Abstract
CCD photometric observations of 9 asteroids were obtained from the Center for Solar System Studies from 2016 January to March.
The Center for Solar System Studies “Trojan Station” (CS3, MPC U81) has two telescopes which are normally used in asteroid family studies such as Jovian Trojans, Hungaria family members or NEAs. During bright moon times, brighter targets are selected to keep the telescopes operating during all clear nights.
All images were made with a 0.4-m or a 0.35-m SCT using an FLI ML-Proline 1001E or FLI ML-Microline 1001E CCD camera. Images were unbinned with no filter and had master flats and darks applied. Measurements were made using MPO Canopus, which employs differential aperture photometry to produce the raw data. Period analysis was done using MPO Canopus, which incorporates the Fourier analysis algorithm (FALC) developed by Harris (Harris et al., 1989). Catalog magnitudes were generally taken from the MPOSC3 catalog, which is based on the 2MASS catalog (http://www.ipac.caltech.edu/2mass) but with magnitudes converted from J-K to BVRI using formulae developed by Warner (2007). The nightly zero points using this catalog have been found to be consistent to about ± 0.05 magnitude, but are occasionally higher.
The Reduced Magnitude in the Y-axis of plots below is Johnson V. These values have been converted from sky magnitudes to unity distance by applying −5*log (rΔ) to the measured sky magnitudes with r and Δ being, respectively, the Sun-asteroid and Earth-asteroid distances in AU. The magnitudes were normalized to the given phase angle, e.g., alpha (6.5°), using G = 0.15, unless otherwise stated. The X-axis is the rotational phase ranging from −0.05 to 1.05.
2150 Nyctimene.
As part of a program of observing Hungaria asteroids to determine pole positions, Warner (2007, 2008, 2012, 2013b, and 2015) determined Nyctimene’s rotational period five times in the past, each time finding a period near 6.13 h. Observations were obtained this year are in hope of improving an ambigious pole solution model. This year’s result of 6.127 h is in good agreement with the prior results and extends the dense dataset by another two years.

3376 Armandhammer.
Pravec (2015) reported a rotational period of 7.9184 h for this Vestoid family member. Cabo (Cabo et al, 2015) reported a period of 6.82 h with some scatter in the resulting lightcurve. Using sparse photometry from the Palomar Transient Factory, Chang (Waszczak et al, 2015) reported a period of 9.4797 h. Our period of 7.916 h agrees with the Pravec results.

3562 Ignatius.
This Vestoid was observed in 2013 April (Falese et al 2014) with a reported period of 2.732 h, in agreement with the findings this year. A limited run was obtained this year while waiting for the Moon to clear the primary target.
| Number | Name | 2016 mm\dd | Pt | Phase | LPAB | BPAB | Period | P.E. | Amp | A.E. | Grp |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2150 | Nyctimene | 03/21–04/02 | 13 | 28.6,27.0 | 242 | 15 | 6.127 | 0.001 | 0.91 | 0.03 | H |
| 3376 | Armandhammer | 01/24–01/26 | 12 | 11.3,12.2 | 101 | −5 | 7.916 | 0.006 | 0.27 | 0.02 | V |
| 3562 | Ignatius | 01/24–01/25 | 63 | 21.3,21.7 | 83 | 0 | 2.73 | 0.003 | 0.21 | 0.02 | V |
| 6394 | 1990 QM2 | 02/13–02/15 | 20 | 6.2,5.4 | 150 | −8 | 3.688 | 0.002 | 0.28 | 0.02 | H |
| 11388 | 1998 VU4 | 02/16–03/10 | 59 | 3.3,8.7 | 143 | −9 | 28.74 | 0.02 | 0.08 | 0.02 | HIL |
| 13504 | 1988 RV12 | 03/13–04/01 | 57 | 1.5,6.2 | 173 | −4 | 26.543 | 0.003 | 0.61 | 0.03 | HIL |
| 21056 | 1991 CA1 | 02/22–02/25 | 10 | 30.6,31.3 | 107 | −1 | 5.6 | 0.01 | 0.26 | 0.03 | H |
| 29298 | Cruls | 02/19–02/21 | 13 | 11.0,10.0 | 161 | 11 | 5.207 | 0.005 | 0.26 | 0.03 | H |
| 32772 | 1986 JL | 02/19–02/23 | 24 | 26.0,25.5 | 168 | 37 | 6.049 | 0.007 | 0.14 | 0.02 | H |

(6394) 1990 QM2.
As part of his Hungaria program, Warner (2008, 2011, 2013a and 2015) observed this asteroid four times in the past finding a period of 3.6873 h. This period is in agreement with this year’s results.

(11388) 1998 VU4.
No previously reported results could be found in the asteroid lightcurve database (LCDB; Warner et al, 2009). With an amplitude of only 0.08 mag., it is possible that the lightcurve could have only a single extrema, or three or more extrema (Harris et al 2014). The RMS error on the Period Spectrum is nearly indistinguishable between 28.74 h and 14.34 h periods. The 28.74 h period is favored because it produces the classic bimodal lightcurve shape. However, further observations are needed for this Hilda to resolve possible aliases.


(13504) 1988 RV12.
No previously reported results could be found in the asteroid lightcurve database (LCDB; Warner et al, 2009) for this Hilda family member.

(21506) 1991 CA1.
Warner (2006 and 2011) observed this Hungaria twice in the past finding a period of 5.58 h which agrees with the results found this year.

21298 Cruls.
Warner (2013) observed this Hungaria in January 2013 finding a rotational period of 7.795 h with a trimodal lightcurve. This year’s observations have slightly larger amplitude and favored a 5.207 h period which is a 1.5 to 1 alias of the 2013 result. While it is possible that a lightcurve with an amplitude of 0.26 mag., could have three extrema (Harris et al, 2014), it is more likely that the bimodal lightcurve is correct. Warner replotted his 2013 data resulting in the best fit of the 5 h range being 5.8 h. However, the Period Spectrum of his 2013 data shows the 5.2 h period as being possible. Several of the scattered data points in the Warner 2013 data are marked as being the first or last observations of that night’s run; which are the most susceptible to airmass issues.


(32772) 1986 JL.
Warner (2013) observed this Hungaria on Christmas Day 2012 finding a period of 6.047 h. This agrees with the period we found this year.

Acknowledgements
This research was supported by NASA grant NNX13AP56G.
The purchase of the FLI-1001E CCD camera was made possible by a 2013 Gene Shoemaker NEO Grant from the Planetary Society.
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