An analysis of the geodesy and relativity experiments of BepiColombo
Introduction
Mercury is one of the most interesting objects of the solar system. The high density, the peculiar 3:2 spin-orbit resonance, the intrinsic magnetic field, and the anomalous perihelion drift of the planet have been some of the most fascinating challenges in the physics of the solar system. So far, only the spacecraft Mariner 10 and MESSENGER (MErcury Surface, Space ENvironment, GEochemistry and Ranging) reached the planet. Mariner 10 surprised the science community with the detection of a relatively strong magnetic field, suggesting that the planet likely hosts a large molten core. In its four years in orbit around Mercury (from April 2011 to April 2015), MESSENGER carried out an extensive characterization of the planet, revealing its dynamic past and present, from an early magma ocean, to the extended volcanism spanning over billions of years, and to the present-day, robustly convective, outer core (Johnson and Hauck, 2016).
BepiColombo (Benkhoff et al., 2010) will be the third mission to reach the planet, and the second one to enter into hermean orbit. The mission has been jointly developed by the European Space Agency (ESA) and the Japanese Aerospace eXploration Agency (JAXA). Planned for launch in October 2018, with arrival at Mercury in December 2025, the nominal mission is scheduled to be one year long, with the possibility of an extension by an additional year. The mission entails the release of two spacecraft in hermean orbit. The Mercury Magnetospheric Orbiter (MMO), developed by JAXA, will be placed into an elliptical polar orbit around the planet (590 × 11600 km altitude), and is devoted to explore the exosphere and the magnetosphere. The Mercury Planetary Orbiter (MPO), provided by ESA, will be inserted in a lower, near-circular, polar orbit (480 × 1500 km altitude), to study the surface and the deep interior.
The Mercury Orbiter Radio science Experiment (MORE, Iess et al., 2009) is one of the 11 instruments and investigations of the MPO. It exploits advanced radio tracking instrumentation both onboard and on ground, enabling highly accurate range and Doppler measurements. The tracking system architecture (Iess, Boscagli, 2001, Simone, Maffei, Gelfusa, Boscagli, 2008, Ciarcia, Simone, Gelfusa, Colucci, De Angelis, Argentieri, Iess, R.) is an evolution of the radio system adopted by the Cassini mission to Saturn. In addition to the deep space transponder used for telemetry, tracking and command functions (TTC) and enabling two downlinks at X and Ka band coherent with a X band uplink, the key onboard instrument is a Ka-band Transponder (KaT), capable of receiving an uplink at 34 GHz and retransmitting it coherently to ground at 32.5 GHz. The multi-frequency radio link in X/X (7.2 GHz uplink / 8.4 GHz downlink), X/Ka (7.2/32.5 GHz) and Ka/Ka (34/32.5 GHz) band allows a nearly complete suppression of plasma noise, the dominant source of noise in S and X band radio links (Bertotti et al., 1993).
The baseline ground station for MORE is DSS 25, a 34 m dish of NASA’s Deep Space Network located in Goldstone (California, USA). DSS 25, previously used for Cassini radio science experiments, is currently the only ground antenna supporting the multifrequency radio link required by MORE with full operational capabilities. The ESA deep space antenna DSA 3 in Malargue (Argentina) has similar capabilities at experimental level. It is expected to reach full operational support of MORE shortly after the launch of BepiColombo. The expected Allan deviation (ADEV) of the Doppler measurements in the hermean phase is 1–2 × 10−14 at 1000 s integration time (4–8 × 10−14 at 60 s). A remarkable difference between the Cassini and BepiColombo radio system is the multifrequency ranging function. Indeed, the MORE KaT is endowed with a novel wide-band ranging system, based upon a high rate (24 Mcps) pseudo-noise ranging code. The requirement on single-shot range accuracy is 30 cm, although the system is expected to perform considerably better (Iess and Boscagli, 2001). On Cassini, range observable were available only at X band.
The scientific goals of MORE span over three areas:
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gravimetry: recovery of the static hermean gravity field and determination of the Love number k2;
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rotation: estimation of Mercury’s rotational state (pole direction and librations in longitude);
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fundamental physics: test different aspects of General Relativity (GR) through the determination of several PPN parameters.
A test of relativistic gravity, exploiting the Shapiro delay (Shapiro, 1964) and the corresponding Doppler shift affecting the propagation of radio-waves (Bertotti et al., 2003), will be performed in the cruise phase to Mercury.
The purpose of this work is twofold. We will give a general review of the MORE investigation, addressing all its aspects (gravimetry, rotation, and fundamental physics), and we will present the expected accuracies obtained from realistic numerical simulations based on the latest mission scenario with launch in October 2018. The work is organized as follows: Section 2 briefly describes the relativistic test performed in cruise. The geodesy (gravimetry and rotation) and the fundamental physics experiments are presented respectively in Section 3 and Section 4. Section 5 introduces the orbit determination method and summarizes the simulation scenario. The results of simulations are presented and discussed in Section 6. In Section 7 we illustrate the prospects and benefits of an extended mission. Section 8 reports on the open issues and future work, followed by the conclusions in Section 9.
Section snippets
The solar conjunction experiment in cruise
According to GR, the presence of any mass induces a curvature in space-time. In a PPN expansion of the Minkowsky metric, the space-time curvature induced by a mass is controlled by the parameter γ, unity in GR. As a consequence, the propagation of radio waves undergoes a deflection, a delay (known as Shapiro delay), and a frequency shift. These phenomena are magnified when the signal path is close to the curvature-generating body, e.g. when the signal is exchanged between a ground antenna and a
The role of Mercury in testing general relativity
Urbain Le Verrier was the first to point out in 1859 that Mercury’s orbit was precessing at a rate (38 arcsec/cy) that could not be explained by perturbations due to known solar system bodies (Le Verrier, 1859). The anomalous precession, slightly adjusted to 43 arcsec/cy by Simon Newcomb (Newcomb, 1882), was matter of speculations for many years. Different explanations were proposed, such as the presence of an additional mass, still hidden to observation, distributed in a belt of many small
The rotational state of Mercury
Mercury’s orbital and rotational periods are respectively 87.96 and 58.65 days (Stark et al., 2015a). The capture in the 3:2 spin-orbit resonance is a consequence of the chaotic dynamics of the planet (Correia and Laskar, 2004), although how exactly and when the capture took place is still an open question (see e.g. Noyelles et al., 2014 for a detailed discussion).
Colombo and Shapiro (1966) and Peale (1969) proposed that Mercury occupies a Cassini state of type 12
The orbit determination method for MORE
The MORE radio science experiment uses the radio observables (e.g. Doppler and range) as input to the orbit determination process. The observables collected at the ground station are compared with the predictions given by a reference solution. The discrepancies are minimized by correcting the spacecraft state and other model parameters in a least squares fit. The well-known weighted least squares correction with a priori information is given by (Tapley et al., 2004)
Numerical simulations
Thanks to its full set of dedicated instrumentation, BepiColombo is expected to improve significantly MESSENGER’s results. We have quantified this potential improvement by means of numerical simulations based on the reference scenario and the assumptions given in Section 5. The simulations include the relativity, geodesy, and rotation experiment in a single setup.
The parameters in the solve-for list related to the fundamental physics test are
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the state vector of Mercury and the velocity
Benefits from an extended mission
The mission BepiColombo has been approved and funded for one year operations at Mercury. However there are excellent chances that the mission could be further extended for at least an additional year before running out of hydrazine to carry out the wheel desaturation maneuvers and loosing attitude control. In this section we assess the benefits of an extended mission for the science goals of the MORE investigation.
Fundamental physics
The DE430 solar system model (Folkner et al., 2014), taken as a reference, shall be slightly refined for the purpose of MORE. The indirect figure effect between Mercury and the Sun causes deviations on the motion of the planet at the level of 1 m over the one year mission, and even more in two years5
Conclusions
In this paper we analysed the radio science experiment of the mission BepiColombo to Mercury, taking into account the current mission profile and the instrument performances resulting from the final tests. We described the physical background of the experiments, and used an up to date scenario to perform numerical simulations covering all investigations to be carried out by MORE, both in fundamental physics and geodesy.
Acknowledgements
We wish to thank members of the Radio Science Laboratory of Sapienza University of Rome for many useful discussions and the support in software development. Luigi I. thanks A. Milani and his research group for fruitful discussions and help in validating the implementation of relativistic models during the visits to the University of Pisa. This work was funded in part by the Italian Space Agency (ASI).
References (91)
- et al.
BepiColombo-comprehensive exploration of Mercury: mission overview and science goals
Planet. Space Sci.
(2010) Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie
Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin)
(1915)- Fienga, A., Manche, H., Laskar, J., Gastineau, M., Verma, A., 2014. INPOP new release: INPOP13b....
Constraining the preferred frame effect α1, α2 parameters from solar system planetary precession
Int. J. Modern Phys. D
(2014)- et al.
A whole new Mercury: messenger reveals a dynamic planet at the last frontier of the inner solar system
J. Geophys. Res.
(2016) - et al.
Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters
Icarus
(2011) The Determination of the Hermean Gravity Field and Topography from Radio Science and Laser Altimeter Data of the Mission BepiColombo
(2013)- et al.
Mercury’s moment of inertia from spin and gravity data
J. Geophys. Res.
(2012) Testing relativity with laser ranging to the moon
Phys. Rev.
(1968)Helioseismic Determination of the Solar Gravitational Quadrupole Moment
Sensitivity study of systematic errors in the BepiColombo relativity experiment
2016 IEEE Metrology for Aerospace (MetroAeroSpace)
Precise cassini navigation during solar conjunctions through multifrequency plasma calibrations
J. Guid. Control Dyn.
Mercury’s tides and interior structure
J. Geophys. Res.
Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity
Astron. Astrophys.
Theory and Experiment in Gravitational Physics
Mass and energy flow in the solar chromosphere and corona
Annu. Rev. Astron. Astrophys.
Future gravitational physics tests from ranging to the BepiColombo Mercury planetary orbiter
Phys. Rev. D
Doppler tracking of spacecraft with multi-frequency links
Astron. Astrophys.
A test of general relativity using radio links with the Cassini spacecraft
Nature
Symmetries and Rank Deficiency in the Orbit Determination Around Another Planet
A dynamo explanation for Mercury’s anomalous field
Geophys. Res. Lett.
The BepiColombo more gravimetry and rotation experiments with the orbit14 software
Mon. Not. R. Astron. Soc.
The rotation of the planet Mercury
Astrophys. J.
Mercury’s capture into the 3/2 spin-orbit resonance as a result of its chaotic dynamics
Nature
Orbital tests of relativistic gravity using artificial satellites
Phys. Rev. D
Constraining the nordtvedt parameter with the BepiColombo radioscience experiment
Phys. Rev. D
Planetary perturbations on Mercury’s libration in longitude
Celest. Mech. Dyn. Astron.
The free librations of Mercury and the size of its inner core
Geophys. Res. Lett.
Mercury’s inner core size and core-crystallization regime
Icarus
The role of Mercury’s core density on its longitudinal librations
Icarus
The cosmic microwave background: the history of its experimental investigation and its significance for cosmology
Classical Quant. Gravity
Numerical estimation of the sensitivity of inpop planetary ephemerides to general relativity parameters
Celest. Mech. Dyn. Astron.
The Planetary and Lunar Ephemerides DE430 and DE431
Interplanetary Network Progress Report, 196
The Effect of Nonhydrostatic Features on the Interpretation of Mercury’s Mantle Density from MESSENGER Results
AAS/Division for Planetary Sciences Meeting Abstracts
Mercury’s gravity field from the first six months of messenger data
Planet. Space Sci.
The curious case of Mercury’s internal structure
J. Geophys. Res.
Italian spring sccelerometer (ISA): a fundamental support to BepiColombo radio science experiments
Planet. Space Sci.
The BepiColombo mission to Mercury: reaction wheels desaturation manoeuvres and the isa accelerometer measurements
Planet. Space Sci.
More: an advanced tracking experiment for the exploration of Mercury with the mission BepiColombo
Acta Astronaut.
Advanced radio science instrumentation for the mission BepiColombo to Mercury
Planet. Space Sci.
The determination of the post-Newtonian parameter γ during the cruise phase of BepiColombo
Classical Quant. Gravity
Phenomenology of the lense-thirring effect in the solar system
Astrophys. Space Sci.
Theory of Satellite Geodesy. Applications of Satellites to Geodesy
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