Precise CCD positions of Triton in 2014-2016 using the newest Gaia DR1 star catalogue

TL;DR

This paper reports precise CCD measurements of Triton’s position from 2014-2016 using Gaia DR1 star catalogue, improving positional accuracy for Neptune’s satellite.

Contribution

It provides new high-precision Triton positions based on extensive CCD observations and Gaia DR1 data, enhancing ephemeris accuracy.

Findings

Mean O-Cs are 0.042 and -0.006 arcsec in RA and Dec.

Observation dispersions are about 0.012 arcsec.

Data covers 15 nights of observations.

Abstract

755 new CCD observations during the years 2014-2016 have been reduced to derive the precise positions of Triton, the first satellite of Neptune. The observations were made by the 1 m telescope at Yunnan Observatory over fifteen nights. The positions of Triton are measured with respect to the stars in Gaia DR1 star catalogue. The theoretical position of Triton was retrieved from the Jet Propulsion Laboratory (JPL) ephemeris nep081xl, while the position of Neptune was obtained from the JPL ephemeris DE431mx. Our results show that the mean O-Cs (observed minus computed) are 0.042 and -0.006 arcsec in right ascension and declination respectively. The dispersions of our observations are estimated at about 0.012 arcsec in each direction.

Tables

Table 1. Table 1: Specifications of the 1 m telescope and CCD detector

Approximate focal length	1330cm
F-Ratio	13
Diameter of primary mirror	100cm
CCD field of view	$7.1\prime$$\times$$7.1\prime$
Size of CCD array	2048$\times$2048
Size of pixel	$13.5\mu \times 13.5\mu$
Approximate angular extent per pixel	0$\stackrel{\prime \prime }{.}$21/pixel

Table 2. Table 2: Observations for Triton and calibration fields. Column 3 and Column 4 list the number for a dense star field and Triton, respectively. Column 5 lists the filter.

Obs Date	Calibration fields		Triton	filter
	Dense Star Fields	No.	No.
2014-10-16	No data available		28	N
2014-10-17	NGC7092	29	41	N
2014-10-18	No data available		37	N
2015-11-03	No data available		21	I
2015-11-04	NGC7092	31	20	I
2016-09-25	NGC1664	49	42	I
2016-09-26	NGC1664	49	42	I
2016-09-27	NGC7209	46	5	I
2016-10-22	NGC7209	48	71	I
2016-10-23	NGC7209	48	70	I
2016-10-24	NGC7209	49	69	I
2016-11-20	NGC1664	49	68	I
2016-11-21	No data available		80	I
2016-11-22	No data available		86	I
2016-11-23	No data available		75	I
total		398	755

Table 3. Table 3: Statistics of (O-C) residuals for Triton before and after GD correction for Each Data Set. Columns 1 is the date. The second column ("Before GDC" or "After GDC") shows the statistics in both directions before or after GD correction. The following columns list the mean (O-C) and its standard deviation (SD) in right ascension and declination, respectively. All units are in arcseconds. The ephemeris used is JPL nep081xl/DE431mx and the reference star catalogue is Gaia DR1 star catalogue.

Date		O-C$>$	SD	O-C$>$	SD
		RA		DEC
2014	Before GDC	0.039	0.011	-0.005	0.014
	After GDC	0.037	0.011	-0.008	0.013
2015	Before GDC	0.040	0.013	0.013	0.019
	After GDC	0.044	0.011	-0.006	0.015
2016	Before GDC	0.039	0.019	0.004	0.022
	After GDC	0.043	0.011	-0.006	0.012
total	Before GDC	0.039	0.018	0.003	0.022
	After GDC	0.042	0.012	-0.006	0.012

Table 4. Table 4: Statistics of (O-C) residuals for Triton using different star catalogue. Columns 1 is the date. The second column shows the star catalogues. The following columns list the mean (O-C) and its standard deviation (SD) in right ascension and declination, respectively. All units are in arcseconds. The ephemeris used is JPL nep081xl/DE431mx.

Date		O-C$>$	SD	O-C$>$	SD
		RA		DEC
2014-10-16	UCAC4	0.028	0.008	0.071	0.009
	Gaia	0.036	0.011	-0.008	0.010
2014-10-17	UCAC4	0.018	0.006	0.080	0.010
	Gaia	0.037	0.009	-0.008	0.011
2014-10-18	UCAC4	-0.007	0.010	0.074	0.013
	Gaia	0.036	0.013	-0.009	0.017
2015-11-03	UCAC4	0.157	0.038	0.060	0.029
	Gaia	0.047	0.012	-0.005	0.017
2015-11-04	UCAC4	0.173	0.028	0.116	0.014
	Gaia	0.041	0.009	-0.007	0.013
2016-09-25	UCAC4	0.073	0.020	0.041	0.018
	Gaia	0.040	0.014	-0.005	0.013
2016-09-26	UCAC4	0.094	0.025	0.053	0.024
	Gaia	0.045	0.014	-0.002	0.011
2016-09-27	UCAC4	0.093	0.028	0.009	0.023
	Gaia	0.052	0.020	-0.004	0.016
2016-10-22	UCAC4	0.088	0.016	-0.052	0.013
	Gaia	0.040	0.010	-0.006	0.010
2016-10-23	UCAC4	0.055	0.010	-0.067	0.010
	Gaia	0.040	0.010	-0.009	0.010
2016-10-24	UCAC4	0.062	0.007	-0.044	0.013
	Gaia	0.034	0.010	-0.012	0.010
2016-11-20	UCAC4	0.033	0.009	0.050	0.011
	Gaia	0.048	0.009	0.002	0.012
2016-11-21	UCAC4	0.047	0.009	0.034	0.012
	Gaia	0.049	0.010	-0.003	0.011
2016-11-22	UCAC4	0.041	0.009	0.030	0.009
	Gaia	0.043	0.010	-0.007	0.010
2016-11-23	UCAC4	0.041	0.012	0.029	0.013
	Gaia	0.046	0.010	-0.010	0.011
total	UCAC4	0.056	0.038	0.020	0.052
	Gaia	0.042	0.012	-0.006	0.012

Table 5. Table 5: Statistics of (O-C) residuals for Triton by using different satellite ephemerides and planetary ephemerides. Columns 1 is the number of observations, column 2 the planetary ephemeris and column 3 the satellite ephemerides. The following columns list the mean (O-C) and its standard deviation (SD) in right ascension and in declination, respectively. Emelyanov15 is a short form of Emelyanov et al. (2015). All units are in arcseconds.

planetary	satellite	O-C$>$	SD	O-C$>$	SD
ephemeris	ephemeris	RA		DEC
INPOP08	Emelyanov15	0.189	0.016	0.022	0.015
INPOP10	Emelyanov15	0.083	0.013	-0.099	0.013
INPOP13C	Emelyanov15	0.062	0.013	-0.059	0.013
EPM2015	Emelyanov15	0.062	0.013	-0.014	0.013
DE405	Emelyanov15	0.149	0.016	-0.028	0.014
DE421	Emelyanov15	0.057	0.013	-0.018	0.013
DE431	Emelyanov15	0.042	0.013	-0.007	0.013
DE431	JPL nep081xl	0.042	0.012	-0.006	0.012

Table 6. Table 6: Compared with other observations. Column 1 lists the author, Column 2 the number of observations. The following columns list the mean (O-C) and its standard deviation (SD) in right ascension and in declination, respectively. All units are in arcseconds.

Author	No.	O-C$>$	SD	O-C$>$	SD
		RA		DEC
Veiga & Vieira Martins(1996)	433	-0.001	0.093	0.032	0.116
Veiga & Vieira Martins(1998)	759	0.014	0.086	-0.007	0.082
Stone (2001)	188	-0.027	0.120	-0.048	0.113
Vieira Martins et al. (2004)	63	0.041	0.151	0.060	0.081
Qiao et al. (2007)	943	0.062	0.062	-0.036	0.053
Qiao et al. (2014)	1095	0.023	0.062	-0.029	0.067
this work	755	0.042	0.012	-0.006	0.012

Table 7. Table 7: Extract of the observations. The first column lists the exposure middle time of each CCD frame in form of Julian Date (UTC). RA and DE are the observed topocentric astrometric positions in right ascension and declination, respectively. The whole table is available on the Web site http://lnfm1.sai.msu.ru/neb/nss/bnepomae.htm.

Date	RA	DE
JD	h m s	$°$ $\prime$ $″$
2456947.01326	22 27 53.1995	-10 25 47.058
2456947.01664	22 27 53.1882	-10 25 47.142
2456947.02484	22 27 53.1623	-10 25 47.373
……	……	……
2457716.05200	22 43 44.6339	-08 59 24.261
2457716.05281	22 43 44.6352	-08 59 24.261
2457716.05362	22 43 44.6361	-08 59 24.232

Full text

††pubyear: 2015††pagerange: Precise CCD positions of Triton in 2014-2016 using the newest Gaia DR1 star catalogue–Precise CCD positions of Triton in 2014-2016 using the newest Gaia DR1 star catalogue

1 Introduction

Triton, the largest moon of Neptune, was discovered on October 10, 1846. It has an retrograde, inclined and circular orbit. This unusual configuration has led to the belief that Triton originally orbited the Sun before being captured in orbit around Neptune (McCord, 1966; McKinnon, 1984). Therefore Triton hold important clues to the evolution of the solar system. In recent years, generous observations of Triton have been made (Veiga & Vieira Martins, 1996; Veiga & Martins, 1998; Stone, 2000, 2001; Vieira Martins et al., 2004; Qiao et al., 2007, 2014) and the precision of these observations is usually about 0.05 to 0.5 arcsec (Emelyanov & Samorodov, 2015). As the newest Gaia DR1 star catalogue is available (Gaia Collaboration et al., 2016a, b), the precision of Triton must be further improved and a quite great CCD field of view allows us to calibrate its geometry accurately (Peng et al., 2012). Furthermore, the high precision of Triton can help improve the precision of Neptune. At present even with the modern planetary ephemeris DE431, measurement uncertainties such as the Earth’s atmosphere and star catalog uncertainties limit position accuracies of Neptune to several thousand kilometers (Folkner et al., 2014). From the statistics conducted by Folkner et al. (Folkner et al., 2014) in their figure 67-76, most astrometric observations of Neptune are not more accurate than 0.2 arcsec except the observations made by Voyager 2. As the position and motion of the planets can be deduced from the ephemerides of the satellites (Robert et al., 2011), the high precision of Triton can help improve the precision of Neptune. Besides, the continuation of observing campaign is necessary for the analysis of long-term physical element, such as the accuracy of the dynamical models (Arlot et al., 2012). Thus we must never stop observing, since an observation not made is a missing observation.

The contents of this paper are arranged as follows. In Section 2, the observations are described. Section 3 presents the method of reduction. In Section 4, we make comparisons and analysis of the residuals. Finally, in Section 5, we draw a conclusion.

2 Observations

Since 2014, we have been engaged in a systematic observation of Triton. All the observations were made with the 1 m telescope at Yunnan Observatory. The site (i.e. IAU code 286) is at longitude E100${\degr}$ 01${\arcmin}$ 51${\arcsec}$, latitude N26${\degr}$ 42${\arcmin}$ 32${\arcsec}$ and height 2000 m above sea level. A total of 755 frames of CCD images have been obtained for the satellite as well as 398 frames of CCD calibration images. The exposure time for each CCD frame ranged from 30 to 120 s, depending on the meteorological conditions. For more instrumental details for the reflector and the CCD detector, see Table 1. In Table 2, the observational sets for Triton and calibration fields are given for each night. Due to the poor weather conditions or the limited time-allocation on October 16, 2014, October 18, 2014, November 3, 2015 and November 21-23, 2016, no calibration fields could be used to derive the geometric distortion (called GD hereafter) patterns of the field of view. Then the GD pattern of the nearest date is applied for as it was done in our previous work (Peng et al., 2015; Wang et al., 2015).

3 Astrometric Reduction

The reduction procedures were carried out according to Peng et al. (2012) and involved the following: (1) The calibration fields and Triton were processed including determining the centers of stars and matching the stars in each CCD frames with those in some reference star catalogue. Here, the Gaia DR1 star catalogue was chosen as the reference star catalogue because of the large number of reference stars available. However, due to the shortage of proper motions for most stars in Gaia DR1 star catalogue, a value of 0 was adopted for the value of proper motion. As the positions of stars in Gaia DR1 are obtained at epoch J2015.0 (Lindegren et al., 2016) and our observations are made near the epoch of Gaia DR1, the effect of proper motions for faint stars can be neglected. Furthermore, as the locations of the stars are randomly distributed in the different fields of view when Triton is observed, the average effect of proper motions to the positional reduction of Triton can be quite cancelled out; (2) An accurate reduction was done including the computations of topocentric apparent position and atmospheric refraction for each matched star in each CCD frame. Then the standard coordinates of each star were calculated. During the computation of the theoretical positions of Triton, the modern ephemeris nep081xl/DE431mx developed by JPL via their Web site http://ssd.jpl.nasa.gov/ is used; (3) The GD patterns were derived from the calibration fields and the pixel positions of stars and Triton were both corrected by using the derived GD. Then the observed position of Triton was obtained by the transformation of the four parameters.

The (O-C) residuals larger than 3 times standard deviation have been rejected and 755 (O-C) residuals were obtained. Figure 1 shows the (O-C) residuals of Triton with respect to the observational epochs. In Figure 1 the results with and without GD corrections are also displayed. Table 3 shows the statistics of (O-C) residuals of Triton before and after GD correction. It can be seen the precision is improved after GD correction.

4 Discussions

In order to make a comparison, the stars in each CCD frame are also matched with the stars from USNO CCD Astrograph Catalogue 4 (UCAC4; Zacharias et al. (2013)) star catalogue. Figure 2 shows the (O-C) residuals by using both Gaia DR1 and UCAC4 star catalogues and Table 4 shows the statistics of (O-C) residuals of Triton by using the two star catalogues. It appears obviously that by using the Gaia DR1 star catalogue the solution has much better agreements and much smaller dispersions in each direction. The mean (O-C) is better than 0.05 arcsec in each direction and the dispersion is better than 0.02 arcsec in each direction. Figure 3 shows a scatter plot of the (O-C) residuals in right ascension and declination with respect to the two different catalogues. It appears that much smaller dispersions can be obtained when Gaia DR1 star catalogue is referred to.

To analyse the observations, we also compared our observations with different planetary and satellite ephemerides which can be downloaded from IMCCE Web site http://www.imcce.fr/ and JPL Web site http://ssd.jpl.nasa.gov/. Table 5 shows the (O-C) residuals by using different ephemerides. From Table 5, we can see that all ephemerides show a small dispersion, but the agreement varies greatly. Specifically, when the same planetary ephemeris DE431 is used, the solutions show a similar agreement. However, when the same satellite ephemeris developed by Emelyanov & Samorodov (2015) is used, the solutions show a very different agreement. Thus the difference between the satellite ephemerides is very small, but the differences among the planetary ephemerides are evident. Obviously, DE431 appears to be a relatively better theory.

To compare our observations with other ones, we also list some major observational statistics of Triton. Table 6 lists some typical residuals of the observations. It can be seen that our observations have a smaller dispersion. In Table 6, the mean (O-C) and its standard deviation come from the literature of the author, the theoretical positions are obtained from JPL ephemeris.

Table 7 lists an extract of our observed topocentric astrometric positions of Triton. The data are presented in the following form: JD denotes the exposure middle time of each CCD frame in the form of Julian Date (UTC). RA, expressed in hours, minutes and seconds are the positions of Triton in right ascension. DE, expressed in degrees, arc minutes and arc seconds are the positions of Triton in declination. The complete data can be obtained in the data base of Natural Satellites of the IMCCE.

5 Conclusions

In this paper, we present 755 CCD observations of Triton, the first satellite of Neptune, taken with the 1 m telescope at Yunnan Observatory. During the reduction, the newest Gaia DR1 star catalogue are used to match the stars in the field of view. Comparisons have been made between the observed positions and the computed ones. The result has shown that after GD correction the mean (O-C) are 0.042 and -0.006 arcsec in right ascension and in declination with respect to JPL ephemeris, respectively. The dispersions of our observations are estimated at about 0.012 arcsec in each direction.

Acknowledgements

We acknowledge the support of the staff of the 1 m telescope at Yunnan Observatory. This research work is financially supported by the National Natural Science Foundation of China (grant nos. U1431227, 11273014) and partly by the Fundamental Research Funds for the Central Universities. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.