The Astronomical Journal, 150:121 (4pp), 2015 October
doi:10.1088/0004-6256/150/4/121
© 2015. The American Astronomical Society. All rights reserved.
VERY LONG BASELINE ARRAY ASTROMETRIC OBSERVATIONS OF MARS ORBITERS
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Ryan S. Park1, William M. Folkner1, Dayton L. Jones1, James S. Border1, Alexander S. Konopliv1, Tomas J. Martin-Mur1, Vivek Dhawan2, Ed Fomalont3, and Jonathan D. Romney2 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109-8099, USA;
[email protected] 2 National Radio Astronomy Observatory, Socorro, NM 87801, USA 3 National Radio Astronomy Observatory, Charlottesville, VA 22903, USA Received 2015 April 27; accepted 2015 August 16; published 2015 September 22
ABSTRACT This paper presents astrometric observations of Mars that are reduced from Very Long Baseline Array (VLBA) measurements of Mars-orbiting satellites. These observations provide angular positions for Mars in the International Celestial Reference Frame (ICRF). Nine observing epochs were used: eight from 2008 and one from 2013. For each epoch, observed R.A. and decl. are provided with associated uncertainties. The post-fit rms residuals of these measurements against JPL’s DE430 ephemeris are 0.13 mas and 0.18 mas for R.A. and decl., respectively, with average uncertainty of 0.24 mas in R.A. and 0.32 mas in decl. The results are generally in good agreement with single-baseline Very Long Baseline Interferometry and range measurements of Mars-orbiting satellites. The VLBA measurements of Mars are used to determine the orientation of the dynamical system of Earth and Mars relative to the ICRF with uncertainty of 0.23 mas. Key words: astrometry – ephemerides – planets and satellites: individual (Mars) – reference systems 1. INTRODUCTION
defined by the orbits of Earth and Mars, with respect to the ICRF in Section 3.
The ephemerides of Earth and Mars are currently determined primarily by range and single-baseline Very Long Baseline Interferometry (VLBI) measurements of spacecraft in orbit about or landed on the planet. Single-baseline VLBI measurements are based on difference in arrival time of a group-delay signal transmitted by the spacecraft to two antennas at separate complexes of the NASA Deep Space Network (DSN) using quasar measurement to calibrate clock, instrumental, and media effects (Curkendall & Border 2013). The single-baseline VLBI measurements determine one component of the plane-of-sky position of Mars with respect to the Earth at the measurement time. The Very Long Baseline Array (VLBA) consists of ten 25 m radio antennas operated by the National Radio Astronomy Observatory. These antennas are located at sites from Mauna Kea, Hawaii to St. Croix, US Virgin Island, providing baselines ranging from a few hundred kilometers to as long as 8600 km. The VLBA has provided astrometric data for various applications (Fomalont & Kopeikin 2003; Fomalont et al. 2010; Jones et al. 2011). With up to ten antennas available, the VLBA can determine both components of the plane of sky position of Mars by measuring the differences in arrival time of the signal from spacecraft orbiting Mars. The VLBA measurements use phase delay that provides potentially greater accuracy than group delay. In practice, uncertainty in the positions of extragalactic radio sources (i.e., quasars) used to calibrate clock and media effects often limits the accuracy of the estimated position. This paper reports nine astrometric observations of Mars in the International Celestial Reference Frame (ICRF) (Ma et al. 2009). Similar observations of Saturn are discussed in (Jones et al. 2011), which provides detailed discussion of VLBA observations, including scheduling, correlation, and calibration of the data. The observations of Mars are used to estimate the orientation of the dynamical reference frame,
2. ASTROMETRIC POSITION DETERMINATION Each VLBA observation of the position of Mars consists of a series of differences in time of arrival of the signal from the spacecraft and from quasars used for calibration. Table 1 shows the observing dates, spacecraft, and VLBA antennas used for each VLBA measurement. Note that most of these observations were taken in 2008 which were used to improve the Mars approach orbit determination accuracy of the Phoenix Mars Mission (Martin-Mur & Highsmith 2009). For this paper, only the data from Mars Reconnaissance Orbiter (MRO) and Mars Odyssey spacecraft were used since Phoenix was not in orbit around Mars. Table 2 shows the reference quasars used for each VLBA observation and their associated uncertainties. None of the quasars used for these measurements are defining courses for ICRF-2. Their positions in the ICRF-2 catalog are based on limited number of observations. Instead, we used positions from Sovers et al. (2014) for a catalog fit to the ICRF-2 defining sources, but with additional observations on the quasars used for the Mars VLBA measurements. The angular separation (i.e., angle between reference quasar and Mars) was typically less than 3 5. For data processing, the formal quasar position uncertainties were increased by 1.4 and 1.1 for R.A. and decl., respectively, and 0.04 mas was set as the minimum uncertainty for both, based on experience from single-baseline VLBI observations. Each VLBA observation was reduced to an astrometric position through a data reduction process discussed in (Jones et al. 2011). The error sources considered in this process were quasar position, station clock, Earth troposphere and ionosphere calibration errors. The error in spacecraft orbits was ignored since they are typically determined to a few meter level (Konopliv et al. 2011), which is much less than the average accuracy of VLBA measurements. The quasar serves as an 1
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Park et al.
Table 1 Observing Dates, Spacecraft, and VLBA Stations Observing Date
Spacecraft
VLBA Antennas
2008 2008 2008 2008 2008 2008 2008 2008 2013
MRO, Odyssey MRO MRO, Odyssey Odyssey Odyssey MRO, Odyssey MRO, Odyssey MRO, Odyssey MRO
OV, KP, PT, SC, MK, BR, LA, NL BR, FD, HN, KP, LA, MK, NL, OV, PT, BR, HN, KP, LA, MK, NL, OV, PT, SC BR, HN, KP, LA, MK, OV, SC BR, FD, HN, KP, LA, MK, NL, OV, PT, BR, FD, HN, KP, LA, MK, NL, OV, PT, BR, FD, HN, KP, LA, MK, NL, OV, PT, BR, FD, HN, KP, LA, MK, NL, OV, PT, BR, HN, KP, LA, MK, NL, OV, PT, SC
Mar May May May May May May May Oct
01 14 17 19 22 23 25a 25b 29
SC
SC SC SC SC
Note. The Mars spacecraft are—MRO: Mars Reconnaissance Orbiter; Odyssey: Mars Odyssey. The VLBA antenna locations are—SC: St. Croix, US Virgin Islands; HN: Hancock, NH; NL: North Liberty, IA; FD: Fort Davis, TX; LA: Los Alamos, NM; PT: Pie Town, NM; KP: Kitt Peak, AZ; OV: Owens Valley, CA; BR: Brewster, WA; MK: Mauna Kea, HI. Table 2 Observing Dates, Reference Quasars, and Associated Formal Uncertainties Observing Date 2008 2008 2008 2008 2008 2008 2008 2008 2013
Mar May May May May May May May Oct
01 14 17 19 22 23 25a 25b 29
Reference Quasar
Angular Separation (deg)
J0557+2413 J0823+2223 J0823+2223 J0842+1835 J0842+1835 J0854+2006 J0854+2006 J0854+2006 J1042+1203
2.1 1.4 1.6 3.4 1.6 3.1 2.5 2.1 2.2
R.A.
05h57m04 08h23m24 08h23m24 08h42m05 08h42m05 08h54m48 08h54m48 08h54m48 10h42m44
Decl.
+24°13′55 +22°23′03 +22°23′03 +18°35′40 +18°35′40 +20°06′30 +20°06′30 +20°06′30 +12°03′31
71358228 759169 759169 09417247 09417247 87492659 87492659 87492659 60524240
R.A. Uncertainty (mas)
Decl. Uncertainty (mas)
0.037 0.22 0.22 0.054 0.054 0.004 0.004 0.004 0.092
0.064 0.39 0.39 0.094 0.094 0.006 0.006 0.006 0.109
2988061 28863 28863 9904965 9904965 6408707 6408707 6408707 2636411
Note. The R.A. and decl. values and uncertainties are from the DSN radio source catalog (Sovers et al. 2014). For the quasar J0823+2223, its location and uncertainty were taken from (Petrov et al. 2008), which provided slightly less error in quasar position. For data reduction, these uncertainties were increased by 1.4 and 1.1 for R.A. and decl., respectively, and 0.04 mas was set as the minimum uncertainty for both. Table 3 Observed Mars Barycenter Positions in ICRF 2.0 Reference Frame Observing Date 2008 2008 2008 2008 2008 2008 2008 2008 2013
Mar 01 May 14 May 17 May 19 May 22 May 23 May 25 May 25 Oct 29
Time (UTC) 02:20:26 01:01:07 02:31:04 02:30:33 23:01:50 22:59:34 03:00:33 22:19:50 15:34:23
Observed R.A. 05h54m56 08h19m14 08h26m09 08h30m40 08h39m23 08h41m39 08h44m17 08h46m07 10h41m37
Observed Decl. +26°15′25 +21°19′43 +20°54′19 +20°37′09 +20°02′43 +19°53′31 +19°42′36 +19°35′00 +09°55′36
833040 897722 170619 162781 468808 156490 871197 369171 225710
22370 16231 97177 39859 13876 07168 83191 14894 87134
R.A. Uncertainty (s)
Decl. Uncertainty (″)
0.000006 0.000022 0.000024 0.000024 0.000013 0.000014 0.000015 0.000014 0.000013
0.00008 0.00044 0.00048 0.00054 0.00025 0.00025 0.00027 0.00027 0.00028
Note. Positions are geocentric at the listed signal reception times. These define the direction vector from the Earth geocenter at signal reception time to Mars position at signal transmission time (earlier than signal reception by the light travel time from Mars). No aberration or relativistic light deflection have been applied.
inertial reference point. Since both clock and media errors are common to both quasar and spacecraft, most of their effects are canceled. Table 3 shows the derived astrometric observations of Mars in ICRF reference frame. Based on nine observing epochs, the average VLBA accuracy was 0.24 mas and 0.32 mas for R.A. and decl., respectively. Note that three measurements taken in May (i.e., May 14, 17, and 19) have much larger measurement uncertainties due to larger uncertainties in the reference quasar and/or the ionospheric calibration. Without these three
measurements, the average VLBA accuracy is 0.19 mas and 0.23 mas for R.A. and decl., respectively. Figure 1 shows the post-fit residuals of the astrometric observations shown in Table 3 against DE430 JPL Mars ephemeris (Folkner et al. 2014). The rms of residual (rms) is 0.13 mas in R.A. and 0.18 mas in decl. The corresponding weighted rms of residuals is 0.76 and 0.71 for R.A. and decl., respectively. Note that 0.1 mas change in plane-of-sky position correspond to about 100 m change in transverse position at the average distance of Mars. 2
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Figure 1. Mars positions based on VLBA data compared to the DE430 JPL Mars ephemeris positions. The error estimates include expected uncertainties in the quasar positions, station clock, and Earth media.
3. EARTH–MARS ORBIT FRAME-TIE ANALYSIS
tied to the ICRF implicitly through the use of the VLBI measurements as part of the ephemeris estimation. The uncertainty in alignment of DE430 with the ICRF has been estimated to be 0.25 mas (Folkner & Border 2015). Here we use the VLBA data to solve for the frame-tie explicitly and evaluate the accuracy of the alignment of DE430 to the ICRF with independent data. We define the rotation from the dynamical frame to the ICRF by small rotations about the x, y, and z axis respectively defined by:
The orbits of Earth and Mars relative to the solar system barycenter can be represented with a total of twelve orbit elements. Three orbital elements describe the shape of the orbit of Earth, three describe the shape of the orbit of Mars, three describe the relative orienting of the orbit of Mars relative to the orbit of the Earth, and three describe the orientation of the orbit of Earth and Mars relative to the ICRF. Radio range measurements to spacecraft at Mars determine the orbit shape parameters and relative orientation of Earth and Mars with high accuracy (Standish & Williams 1990). The largest uncertainty in the Earth and Mars ephemerides is in the uncertainty in the orientation of their the dynamical frame defined by the orbits of Earth, moon, and Mars with respect to the ICRF. Prior to the establishment of the ICRF, the celestial reference frame was, in part, determined by the estimate of the ephemeris through the mean orbit plane of the Earth. With the ICRF now defined in terms of consistent positions of defining extragalactic radio sources, the orientation of the dynamical frame with respect to the ICRF (i.e., frame-tie) must be estimated. This was initially estimated explicitly through comparisons of estimates of Earth rotation using VLBI data, tied to the ICRF, and lunar laser ranging data, tied to the dynamical frame through the estimated orbits of Earth and moon (Folkner et al. 1994). Starting with VLBI observations of the Magellan spacecraft in orbit about Venus, the dynamical frame has been
⎡1 0 0 ⎤ ⎢ RX ( qx ) = 0 cos qx - sin qx ⎥ , ⎢ ⎥ ⎣ 0 sin qx cos qx ⎦ ⎡ cos qy 0 sin qy ⎤ ⎢ ⎥ RY ( qy ) = ⎢ 0 1 0⎥, ⎢⎣ - sin qy 0 cos qy ⎥⎦ ⎡ cos qz -sin qz 0 ⎤ RZ ( qz ) = ⎢⎢ sin qz cos qz 0 ⎥⎥ . ⎣ 0 0 1⎦
These rotations are positive in the sense that they represent a transformation between two coordinate systems with the final coordinate system’s basis vectors being rotated from the initial 3
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Table 4 Estimated Orientation of the Earth Orbit (from Ephemeris DE430) with Respect to the ICRF Name θx θy θz
Estimate (mas)
Uncertainty (mas)
0.14 0.03 −0.19
0.29 0.25 0.12
This research was in part carried out at the National Radio Astronomy Observatory. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This work made use of the Swinburne University of Technology software correlator, developed as part of the Australian Major National Research Facilities Programme and operated under license.
system’s basis vectors by a right-handed rotation of angle θx, θy, or θz about the designated axis. We have combined the VLBA observations of Mars described above with range measurements to Mars spacecraft to estimate the frame-tie. The results are presented in Table 4. The estimated uncertainties in the rotation angels are comparable with 0.2 mas which is the uncertainty expected based on single-baseline VLBI data. The estimated rotation angles are less than 0.2 mas, showing that the implicit frame-tie achieved by use of the single-baseline VLBI data is effective within the estimated uncertainties.
REFERENCES Curkendall, D. W., & Border, J. S. 2013, Delta-DOR: The One-Nanoradian Navigation Measurement System of the Deep Space Network—History, Architecture, and Componentry, The Interplanetary Network Progress Rep. 42-193 (Pasadena, CA: Jet Propulsion Laboratory) Folkner, W. M., & Border, J. S. 2015, in Highlights of Astronomy 16, ed. T. Montmerle (Cambridge: Cambridge Univ. Press), 219 Folkner, W. M., Charlot, P., Finger, M. H., et al. 1994, AJ, 141, 29 Folkner, W. M., Williams, J. G., Boggs, D. H., Park, R. S., & Kuchynka, P. 2014, The Planetary and Lunar Ephemeris DE 430 and DE 431, The Interplanetary Network Progress Rep. 42-196 (Pasadena, CA: Jet Propulsion Laboratory) Fomalont, E., Kopeikin, E., Jones, D., Honma, M., & Titov, O. 2010, in IAU Symp. 261, Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis, ed. S. Klioner, P. K. Seidelmann & M. Soffel (Cambridge: Cambridge Univ. Press), 291 Fomalont, E. B., & Kopeikin, S. M. 2003, ApJ, 598, 704 Jones, D. L., Fomalont, E., Dhawan, V., et al. 2011, AJ, 141, 29 Konopliv, A. S., Asmar, S. W., Folkner, W. M., et al. 2011, Icar, 211, 401 Ma, C., Arias, E. F., Bianco, G., et al. 2009, ITN, 35 Martin-Mur, T. J., & Highsmith, D. E. 2009, in 21st Int. Symp. on Space Flight Dynamics, Mars Approach Navigation Using the VLBA, http://issfd.org/ ISSFD_2009/Orbit DeterminationI/MartinMur.pdf Petrov, L., Kovalev, Yu. Y., Fomalont, E., & Gordon, D. 2008, AJ, 136, 580 Sovers, O. J., Romero-Wolf, A., Kroger, P., & Jacobs, C. S. 2014, DSN Radio Source Catalog, http://deepspace.jpl.nasa.gov/dsndocs/810-005/107/ catalog-fixed.txt Standish, E. M., & Williams, J. G. 1990, in Inertial Coordinate Systems on the Sky, ed. J. H. Lieske & V. K. Abalakin (Dordrecht: Kluwer), 173
4. CONCLUSIONS We have presented nine astrometric observations of Mars derived from VLBA measurements. These VLBA observations provide additional constraints on Mars ephemeris with average accuracy of 0.24 mas in R.A. and 0.32 mas in decl. The VLBA observations show that the orientation of the Earth orbit determined through use of single-baseline VLBI observations in the ephemeris estimation process is aligned with the ICRF with accuracy better than 0.3 mas. This research was in part carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
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