/polar axis body-fixed frame (Seidelmann et al. 2002) using NASA's Navigation and Ancillary Information Facility (NAIF) SPICE tools (Acton 1996; Acton et al. 2018).

We used astrometric observations obtained during the apparition to clearly detect solar radiation pressure acting on 2020 CD₃ and measure its area-to-mass ratio, $A/m=(0.65\pm 0.05)\,\times {10}^{-3}$ m² kg⁻¹. This value implies a natural origin for 2020 CD₃ because it is consistent with A/m for other natural objects in the same size range (Micheli et al. 2012, 2013, 2014; Mommert et al. 2014a, 2014b; Farnocchia et al. 2017) and much lower than typical for artificial objects (Jenniskens et al. 2016).

The derived photometric colors ($g^{\prime} -r^{\prime} =0.8\pm 0.1$, $r^{\prime} -i^{\prime} =0.15\pm 0.05$) support 2020 CD₃'s natural origin as we do not detect extreme reddening, which is associated with artificial objects (Miles 2011). Our broadband photometry suggests that 2020 CD₃ belongs to the group of silicate asteroids (Figure 2(a)), i.e., to the S or V complexes in the asteroid taxonomy (DeMeo & Carry 2013). Based on physical characterization alone, we cannot exclude that 2020 CD₃ is lunar ejecta, as lunar colors are similar to those of V-type asteroids. The C and X complexes, however, can be ruled out.

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We also extracted low-precision Gaia G-band photometry (Jordi et al. 2010) from our astrometric observations to derive the photometric phase curve and used it in an independent approach to constrain the spectral classification. The observations of 2020 CD₃ are limited to phase angles $36^\circ \lt \alpha \lt 56^\circ$ so that the backscattering region is not covered at all. The poor phase-curve coverage does not allow for the photometric data to be fit with the standard $({H}_{V},{G}_{1},{G}_{2})$ system in linear brightness space (Muinonen et al. 2010). Instead, we resort to the alternative technique of fitting for (H_V , G₁₂) in nonlinear magnitude space (Penttilä et al. 2016), where G₁₂ is forced to stay nonnegative and, thus, physically meaningful. The nominal solution, after converting G₁₂ to (G₁, G₂) and G band to V band assuming $V-G=0.2$, is $({H}_{V},{G}_{1},{G}_{2})=({31.88}_{-0.05}^{+0.03},{0.0}_{-0.0}^{+0.10},{0.535}_{-0.069}^{+0.0})$ (Figure 2(b)). We note that the formal uncertainty estimate for G₁₂ is meaningless because its nominal value is a result of forcing it to be nonnegative and the above uncertainty estimates have been obtained by bootstrapping.

Assuming characteristic slope parameters $({G}_{1},{G}_{2})$ for different asteroid taxonomic types (Shevchenko et al. 2016) and fitting only for H_V , we find better fits when using slope parameters typical for E, S, and M types than for P, C, and D types (Figure 2(b) and Table 5). Fixing the slope parameters and fitting only for H_V results in lower values for the Bayesian Information Criterion than fitting for both H_V and G₁₂, suggesting that the amount of data is not necessarily sufficient for a meaningful ${H}_{V},{G}_{12}$ fit let alone a full ${H}_{V},{G}_{1},{G}_{2}$ fit. The fit is also consistent with slope parameters typical for asteroid (4) Vesta (Gehrels 1967; Shevchenko et al. 2016), the most prominent member of V-type asteroids. These results are in excellent agreement with the photometric colors.

Table 5. Fits of the $H,{G}_{1},{G}_{2}$ System to the Photometric Phase Curve of 2020 CD₃

Fit Type	HV	G1	G2	wRMS	ΔBIC
H(E)	32.13	0.1505	0.6005	1.632	0.000
H(S/M)	31.79	0.2588	0.3721	1.635	0.4107
H(P)	31.63	0.8343	0.04887	1.658	3.310
H(C)	31.54	0.8228	0.01938	1.661	3.686
H(D)	31.69	0.9617	0.01645	1.661	3.763
$H,{G}_{12}$	31.88	0.000	0.5324	1.630	4.418

Note. The first five fits assume values for the G₁ and G₂ parameters typical for the spectral types mentioned in the parentheses and fit for H only. The last fit allows for both H and G₁₂ parameters to be fitted, but requires $0\lt {G}_{12}\lt 1$, which is a physically meaningful range. The last two columns provide the weighted r s (wRMS) value and the Bayesian Information Criterion with respect to its lowest value (ΔBIC). These results have been computed with the online calculator available at http://h152.it.helsinki.fi/HG1G2/.

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In an alternative, synoptic, approach when fitting the radial component A₁ to photometry, the fit to the photometric phase curve results in an absolute magnitude ${H}_{V}=31.9\pm 0.8$ for 2020 CD₃. The value is consistent with a purely photometric fit, but the error estimates are more conservative. Assuming the distribution of possible values of the geometric albedo (${p}_{V}=0.26\pm 0.08$ for S types, and 0.34 ± 0.11 for V types; Mainzer et al. 2012) and the phase-curve fit for the H magnitude for S- or V-class asteroids, we obtain a diameter of ${1.2}_{-0.2}^{+0.4}$ m, 1 of the 10 smallest NEOs ever found as of 2020 August 10, and among the best characterized with colors, rotation period, and AMR. The derived size is consistent with the nondetection of 2020 CD₃ by the Arecibo radar assuming a nonmetallic material composition, excluding an artificial body or an M-type asteroid (P. Taylor 2020, personal communication).

Thus, all our evidence suggests that 2020 CD₃ is of spectral type S or V. Although little is known of the color distribution of meter-class asteroids, our result is consistent with the observed taxonomic distribution of NEOs with diameters <200 m where S-class objects dominate (Binzel et al. 2019). Furthermore, it is consistent with extrapolations of the asteroid taxonomic and orbital element distribution to small NEOs on Earth-like orbits, the minimoon source population, which suggest that for H ∼ 24.5, corresponding to S-type asteroids of ∼40 m diameter, S types make up about 40% of the population (Jedicke et al. 2018b).

The lightcurve of 2020 CD₃, despite its relatively low S/N, shows a strong peak at 0.026 hr in a Lomb–Scargle periodogram and a clear minimum in χ² residuals from Fourier fits to the data at a period = 0.0530 hr (Figure 3). These reduced χ² residuals (normalized by the degrees of freedom) were computed for third-order Fourier fits across a range of periods from 0.0001 to 2 hr at a step size of 0.0001 hr. Second- and fourth-order Fourier series produced overall higher χ² values. An approximate 1σ error on the period of 0.0011 hr was estimated as the FWHM of the deepest minimum in the χ² plot. Phasing the data to periods at the limits of this uncertainty range resulted in clear decoherence of the periodic signal. The best-fit period 0.0530 ± 0.0011 hr is consistent with the Lomb–Scargle periodogram. In particular, given the apparent ∼0.5 mag peak-to-peak amplitude, the second-order harmonic (P = 0.053 hr) is the most probable interpretation of the Lomb–Scargle peak for data obtained at a phase angle of 55° (Butkiewicz-Bąk et al. 2017). We note that the best-fit rotational period is shorter than the individual integration times of the color photometry. Therefore, the brightness variation due to the rotation of 2020 CD₃ is averaged out in individual photometric color measurements. Assuming a double-peaked lightcurve, a period of about 3.2 minutes (∼190 s) is a reasonable interpretation; however, due to the low S/N of these data, the period is not strongly constrained. Nonprincipal axis rotation cannot be ruled out with the available data. The observed rotational period is at least an order of magnitude slower than the predicted mean value from a Maxwellian rotational distribution for meter-sized objects (Bolin et al. 2014). This implies that radar may be better suited for the detection of minimoons than had been previously anticipated, because the radar signal is smeared less by asteroid rotation than suggested by extrapolations of size–rotation-rate models.

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The two unknowns in Equation (1) are the albedo and density, but they are constrained by the other measured parameters. Given that our photometric model implies that 2020 CD₃ is either an S- or V-type asteroid, we generated synthetic albedos for 10,000 of each type according to the type-specific albedo distributions of Mainzer et al. (2012). Similarly, we generated the same number of random A₁ values using a normal distribution with a mean and width given by the central value and uncertainty on our measured ${A}_{1}=(3.1\pm 0.2)\times {10}^{-9}$ m s⁻². The pairs of synthetic albedo A₁ values were then used to calculate the object's density (Figures 2(c)–(d)). For the S-type assumption, we find $\rho =2.1\pm 0.4$ g cm⁻³ whereas for the V-type assumption, ρ = 2.4 ± 0.5 g cm⁻³. In both cases, the inferred density is consistent with typical asteroid densities (Carry 2012). We note that the possible effect of the Yarkovsky force can potentially increase the estimated density values by 10%–20% (Chesley et al. 2014) so that our density estimates represent the lower bound of values. However, this does not have a major impact on the interpretation of the results.

Thus, our physical characterization of 2020 CD₃ indicates that it is a silicate body, perhaps a free-floating analog of what appear to be monolithic boulders found on the surface of larger asteroids such as (25143) Itokawa, the S-type asteroid investigated in situ by the Hayabusa spacecraft (Saito et al. 2006). Alternatively, it could be a small rubble-pile aggregate more like 2008 TC₃ (e.g., Jenniskens et al. 2009). While the internal structure of meter-scale asteroids is currently unknown, we expect that favorable appearances of small NEOs and future minimoons will provide more opportunities for detailed characterization of these small asteroids.

Integrating 2020 CD₃'s trajectory into the past indicates that it was bound to Earth and its orbit was deterministic after a close approach to the Moon on 2017 September 15 (Figure 4(a)). Prior to this encounter, there are three possible behaviors: (1) 97.3% escape the Earth–Moon system, corresponding to a scenario in which this encounter is responsible for the capture of 2020 CD₃ by the Earth–Moon system; (2) 1.4% intersect the Moon's surface, which corresponds to the hypothesis that 2020 CD₃ is lunar ejecta; and (3) 1.3% remain in Earth orbit (potentially for more than 10 yr). Therefore, we conclude that 2020 CD₃ was in orbit around Earth since at least 2017 September 15. Since then, it completed 11 orbits around the Earth with intervals between successive perigees of 70–90 days. Its minimum geocentric distance was between 12,900 and 13,400 km on 2019 April 4, and it escaped Earth's Hill sphere (∼0.01 au) on 2020 March 7 after a final perigee on 2020 February 13 at a geocentric distance of about 47,000 km. Oddly, it passed its last perigee just two days before its discovery. 2020 CD₃'s Earth-like orbit means it has a long synodic orbital period so it will not approach Earth again until 2044 March at about 10 lunar distances, well outside Earth's Hill sphere.

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The capture duration of 2020 CD₃ of at least 2.7 yr (Figure 4(b)) may seem exceptionally long considering that orbital simulations suggest that the average capture duration of minimoons is about nine months (Fedorets et al. 2017). However, there is an inverse correlation between the average capture duration and the minimum lunacentric distance when the encounter distance is less than 30,000 km (Figure 4(c)). In such cases, minimoons may become captured over years or even decades. Although only ∼2% of minimoons have capture durations greater than three years, those objects' total capture duration time is 23% of the cumulative capture duration time of all simulated minimoons. Based on the close encounter of 2020 CD₃ with the Moon, it is not surprising that 2020 CD₃ undergoes a longer geocentric capture than an average minimoon. The distribution of possible capture durations of 2020 CD₃ is thus in agreement with theoretical predictions (Figure 4(b)).

We argue that a lunar origin for 2020 CD₃ is highly unlikely (see Section 4.3) and therefore assume that the object originated in the main asteroid belt. Based on its precapture heliocentric orbit, it has a (72 ± 1)% probability of having been ejected by the ν₆ secular resonance with, primarily, Saturn (Granvik et al. 2018). A provenance in the inner main belt would also favor its identification in the S-type taxonomy because S types dominate that region of the belt. There is a (28 ± 1)% probability for it having originated in the Hungaria region and a negligible (0.5 ± 0.03)% probability that it was ejected from the outer region of the main belt by the 3:1 mean-motion resonance with Jupiter. The reported uncertainties on the probabilities are the standard error on the mean across several discrete cells in the Granvik et al. (2018) NEO population model. An inner belt source for 2020 CD₃ is in agreement with a silicate-rich asteroid composition, which is dominant in that region (DeMeo & Carry 2014).

There is a possibility that 2020 CD₃ could have been spall ejected by a recent lunar impact event (Section 4.2), and we assess the likelihood of this scenario by examining the contemporary production rate of small craters on the Moon.

The largest crater to form annually on the Moon is approximately 50 m in diameter based on a survey of fresh impact craters identified on the Moon using "before" and "after" images from the Lunar Reconnaissance Orbiter (LRO) Narrow Angle Camera (NAC; Speyerer et al. 2016). Accordingly, if 2020 CD₃ was launched from the lunar surface on 2017 September 15, a crater of this scale would need to be capable of launching a meter-sized minimoon off the Moon and onto the trajectory described above.

An asteroid striking the Moon creates a crater approximately 20 times its own size (Melosh 1989) so a 2.5 m diameter projectile can make a 50 m diameter crater. Hirase et al. (2004) investigated the relationship of ejecta velocity relative to the ejecta-to-impactor diameter ratio in laboratory experiments, an analysis of secondary craters produced by lunar and Martian craters, and ejecta from the asteroid (4) Vesta that make up the Vesta family (often called Vestoids). At an ejecta/impactor diameter ratio of ∼0.4, corresponding to the ejection of a 1 m diameter minimoon by a 2.5 m diameter projectile, the typical ejection speeds are a few tens of m s⁻¹ and certainly <100 m s⁻¹—much smaller than the lunar escape velocity (∼2400 m s⁻¹). Indeed, the results of Hirase et al. (2004) analysis suggest that launching a 1 m diameter minimoon off the lunar surface requires the impact of a kilometer-scale asteroid, an unlikely event that surely would have been noticed on or soon after 2017 September 15. Furthermore, the population of NEOs is ≳90% known at this time, and no impacts were predicted on that date. Accordingly, we reject a lunar ejecta origin for 2020 CD₃. In summary, while NEO-based models (Granvik et al. 2012; Fedorets et al. 2017) indicate that an annual capture of a meter-sized asteroid is likely, the production of similar-sized lunar ejecta at the same rate can be ruled out. Hence, minimoon capture from the NEO population is a dominating mechanism for maintaining the minimoon steady-state population.

An additional blow to the lunar origin hypothesis for 2020 CD₃ comes from lunar meteorites that were blasted off the Moon in the past. Warren (1994), whose analysis builds on the work of Melosh (1985), argues that most lunar meteorites came from lunar craters that were hundreds of meters to several kilometers in diameter and that the meteoroid precursor bodies to the meteorites were 2–10 cm in diameter prior to entering Earth's atmosphere. Lunar meteorite cosmic-ray exposure ages indicate that only about half took less than 100,000 yr to get to Earth (Warren 1994). Given that minimoon orbital lifetimes are typically on the order of a year, it implies that those meteoroids spent most of their time on heliocentric orbits before being delivered back to Earth, not in the Earth–Moon system. Taken together, it suggests that it is difficult for small craters to launch sizable bodies off the Moon; if small impact events could do so, we might expect very young lunar meteorites to dominate the fall and find record on Earth.

We emphasize that the impact capable of producing an ejecta of the size of 2020 CD₃ would have been very bright. Moreover, the distribution of the subset of sample orbits originating from the Moon point the majority of them to the part of the dark size of the Moon facing toward Earth, providing optimal observing conditions (see the Appendix). No major impacts have been reported, including the NELIOTA telescope (Xilouris et al. 2018), the NASA lunar impact monitoring (W. Cooke 2020, private communication). Moreover, no reports of new kilometer-sized craters on the Moon have been announced.

In summary, we consider the lunar origin of 2020 CD₃ to be extremely unlikely.

The discovery of 2020 CD₃ occurred at the last window of opportunity (Figure 5). However, simulations by Fedorets et al. (2020), and the fact that 2006 RH₁₂₀ was discovered only three months into its captured time period of one year, suggest that the last-minute discovery of 2020 CD₃ is not a typical situation. During the undisputed capture period of 2.7 yr, there were six distinct intervals during which 2020 CD₃ was brighter than the discovery observatory's (CSS's Mt. Lemmon) limiting magnitude (Figure 5). It even briefly reached V < 16 when it approached to within about 20,000 km, below the orbits of geosynchronous satellites. The problem is that during the detectability windows, when it was bright and close to Earth, it also had a high apparent rate of motion so that it would have left a trailed image on the detector, spreading out the light from the object and reducing the per-pixel S/N to a level below the system's detection threshold. Taking these trailing losses into account, there were only three 2 hr time segments during the entire 2.7 yr in which 2020 CD₃ was detectable by the Mt. Lemmon telescope, corresponding to ∼0.03% of the time under the best of circumstances. A similar analysis for the Pan-STARRS1 telescope (Chambers et al. 2016) finds that there were only four short time periods during which it could have detected 2020 CD₃. Pan-STARRS1 reaches a fainter limiting magnitude than Mt. Lemmon due to its larger aperture and better seeing statistics, but its smaller pixels makes it less sensitive to fast-moving objects like minimoons.

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We expect there to exist a much larger but undiscovered population of minimoons that are similar or smaller in size than 2020 CD₃ (Fedorets et al. 2017; Granvik et al. 2012)—they are just difficult to detect due to their faintness, rate of motion, and infrequent windows of observational opportunity (Figure 5). Estimating the minimoon population's size–frequency distribution by debiasing the discovered population of two objects is essentially impossible given that they are so difficult to detect and were at the limit of the system's detection capability. In addition to the two minimoons discovered by CSS, observations of meteors created by meteoroids that had a high probability of being geocentric prior to entering the atmosphere (Clark et al. 2016; Shober et al. 2019) support the existence of a minimoon population. These meteor observations are also difficult to convert into a minimoon population estimate because a meteor's apparent brightness, in both the optical and radar, is dominated by the meteoroids diameter and its speed. Because meteors generated by minimoons have the lowest possible meteor speed, essentially equal to Earth's escape speed, they are the faintest possible meteors. Thus, in order for them to be bright enough to be detected, they must be large and therefore rare.

To quantify the detection frequency of minimoons, we apply Bolin et al.'s (2014) modeling of the performance of Pan-STARRS1 survey (PS1; Chambers et al. 2016) to the CSS's Mt. Lemmon observatory that discovered both of the telescopically identified minimoons. The application is appropriate because the two observatories have roughly similar capabilities, especially considering all the difficulties involved in modeling the detection of faint, fast-moving minimoons, and the statistics of just two objects. The modeled PS1 survey has a peak probability of detecting minimoons at H_V  = 31.5 ± 1.5 so Mt. Lemmon's discovery of 2020 CD₃ with H_V  = 31.9 ± 0.8 is not surprising. Furthermore, Bolin et al. (2014) estimated that PS1 (and therefore Mt. Lemmon) could detect about 0.01 minimoons per lunation or about one every ∼8.1 yr as compared to the ∼14 yr interval since CSS's discovery of 2006 RH₁₂₀. We think the ∼2× discrepancy in the time interval is not significant given that (1) Bolin et al. (2014) used the earlier and larger minimoon size–frequency distribution of Granvik et al. (2012) compared to the revised distribution of Fedorets et al. (2017) and because (2) it is intrinsically difficult to model discovery rates at the limits of detectability in both flux and rate of motion (see Figure 5). Moreover, assuming Poisson-like discovery statistics and that the CSS Mt. Lemmon survey has been in operation at roughly the same capability level for 20 yr, over the same period, there is a ∼68% probability of discovering ≤2 minimoons. Therefore, the discovery of 2020 CD₃ 14 yr after the discovery of 2006 RH₁₂₀, a minimoon with H_V  = 29.9 ± 0.3, is in line with the capture frequency of minimoons predicted by existing population models and consistent with their predicted discovery rate (Bolin et al. 2014).

An additional complication in debiasing the minimoon population identified in asteroid surveys is the difficulty of identifying rare natural objects among numerous artificial ones (Jedicke et al. 2018a). As sky surveys have become more powerful and efficient at identifying faint and trailed objects, they have been detecting ever more artificial geocentric objects, often on minimoon-like orbits. Distinguishing both 2020 CD₃ and 2006 RH₁₂₀ from artificial objects upon their discovery was initially inadvertently affected by human biases that objects on geocentric orbits are artificial and correcting the observation statistics for this bias will be difficult.