Goldstone Radar Observations of Horseshoe-orbiting Near-Earth Asteroid 2013 BS45, a Potential Mission Target

Near-Earth asteroid (NEA) 2013 BS45 was discovered on 2013 January 20 by J. V. Scotti with the 0.9 m Spacewatch telescope at Steward Observatory (MPEC 2013-B72). The asteroid has an absolute magnitude of H = 25.9 (JPL Horizons database: https://ssd.jpl.nasa.gov/horizons.cgi, Giorgini et al. 1996), but no other physical properties are known. There are no light curves or visible-infrared spectra measured for this object. Prior to the radar experiment, we guessed a diameter of ∼20 m from the asteroid's absolute magnitude and by assuming an optical albedo of 0.2.

2013 BS45 is currently the main backup target for the NEA Scout mission (Pezent et al. 2018). The primary target of NEA Scout is another small asteroid, 1991 VG, with an absolute magnitude of H = 28.3. The Pezent et al. (2018) dynamical study also considered 2013 RZ53, 2007 UN12, and 2008 EA9 as backup targets. Only 1991 VG and 2013 BS45 have well determined orbits, with Orbit Condition Code of 0, according to the JPL Horizons database.

NEA Scout will be launched as a secondary payload on NASA's Space Launch Vehicle Exploration Mission One in 2019 December. The spacecraft could reach 1991 VG within 2 yr and 2013 BS45 within 3.5 yr (Pezent et al. 2018). 2013 BS45 has the brightest absolute magnitude and may be the largest object among the potential NEA Scout destinations, and it is the only candidate target for which radar observations exist. 2013 BS45 is also on the Near-Earth Object Human Space Flight Accessible Targets Study list (https://cneos.jpl.nasa.gov/nhats/) where it ranks among the most accessible objects with an Orbit Condition Code of 0.

2013 BS45 has an Earth-like orbit with a semimajor axis, a, of 0.99 au, eccentricity, e, of 0.08, and an inclination, i, of 08. It belongs to the Aten class of NEAs. When viewed in a rotating reference frame that follows Earth around the Sun, the orbit is shaped like a horseshoe with Earth located between the ends (Figure 1). One of us (P. W. Chodas 2018, personal communication) noted the asteroid's resonant behavior only 4 days after the asteroid's discovery. de la Fuente Marcos & de la Fuente Marcos (2013) were the first to publish a dynamical study of the 2013 BS45's orbit. They noted that the asteroid would remain in a symmetric horseshoe orbit for about 1000 yr with a libration period of ∼160 yr. The most recent close approach was at 0.0126 au on 2013 February 12 shortly after the asteroid's discovery. Here we report radar observations that put constraints on the diameter, period of rotation, optical albedo, and radar scattering properties for this object.

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2013 BS45 approached Earth within 0.0126 au (4.9 lunar distances) on 2013 February 12, only three weeks after its discovery. Assuming a purely ballistic trajectory, the 2013 flyby was the closest in more than 230 yr and for at least the next 300 yr. We observed it at Goldstone (8560 MHz, 3.5 cm) on February 10, 12, and 13 (Table 1) as a target-of-opportunity during time originally scheduled to observe (3752) Camillo. 2013 BS45 was too far north for Arecibo to observe it during the week of the closest approach, and planned observations at Arecibo on February 14–18 were canceled due to equipment problems.

Based on the close approach distance, a diameter that we assumed would be roughly 20 m, and an assumed period of 0.5 hr, we estimated maximum signal-to-noise ratios (S/Ns) for 2013 BS45 of 160 per day. We expected to obtain echo power spectra, ranging measurements, and possibly delay-Doppler images.

We used two observing set-ups: an unmodulated continuous waveform (CW) and a binary phase-coded (BPC) CW. We transmitted a circularly polarized electromagnetic wave that reflects off the target in both the same (SC) and opposite (OC) sense of circular polarization as the transmitted wave. Echoes from a surface that is smooth at decimeter scales will return almost entirely in the OC polarization. SC echoes can result from multiple scattering from rough surfaces, single scattering from surfaces with radii of curvature comparable to the radar wavelength, and from coherent backscattering. The ratio of the echo power strengths, SC/OC, is a proxy for the target's near-surface complexity or roughness (Ostro et al. 2002).

The target's rotation spreads the reflected signal in Doppler frequency. The Doppler broadening or bandwidth of the echo is defined as

$$\begin{eqnarray}&&B=\tfrac{4\pi D}{\lambda P}\cos (\delta ),\end{eqnarray} \tag{ 1 }$$

where B is the bandwidth, P is the rotation period, D is the diameter, λ is the radar wavelength, and δ is the subradar latitude.

We started observing 2013 BS45 on February 10 with a CW set-up (Table 1). The echo bandwidth was at least 120 Hz, and we updated the JPL orbital solution 14 with a Doppler correction of +40 Hz (Table 4). On the second day, we obtained 10, 11, and 1 μs ranging detections with our BPC set-up. These observations are coarse-resolution imaging that puts the echo into 1–2 pixels for the purpose of improving the orbital solution. On the last day, February 13, we obtained more CW echo power spectra and ranging data at resolutions up to 0.125 μs (18.75 m). Table 1 summarizes the observations.

Figures 2(A) and (C) show daily sums of echo power spectra obtained on February 10, 12, and 13 processed with 10 Hz and 20 Hz resolutions, respectively. The OC echoes appear fairly symmetric and have weak S/Ns. The low S/Ns precluded subdividing the data to look for bandwidth variations and other features. The asteroid traversed 25° across the sky on February 10–13, but the spectra do not show obvious bandwidth changes that would suggest a shift in the subradar latitude (Equation (1)).

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Table 2 lists echo bandwidths from each day estimated by eye and by fitting curves to the spectra reduced at 10 and 20 Hz resolutions. The bandwidths were estimated by first fitting a second-order polynomial to the adjacent points that have S/Ns above 2, followed by determining the width where the fit crosses the 2σ line. This is a very conservative approach, and we treat the results as lower bounds. For completeness, we also include in Table 2 the bandwidth measurements based on the zero-σ crossing based on both fits and estimated by eye.

The 10 and 20 Hz resolution data yield daily bandwidths of at least 120 Hz (Table 2) based on polynomial fits and the 2σ threshold. For comparison, bandwidths estimated visually based on where the data points cross the 2σ threshold are at least 100 Hz. We summed all available data from February 10–13 to increase the S/Ns, and the final sums are shown in Figures 2(B) and (D). The lower bandwidth estimates from the fits are 130 Hz for 10 Hz resolution data and 120 Hz for 20 Hz resolution data. The visually estimated values are 130 and 140 Hz for the two processing resolutions. The differences in the fitted and visually estimated bandwidths are caused by the shape of the second-degree polynomial function that is only a rough approximation of the true shape of the echo. We repeated this entire analysis with the zero-σ cut-off and we found that the lower bandwidth estimate would have increased by at least 10 Hz. For echoes with strong S/Ns, the edge frequencies are usually obvious, but for weak S/Ns such as those here, receiver noise obscures the edges.

Let us adopt a bandwidth of 120 Hz as a conservative lower bound and explore its implications for the rotation period and diameter. We can obtain an approximate diameter using an expression from Harris & Harris (1997):

$$\begin{eqnarray}&&D=\left(\tfrac{1329\,\mathrm{km}}{\sqrt{{p}_{v}}}\right)\times {10}^{-0.2H},\end{eqnarray} \tag{ 2 }$$

where H is the absolute magnitude and p_V is the optical albedo. If we use H = 25.9 and adopt p_V = 0.20, which is a typical S-class albedo (Pravec et al. 2012), then we obtain D = 20 m. If we combine this diameter with the lower bound on the bandwidth of 120 Hz, then Equation (1) strongly suggests that 2013 BS45 is a very rapid rotator with a period that could be less than one minute. If 2013 BS45 is larger than 20 m, then the rotation period could be slower, but it seems unlikely that the period is much slower than several minutes.

The rotation period can be refined if we have radar constraints on the object's size. The 18.75 m resolution image from February 13 shows an echo that occupied a single row after ∼30 minutes of data integration (Figure 3). If the asteroid were a sphere, then the visible extent would correspond to its radius. If we assume that 2013 BS45 is a sphere, then its diameter is at most 37.5 m.

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If we assume D ≤ 37.5 m, then Equation (1) places an upper bound on the period of P ≤ 1.9 minutes × cos (δ). According to the Asteroid Lightcurve Database (http://www.MinorPlanet.info/lightcurvedatabase.html, Warner et al. 2009, 2018 June 23 update), 2013 BS45 is in the top 14% among the most rapidly rotating NEAs with H ≥ 23.

Table 3 lists the disk-integrated properties. The OC cross-section obtained from a weighted sum of all the data is ${\sigma }_{\mathrm{OC}}$ = 1.0 × 10⁻⁴ km² ± 35%. We assigned a 35% error in order to account for systematic calibration and pointing errors (Benner et al. 1997; Ostro et al. 2003) such as small deviations from the OC system temperature of 18 K that we adopted in the radar cross-section calculations.

Table 3.  Disk-integrated Properties

Date	Runs	Looks	RTT	OC	σOC × 10−4	SC/OC
UTC			(s)	S/N	(km2)
Feb 10	137	26460	12.9	16	1.0	0.23 ± 0.07
Feb 12	30	4800	12.5	12	1.4	$0.{04}_{-0.04}^{+0.08}$
Feb 13	72	12520	12.7	13	1.0	0.27 ± 0.09
All data	239	43780	⋯	22	1.0	0.21 ± 0.0.05

Note. Disk-integrated radar properties. σ_OC is the OC radar cross-section and SC/OC is the circular polarization ratio estimated from the echo power spectra processed with 20 Hz resolution (Figure 2(C)). We adopted the OC system temperature of 18 K and the SC system temperature of 19 K in our calculations. The 1σ errors on the SC/OC values were calculated based on Appendix I in Ostro et al. (1983). We list the number of runs and number of looks for the start-stop times listed in Table 1. We list the round-trip time to the object at the time of the observations. OC S/Ns are the optimally filtered S/Ns for the OC echo power spectra. The last line, All Data, shows values calculated from a weighted sum of all the data (Figure 2(D)). The OC radar albedo (η_OC) is calculated by dividing the weighted sum radar cross-section by the object's projected surface area, which was calculated by approximating the asteroid's shape with a sphere with a diameter of 37.5 m, the maximum value consistent with our imaging data. OC radar albedo η_OC = σ_OC/Area ≥ 0.09.

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Table 3 also lists the circular polarization ratio, SC/OC, for each day. The values show significant variations from day-to-day, which is often seen for NEAs with low S/Ns (Benner et al. 1997; Brozović et al. 2018). The SC/OC value from a weighted average of all the data is 0.21 ± 0.05. For the SC/OC error, most systematic effects cancel, and the remaining uncertainty is largely statistical and stems from the receiver noise (Ostro et al. 1983). For comparison, the mean SC/OC for 214 NEAs reported by Benner et al. (2008) is 0.34 ± 0.25 and for 27 objects within the same study with an H > 23, SC/OC = 0.28 ± 0.23. 2013 BS45 has a slightly lower value of SC/OC than most NEAs implying a near-surface that is relatively smooth on decimeter spatial scales.

Benner et al. (2008) found that the C-class taxonomy has SC/OC = 0.28 ± 0.12 (N = 17), the S class has SC/OC = 0.27 ± 0.08 (N = 70), while the E, V, and X taxonomies have a mean SC/OC > 0.6. As such, the circular polarization ratio suggests that 2013 BS45 could be an S-class or C-class object, and it probably excludes the V and E classes. For comparison, the SC/OC of three NEAs visited by spacecraft are 0.28 ± 0.06 for 433 Eros (Magri et al. 2001), 0.29 ± 0.01 for 4179 Toutatis (Ostro et al. 1999), and 0.27 ± 0.04 for 25143 Itokawa (Benner et al. 2008). SC/OC for future spacecraft targets are 0.19 ± 0.03 for 101955 Bennu (Nolan et al. 2013) and 0.20 ± 0.02 for 65803 Didymos (Benner et al. 2008).

We obtain a lower bound on the OC radar albedo of η_OC ≥ 0.09 by dividing the weighted sum of the OC cross-section, 1.0 × 10⁻⁴ km², by the projected area of a sphere with an equivalent diameter set to an upper bound of the object's size. For comparison, the average OC albedo calculated from 40 NEAs that have been observed by radar and that have an estimate of their sizes is η_OC = 0.20 ± 0.12, https://echo.jpl.nasa.gov/~lance/asteroid_radar_properties/nea.html).

The nominal OC radar cross-section can be used to constrain the diameter of 2013 BS45 if we assume some extreme values of the radar albedo. If we adopt a very low radar albedo of 0.02, similar to that reported for NEA 1566 Icarus (Greenberg et al. 2017), then we get an upper bound on the diameter of D ≤ 80 m. If we adopt a very high radar albedo of 0.58, equal to the value reported for a metallic NEA (6178) 1986 DA (Ostro et al. 1991) as our upper bound on η_OC, then we get a lower bound on the diameter of D ≥ 15 m. We can exclude the diameter of ∼80 m computed from assuming the low radar albedo value based on the range extent in the 18.75 m resolution image, but the diameter of ∼15 m obtained from the high radar albedo value is not excluded by the data, and it represents a reasonable lower bound on the object's size.

We can constrain the visual geometric albedo from the bounds on the equivalent diameter, 15 m ≤ D ≤ 37.5 m, and the absolute visual magnitude of H = 25.9. The optical albedo calculated using Equation (2) gives 0.05 ≤ p_V ≤ 0.35. The wide range of optical albedos allowed does not rule out any of the spectral classes.

Table 4 lists three Doppler and three delay radar measurements and their residuals with respect to the final orbital solution 32. The Doppler measurements were estimated based on the polynomial fits shown in Figure 2. The Doppler measurements in Table 4 replaced a single Doppler measurement that was estimated visually during the observations on February 10. The round-trip delay measurements are those reported during the track. At the time of the observations, the radar astrometry reduced the 3σ time-delay uncertainties by a factor of ∼3200.

Our orbital model uses the DE431 planetary ephemeris, an Earth J₂ oblateness model, and 16 asteroid perturbers. Earth-encounter predictability using the ballistic (gravity-only) dynamics was extended by 75 yr due to radar astrometry from 1777–2247 to 1777–2322. The interval of predictability is almost certainly shorter due to a Yarkovsky acceleration not characterized by the current short-measurement arc but likely to exist at some level. The next close approach will occur in 2090 September, as the asteroid completes another libration cycle in its horseshoe orbit.

2013 BS45's one-year data arc is too short to be sensitive to the Yarkovsky effect. In trial solutions with the revised radar astrometry, the 1σ uncertainty for the result is three times larger than the estimated value itself: A2 = (−1.24787029063 ± 3.172336) × 10⁻¹² au d⁻². 2013 BS45 is a rapid rotator, and the diurnal component of the Yarkovsky effect can be expected to average out due to the surface being nearly in thermal equilibrium. The Yarkovsky effect will be dominated by a seasonal component whose magnitude depends on the pole orientation and thermal inertia, which are unknown.

A number of near-Earth objects with a resonant behavior similar to 2013 BS45 have been studied: 3753 Cruithne (Wiegert et al. 1997), 54509 YORP (Wiegert et al. 2002; Margot & Nicholson 2003), 2001 GO2 (Brasser et al. 2004), 2002 AA29 (Connors et al. 2002; Ostro et al. 2003; Brasser et al. 2004), and (419624) 2010 SO16 (Christou & Asher 2011). 2013 BS45 belongs to the Arjuna orbital domain defined by 0.985 au < a < 1.013 au, e < 0.1, and i < 856. The JPL Small-Body Database Search Engine (https://ssd.jpl.nasa.gov/sbdb_query.cgi) lists 21 Arjuna-class objects discovered to date, and of those, 2013 BS45 has the fifth brightest absolute magnitude.

5.1. Rapid Rotation of 2013 BS45

5.2. 2013 BS45 as a Spacecraft Mission Target

5.3. Radar Observations of the Arjuna-class Objects

This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). This material is based in part upon work supported by NASA under the Science Mission Directorate Research and Analysis Programs and the Human Exploration and Operations Mission Directorate Advanced Exploration Systems Program. We would like to thank Chris Magri for a thorough and helpful review of this manuscript.