47th Lunar and Planetary Science Conference (2016)
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THE GRAVITY FIELD OF MERCURY AFTER MESSENGER. Erwan Mazarico1, Antonio Genova2, Sander
Goossens3, Frank G. Lemoine1, David E. Smith2, Maria T. Zuber2, Gregory A. Neumann1 and Sean C. Solomon4,5.
1Planetary Geodynamics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA ([email protected]); 2Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; 3Center for Research and Exploration in Space Science and Technology, University of Maryland, Baltimore County, Baltimore, MD 21250, USA; 4Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY 10964, USA; 5Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, DC 20015, USA.
Introduction: The NASA MESSENGER mission
[1] ended its operations on 30 April 2015, after more
than 4 years in orbit around Mercury. Over the course
of >4100 revolutions, a wealth of radio tracking data
and altimetric range measurements were acquired by
the MESSENGER spacecraft and the onboard Mercury
Laser Altimeter (MLA) [2]. The gravity and topography products that can be derived from those datasets
provide important geophysical constraints to better
understand Mercury and its evolution, from its deep
internal structure [3] when combined with groundbased radar observations [4] to its crust [5].
During the final year of the mission, the remaining
propellant was utilized to observe Mercury from very
low altitudes, down to 5 km, compared with the initial
200 km periapsis. Favorable Earth viewing geometry
allowed radio tracking down to ~25 km between August and October 2014. Such lower periapsis altitudes
greatly enhanced the sensitivity of the MESSENGER
dataset, especially to shorter-wavelength gravity
anomalies. Figure 1 shows the minimum tracking altitude of MESSENGER over Mercury’s surface and
illustrates the substantial increase in resolution that can
be expected from the MESSENGER extended mission
data compared with earlier solutions [6,7].
Global Gravity Solution: The complete tracking
data, to 30 April 2015, were analyzed and included in
the latest gravity solutions obtained at the NASA Goddard Space Flight Center. The noise level during each
tracking pass was evaluated and used in the weight,
after spline detrending to ensure that short-wavelength
gravity signals contribute. Regularization (Kaula) was
applied above spherical harmonic degree l=10.
An intermediate degree and order 75 solution
(HgM006) was used by the navigation team to design
and fly the final “hover campaign” [8,9].
Our new HgM007 solution is to degree and order
100. Unlike previous solutions obtained in the “principal axes” frame [10], HgM007 is expressed in the reference frame adopted for the final MESSENGER
Planetary Data System data release. On the basis of the
work of Margot [4] and new spin rate (6.1385108°/
day) constraints [7], the reference longitude
(329.5988°) was selected to maintain Hun Kal at
-20°E. The HgM007 field is archived at the PDS.
The uneven low-altitude data coverage (Figure 1)
leads to a spatially variable resolution. As earlier [2],
we computed a degree strength map from the full covariance matrix obtained during the inversion. The
degree strength at each location is the degree at which
the computed error spectrum intersects the Kaula constraint. Compared with previous fields such as HgM005, the degree strength reaches >75 at specific locations at northern latitudes. The gravity anomalies over
northern latitudes show detailed features correlated
with topography (e.g., impact craters, see Figure 2).
MLA altimetric data were used as an additional tracking measurement to improve orbit determination, particularly when radio tracking was not available.
up to March 2, 2015
up to March 15, 2012
minimum tracking altitude (km)
no data
orthographic plots centered at
0°E / 180°E and 45°N
Figure 1. Coverage maps of the minimum altitude of the tracking data included in the gravity solutions. Black and white
indicate >500 and <100 km altitude, respectively. Orthographic projections centered at 0°E / 180°E and 45°N.
47th Lunar and Planetary Science Conference (2016)
Local Gravity Solution: In order to resolve even
shorter wavelengths than permitted by our current
global approach, we developed companion solutions to
the global gravity solutions, using local analysis techniques demonstrated with GRAIL [11].
Starting with a “background” spherical harmonic
field, we estimated gravity anomaly corrections at a
scale of 1º x 1º (corresponding to l~180). Such local
gravity anomalies were arranged on a grid between 10°
N and 88°N. We use the Stokes formulation to express
the gridded gravity anomalies.
Anomaly values with respect to the global model
were estimated at the center coordinates of grid cells,
such that : Δgfull = Δgadj + ΔgGLOBAL. The solution was
constrained spatially (neighbor smoothing) over the
full anomaly (global background and adjustments).
Instead of forming the information matrices directly from the range-rate data used in the orbit determination, as is typical, we used the line-of-sight (LOS) derivatives of those Doppler data residuals. We constructed the LOS derivatives by numerical differentiation of the time-series (on a pass-by-pass basis). Derivatives of Doppler data are akin to accelerations, and
they are more sensitive to local, short-wavelength signals in the gravity field than the normal Doppler residuals. The smoothing factor was varied empirically, to
find the best compromise between smoothing and resolution.
The correlation of the local model with MLA
topography over two 30° spherical caps at northern
latitudes is shown in Figure 3. The local model maintains higher correlation at higher degrees than the
global model.
Conclusions: The first spacecraft to orbit Mercury,
MESSENGER acquired a large radio tracking dataset
and furthered our understanding of the planet’s interior.
In particular, the extension of the MESSENGER misLow-altitude area centered on (60°N, -60°E)
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sion beyond its first year provided data much more
sensitive than originally anticipated. The analysis of
the late 2014 low-altitude data to produce gravity
fields with high resolution in the northern hemisphere
will allow new geophysical analyses of the crust and
lithosphere of Mercury.
References: [1] Solomon S.C. et al. (2007), Space
Sci. Rev. 131, 3-39. [2] Zuber M.T. et al., Science 336,
217-220. [3] Hauck S.A., II, et al. (2013), JGR Planets
118, 1204-1220. [4] Margot J.-L. et al. (2012), JGR
117, E00L09. [5] James P.B. et al. (2015), AGU,
P53A-2102. [6] Smith D.E. et al. (2012), Science 336,
214-217. [7] Mazarico E. et al. (2014), JGR Planets,
2417-2436. [8] McAdams J.V. et al. (2015), Astrodyn.
Spec. Conf., AAS 15-634. [9] Bryan C.G. et al. (2015),
AGU, P34A-02. [10] Margot J.-L. (2009), Celest.
Mech. Dyn. Astron. 105, 329-336. [11] Goossens S.J.
et al. (2014), GRL 41, 3367-3374.
HgM007 gravity
anomalies
mGal
120
80
40
0
−40
−80
Figure 2. Gravity anomalies (in mGal) for model
HgM007. North polar stereographic projection to
55°N.
Suisei Planitia area centered on (65°N, -150°E)
Figure 3. Localized correlations (lwin=20) for a low-altitude area (left) and the Suisei Planitia area (right). The local model
and LOS derivative data produce models with improved correlations with topography.