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Impact analysis of the transponder time delay on radio-tracking observables
Abstract
Accurate tracking of probes is one of the key points of space exploration. Range and Doppler techniques are the most commonly used. In this paper we analyze the impact of the transponder delay, i.e. the processing time between reception and re-emission of a two-way tracking link at the satellite, on tracking observables and on spacecraft orbits. We show that this term, usually neglected in the standard formulation of space observables, can actually be relevant for future missions with high nominal tracking accuracies or for the re-processing of old missions. We present several applications of our formulation to Earth flybys, the NASA GRAIL and the ESA BepiColombo mission.
... where δt B represents the delay between the reception and retransmission of the signal at station B, typically < 1 ms for radio data (Bertone et al., 2018), up to the order of 1 minute for ILR . ...
At present, tracking data for planetary missions largely consists of radio observables: range-rate range and angular position. Future planetary missions may use Interplanetary Laser Ranging (ILR) as a tracking observable. Two-way ILR will provide range data that are about 2 orders of magnitude more accurate than radio-based range data. ILR does not produce Doppler data, however. In this article, we compare the relative strength of radio Doppler and laser range data for the retrieval of parameters of interest in planetary missions, to clarify and quantify the science case of ILR, with a focus on geodetic observables. We first provide an overview of the near-term attainable quality of ILR, in terms of both the realization of the observable and the models used to process the measurements. Subsequently, we analyze the sensitivity of radio-Doppler and laser-range measurements in representative mission scenarios. We use both an analytical approximation and numerical analyses of the relative sensitivity of ILR and radio Doppler observables for more general cases. We show that mm-precise range normal points are feasible for ILR, but mm-level accuracy and stability is unlikely to be attained, due to a combination of instrumental and model errors. ILR has the potential for superior performance in observing signatures in the data with a characteristic period of greater than 0.33-1.65 hours This indicates that Doppler tracking will typically remain the method of choice for gravity field determination and spacecraft orbit determination in planetary missions. Laser ranging data, however, are shown to have a significant advantage for the retrieval of rotational and tidal characteristics from landers. Similarly, laser ranging data will be superior for the construction of planetary ephemerides and the improvement of solar system tests of gravitation.
... The specific error sources can vary depending on the inter-satellite tracking method employed. Common error sources in IRTR include multipath errors (where the signal reaches the receiver via multiple paths), attitude control and knowledge errors, thermal variations within the instruments, oscillator noise, time-tag errors, and delays introduced by the transponders used in the ranging process (Bertone et al., 2018;Kim and Lee, 2009). On the other hand, preliminary research by Grenfell (2024) suggests that clocks, event timers, and detectors are the main sources of errors in ILTR. ...
... We use information on the center-of-mass (COM) position and the locations of the antenna phase centers for precision modeling of the path of the radio signal from DSN station to spacecraft. Antenna transponder delay information is also taken into account (e.g., Bertone et al. 2018). ...
The Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) mission collected a sample from the rubble-pile asteroid (101955) Bennu for return to Earth. For the successful Touch And Go sample acquisition maneuver, the shape and mass of the asteroid needed to be known precisely. Here we use a combination of radiometric, image landmark, and laser altimetry data to determine Bennu’s mass, shape, and orientation simultaneously and to verify existing models thereof. Our shape determination consists of estimating a scale factor and three frame rotation angles that apply to both the global digital terrain model (GDTM) and the landmark coordinates. We use a data type called image constraints, where we take the difference of the observation of the same landmark in images taken at two different times. We analyze data from two phases of the OSIRIS-REx mission, Orbital B and Recon B, and show that interphase image constraints greatly reduce interdependencies between estimated parameters for mass, GDTM scale, and biases on the altimetry data. This results in an improved solution for the mass and shape relative to considering a single mission phase. We find Bennu’s gravitational parameter GM to be 4.89256 ± 0.00035 m ³ s ⁻² , and we find a scale factor of 1.000896 ± 0.00036 for the altimetry-based GDTM. Using the scaled volume, this results in a bulk density of 1191.57 ± 1.74 kg m ⁻³ , which is within the uncertainties of previous analyses but more precise.
... where t sc r is the time of reception of the uplink signal by the spacecraft and Δ u (t sc r ) and Δ d (t sc t ) are one-way Doppler tropospheric corrections computed according to Equation 20, with c = u (t sc r ) and c = d (t sc t ), respectively. Since the transponding time is of a few μs only (Bertone et al., 2018) (i.e., ≪t c ), one can consider that t sc r = t sc t , simply denoted t sc from now on. The sum of the last two terms in Equation 22 corresponds to the total Mars troposphere contribution to the two-way Doppler measurement recorded at t gs r at the Earth ground station. ...
The tropospheric propagation effect is one of several sources of error in radio science measurements. Systematically calibrated for the Earth troposphere disturbances, the ranging and Doppler data provided by the Martian landers have not been corrected so far for Mars troposphere effects. These effects were considered negligible because the Mars atmosphere is a hundred times less dense than that of the Earth. The constantly improving lander data accuracy and the challenging science objectives of the InSight‐Rotation and Interior Structure Experiment (RISE) and ExoMars‐2022‐LaRa radio science experiments motivated this work. We propose here a simple model to compute the Mars troposphere errors affecting a radio wave transponded from the surface of Mars. The troposphere zenithal delay is first derived from the surface pressure at the lander location. We use a mapping function to infer the slant delay (range errors) induced by the troposphere of Mars. Being proportional to range rates, the contribution of Mars troposphere to the Doppler measurements is derived from the slant delays. Using our model, an elevation threshold of 15° above the lander is identified, below which the Doppler data should be calibrated for Mars troposphere. When applied to the X‐band Doppler data from Mars surface missions, the model predicts significant Mars troposphere contribution for less than 1% of RISE data, 2% of Opportunity data, and 2.5% of Pathfinder data. Among these tracking passes, some are strongly affected by the troposphere of Mars, with Doppler errors reaching sometimes more than 3 times the nominal noise level (>10 mHz at 60 s integration time).
... Subsequently the lander will transmit it to the spacecraft at epoch and the Earth station will receive it at epoch. In our simulation, we did not consider device hardware delay during signal transmission such as the transponder delay of probes, which would be calibrated on the ground before launch (Bertone et al. 2017). The four-way Doppler is computed by differencing four-way range with time intervals; the four-way range can be obtained in this form: ...
The exploration of the planet Mercury requires software applications that can execute Precise Orbit Determination (POD) and estimate dynamic parameter solutions. In this paper, we present MERcury Gravity REcovery and Analysis System (MERGREAS), a new software product that is designed to support the future Chinese Mercury explorations. To validate the software we crosschecked the MERGREAS functionalities against the GEODYN-II. Simulated orbit determination experiments show that the differences between MERGREAS and GEODYN-II in the X, Y , and Z directions were 0.2, 0.7, and 0.5 m respectively with the arc length of 24 h. The integration interval for both software platforms was 10s. The MERGREAS software can utilize four-way Doppler measurements for spacecraft orbit determination as well as precise positioning of a Mercury lander. In simulations, we show that when the four-way Doppler data are included, the accuracy in Mercury spacecraft orbit determination can reach the centimeter level and the lander positioning accuracy can be refined to decimeter 4 Observatoire géodésique de Tahiti, BP 6570, 98702 Faa'a, Tahiti, French Polynesia level. Furthermore, when we considered the influence of the Mercury gravity errors, measurement bias, and Mercury orientation model errors in POD with MERGREAS, the errors in the orbiter position ranged as high as 300 meters with a lander position deviation of about 10 meters. The Mercury gravity field solution was improved and the accuracy of the Mercury tidal Love number k 2 increased by an order of magnitude when simulated four-way Doppler data were added. The more precise k 2 value enhanced the accuracy of the constraints used in internal physical parameters estimation for Mercury. These results provide a reference for future Chinese Mercury exploration missions.
... Ranges during the next months of the mission would sample the longer periods. Any radio-ranging system biases (Bertone et al. 2018) would affect the derived value of the X coordinate since a-X + bias is determined well. Radio tracking requires power on the Moon. ...
The analysis of range or Doppler data between sites on the Earth and Moon requires an accurate computation of the lunar orbit and detailed models of the orientation of the Earth and Moon. Models constructed to understand range and range rate can lack detail, but if they include the largest lunar orbit variations, tracking stations on a rotating Earth, and lunar sites on a synchronously rotating Moon, then they will display the largest effects for orbit elements, Earth orientation, tracking station locations, and lunar site coordinates. The range and range rate are expanded into periodic series. To understand accurate solutions, the largest periodic terms that are sensitive to various solution parameters indicate the sensitivity of data to solution parameters and the time spans needed for their determination. Conclusions include: cylindrical coordinates work well for sites on the rapidly rotating Earth, but Cartesian coordinates are more natural for the synchronously rotating Moon since the series for the three coordinate projections are distinct. For range and range rate data, daily, semimonthly, monthly, and longer periods are present. For Doppler data, the daily periods may be stronger and more useful than the long periods, particularly for terms associated with the terrestrial tracking station. Doppler data do not determine the lander coordinate toward the Earth well. Observational strategies for range and Doppler data are not identical. For all data types, one wishes a variety of hour angles, lunar declinations, times of month, and longer periods. A long span of high-quality range data can improve the lunar orbit, orientation of the Earth’s equator, and physical librations. The locations of new lunar sites or new tracking stations can be determined from shorter spans of data.
... where δt B represents the delay between the reception and retransmission of the signal at station B, typically < 1 ms for radio data (Bertone et al. 2018), up to the order of 1 minute for ILR . ...
At present, tracking data for planetary missions largely consists of radio observables: range-rate range and angular position. Future planetary missions may use Interplanetary Laser Ranging (ILR) as a tracking observable. Two-way ILR will provide range data that are about 2 orders of magnitude more accurate than radio-based range data. ILR does not produce Doppler data, however. In this article, we compare the relative strength of radio Doppler and laser range data for the retrieval of parameters of interest in planetary missions, to clarify and quantify the science case of ILR, with a focus on geodetic observables. We first provide an overview of the near-term attainable quality of ILR, in terms of both the realization of the observable and the models used to process the measurements. Subsequently, we analyze the sensitivity of radio-Doppler and laser-range measurements in representative mission scenarios. We use both an analytical approximation and numerical analyses of the relative sensitivity of ILR and radio Doppler observables for more general cases. We show that mm-precise range normal points are feasible for ILR, but mm-level accuracy and stability is unlikely to be attained, due to a combination of instrumental and model errors. ILR has the potential for superior performance in observing signatures in the data with a characteristic period of greater than 0.33-1.65 hours This indicates that Doppler tracking will typically remain the method of choice for gravity field determination and spacecraft orbit determination in planetary missions. Laser ranging data, however, are shown to have a significant advantage for the retrieval of rotational and tidal characteristics from landers. Similarly, laser ranging data will be superior for the construction of planetary ephemerides and the improvement of solar system tests of gravitation.
In recent years, there is a growing interest in small satellites for deep space exploration. The current approach for planetary navigation is based on ground-based radiometric tracking. A new era of low-cost small satellites for space exploration will require autonomous deep space navigation. This will decrease the reliance on ground-based tracking and provide a substantial reduction in operational costs because of crowded communication networks. In addition, it will be an enabler for future missions currently impossible. This review investigates available deep space navigation methods from an autonomy perspective, considering trends in proposed deep space small satellite missions. Autonomous crosslink radiometric navigation, which is one of the best methods for small satellites due to its simplicity and the use of existing technologies, is studied, including available measurement methods, enabling technologies, and applicability to the currently proposed missions. The main objective of this study is to fill the gap in the scientific literature on the autonomous deep space navigation methods, deeply for crosslink radiometric navigation and to aim at showing the potential advantages that this technique could offer to the missions being analysed. In this study, a total of 64 proposed deep space small satellite missions have been analysed found from a variety of sources including journal papers, conference proceedings, and mission websites. In those missions, the most popular destinations are found to be cislunar space and small bodies with the purpose of surface mapping and characterization. Even though various autonomous navigation methods have been proposed for those missions, most of them have planned to use the traditional ground-based radiometric tracking for navigation purposes. This study also shows that more than half of the missions can benefit from the crosslink radiometric navigation through the inter-satellite link.
Navigation of deep space probes is most commonly operated using the spacecraft Doppler tracking technique. Orbital parameters are determined from a series of repeated measurements of the frequency shift of a microwave carrier over a given integration time. Currently, both ESA and NASA operate antennas at several sites around the world to ensure the tracking of deep space probes. Just a small number of software packages are nowadays used to process Doppler observations. The Astronomical Institute of the University of Bern (AIUB) has recently started the development of Doppler data processing capabilities within the Bernese GNSS Software. This software has been extensively used for Precise Orbit Determination of Earth orbiting satellites using GPS data collected by on-board receivers and for subsequent determination of the Earth gravity field. In this paper, we present the currently achieved status of the Doppler data modeling and orbit determination capabilities in the Bernese GNSS Software using GRAIL data. In particular we will focus on the implemented orbit determination procedure used for the combined analysis of Doppler and intersatellite Ka-band data. We show that even at this earlier stage of the development we can achieve an accuracy of few mHz on two-way S-band Doppler observation and of 2 µm/s on KBRR data from the GRAIL primary mission phase.
The planetary and lunar ephemerides DE430 and DE431 are generated by fitting numerically integrated orbits of the Moon and planets to observations. The present-day lunar orbit is known to submeter accuracy through fitting lunar laser ranging data with an updated lunar gravity field from the Gravity Recovery and Interior Laboratory (GRAIL) mission. The orbits of the inner planets are known to subkilometer accuracy through fitting radio tracking measurements of spacecraft in orbit about them. Very long baseline interferometry measurements of spacecraft at Mars allow the orientation of the ephemeris to be tied to the International Celestial Reference Frame with an accuracy of 0''.0002. This orientation is the limiting error source for the orbits of the terrestrial planets, and corresponds to orbit uncertainties of a few hundred meters. The orbits of Jupiter and Saturn are determined to accuracies of tens of kilometers as a result of fitting spacecraft tracking data. The orbits of Uranus, Neptune, and Pluto are determined primarily from astrometric observations, for which measurement uncertainties due to the Earth's atmosphere, combined with star catalog uncertainties, limit position accuracies to several thousand kilometers. DE430 and DE431 differ in their integrated time span and lunar dynamical modeling. The dynamical model for DE430 included a damping term between the Moon's liquid core and solid mantle that gives the best fit to lunar laser ranging data but that is not suitable for backward integration of more than a few centuries. The ephemeris DE431 is similar to DE430 but was fit without the core/mantle damping term, so the lunar orbit is less accurate than in DE430 for times near the current epoch, but is more suitable for times more than a few centuries in the past. DE431 is a longer integration (covering years -13,200 to +17,191) than DE430 (covering years 1550 to 2650).
We have derived a gravity field solution in spherical harmonics to degree and order 900, GRGM900C, from the tracking data of the GRAIL Primary (March 1 – May 29, 2012) and Extended Missions (August 30 – December 14, 2012). A power law constraint of of 3.6 × 10−4/ℓ2, was applied only for degree ℓ greater than 600. The model produces global correlations of gravity, and gravity predicted from lunar topography of ≥ 0.98 through degree 638. The model's degree strength varies from a minimum of 575–675 over the central nearside and farside to 900 over the polar regions. The model fits the Extended Mission Ka-Band Range Rate data through 17 November, 2012 at 0.13 µm/s RMS, whereas the last month of KBRR data obtained from altitudes of 2–10 km fit at 0.98 µm/s RMS, indicating that there is still signal inherent in the tracking data beyond degree 900
Given the extreme accuracy of modern space science, a precise relativistic
modeling of observations is required. In particular, it is important to
describe properly light propagation through the Solar System. For two decades,
several modeling efforts based on the solution of the null geodesic equations
have been proposed but they are mainly valid only for the first order
Post-Newtonian approximation. However, with the increasing precision of ongoing
space missions as Gaia, GAME, BepiColombo, JUNO or JUICE, we know that some
corrections up to the second order have to be taken into account for future
experiments. We present a procedure to compute the relativistic coordinate time
delay, Doppler and astrometric observables avoiding the integration of the null
geodesic equation. This is possible using the Time Transfer Function formalism,
a powerful tool providing key quantities such as the time of flight of a light
signal between two point-events and the tangent vector to its null-geodesic.
Indeed we show how to compute the Time Transfer Functions and their derivatives
(and thus range, Doppler and astrometric observables) up to the second
post-Minkowskian order. We express these quantities as quadratures of some
functions that depend only on the metric and its derivatives evaluated along a
Minkowskian straight line. This method is particularly well adapted for
numerical estimations. As an illustration, we provide explicit expressions in
static and spherically symmetric space-time up to second post-Minkowskian
order. Then we give the order of magnitude of these corrections for the
range/Doppler on the BepiColombo mission and for astrometry in a GAME-like
observation.
A new iterative method for calculating the travel time of a photon as a
function of the spatial positions of the emitter and the receiver in the field
of a static, spherically symmetric body is presented. The components of the
metric are assumed to be expressible in power series in m/r, with m being half
the Schwarzschild radius of the central body and r a radial coordinate. The
procedure exclusively works for a light ray which may be described as a
perturbation in powers of G of a Minkowskian null geodesic, with G being the
Newtonian gravitational constant. It is shown that the expansion of the travel
time of a photon along such a ray only involves elementary integrals whatever
the order of approximation. An expansion of the impact parameter in power
series of G is also obtained. The method is applied to explicitly calculate the
perturbation expansions of the light travel time and the impact parameter up to
the third order. The full expressions yielding the terms of order G^3 are new.
The expression of the travel time confirms the exstence of a third-order
enhanced term when the emitter and the receiver are in conjunction relative to
the central body. This term is shown to be necessary for determining the
post-Newtonian parameter at a level of accuracy of 10^-8 with light
rays grazing the Sun.
Given the extreme accuracy of modern space astrometry, a precise relativistic
modeling of observations is required. Concerning light propagation, the
standard procedure is the solution of the null-geodesic equations. However,
another approach based on the Time Transfer Functions (TTF) has demonstrated
its capability to give access to key quantities such as the time of flight of a
light signal between two point-events and the tangent vector to its
null-geodesic in a weak gravitational field using an integral-based method. The
availability of several models, formulated in different and independent ways,
must not be considered like an oversized relativistic toolbox. Quite the
contrary, they are needed as validation to put future experimental results on
solid ground. The objective of this work is then twofold. First, we build the
time of flight and tangent vectors in a closed form within the TTF formalism
giving the case of a time dependent metric. Second, we show how to use this new
approach to obtain a comparison of the TTF with two existing modelings, namely
GREM and RAMOD. In this way, we evidentiate the mutual consistency of the three
models, opening the basis for further links between all the approaches, which
is mandatory for the interpretation of future space missions data. This will be
illustrated through two recognized cases: a static gravitational field and a
system of monopoles in uniform motion.
During the last decade, the precision in the tracking of spacecraft has constantly improved.
The discovery of few astrometric anomalies, such as the Pioneer and Earth flyby anomalies,
stimulated further analysis of the operative modeling currently adopted in Deep Space
Navigation (DSN). Our study shows that some traditional approximations lead to neglect
tiny terms that could have consequences in the orbit determination of a probe in specific
configurations such as during an Earth flyby. Therefore, we suggest here a way to improve
the light time calculation used for probe tracking.
Abstract. Mercury has always excited a great interest in the scientific establishment because
of its proximity to the Sun that represents, however, the principal obstacle for its
observations from Earth and spacecraft exploration. BepiColombo is, therefore, one of the
most challenging long-term planetary projects that foresees two spacecraft dedicated to
the exploration of Mercury’s environment. The mission allows better understanding of the
planet itself as well as the formation of our Solar System. The density of Mercury does not
conform to that of the other terrestrial planet and for this reason the evaluation of Mercury’s
interior structure is one of the fundamental objectives of the mission. The Mercury Orbiter
Radio Science Experiment (MORE) is one of BepiColombo’s investigations, designed to
provide an accurate estimation of Mercury’s gravity field and Love number k2 by means
of highly stable, multi-frequency radio links in X and Ka band. Gravity not only provides
crucial information on the interior structure of the planet, but also, allows a good orbit determination
of the spacecraft. After an introduction to the mission and the MORE experiment,
we report on numerical simulations aiming at a realistic assessment of the attainable accuracy
in the determination of Mercury’s gravity field. The best results are obtained with a
batch-sequential filter, which proves to cope well the complexity of the noise and dynamical
models.
The Holy GRAIL?
The gravity field of a planet provides a view of its interior and thermal history by revealing areas of different density. GRAIL, a pair of satellites that act as a highly sensitive gravimeter, began mapping the Moon's gravity in early 2012. Three papers highlight some of the results from the primary mission. Zuber et al. (p. 668 , published online 6 December) discuss the overall gravity field, which reveals several new tectonic and geologic features of the Moon. Impacts have worked to homogenize the density structure of the Moon's upper crust while fracturing it extensively. Wieczorek et al. (p. 671 , published online 6 December) show that the upper crust is 35 to 40 kilometers thick and less dense—and thus more porous—than previously thought. Finally, Andrews-Hanna et al. (p. 675 , published online 6 December) show that the crust is cut by widespread magmatic dikes that may reflect a period of expansion early in the Moon's history.
Satellite laser ranging (SLR) and lunar laser ranging (LLR) systems are single-ended instruments, i.e. they measure the roundtrip transit time of a laser pulse to a passive optical reflector. Since such single-ended systems are incapable of ranging beyond the Moon to the planets, we consider the feasibility of a two-way asynchronous (i.e. independently firing) interplanetary laser transponder pair, capable of decimeter ranging and subnanosecond time transfer from Earth to a spacecraft anywhere within the inner Solar System. After introducing the transponder link equation and the concept of “balanced” transponders, we describe how range and time can be transferred between terminals, and preview the potential advantages of photon counting asynchronous transponders for interplanetary applications. We then develop mathematical models for the various sources of noise in an interplanetary transponder link including planetary albedo, solar or lunar illumination of the local atmosphere, and laser backscatter off the local atmosphere. After introducing the key engineering components of an interplanetary laser transponder, we develop an operational scenario for the acquisition and tracking of the opposite terminal. We then use the theoretical models of the previous sections to perform an Earth–Mars link analysis over a full synodic period of 780 days under the simplifying assumption of coaxial, coplanar, circular orbits. We demonstrate that, using slightly modified versions of existing space and ground based laser systems, an Earth–Mars transponder link is not only feasible but quite robust. We also demonstrate through analysis the potential advantages of compact, low output power (<300 mW), photon-counting transponders, which utilize NASA's developmental SLR2000 satellite laser ranging system as the Earth terminal and offer some concluding remarks regarding future applications.
The latest version of the planetary ephemerides developed at the Paris
Observatory and at the Besancon Observatory is presented here. INPOP08 is a
4-dimension ephemeris since it provides to users positions and velocities of
planets and the relation between TT and TDB. Investigations leading to improve
the modeling of asteroids are described as well as the new sets of observations
used for the fit of INPOP08. New observations provided by the European Space
Agency (ESA) deduced from the tracking of the Mars Express (MEX) and Venus
Express (VEX) missions are presented as well as the normal point deduced from
the Cassini mission. We show the huge impact brought by these observations in
the fit of INPOP08, especially in terms of Venus, Saturn and Earth-Moon
barycenter orbits.
Modeling most of the tests of general relativity requires to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant G (general post-Minkowskian expansion). Our method is self-sufficient, in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function are necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.
The upcoming Juno spacecraft measurements have the potential of improving our knowledge of Jupiter's gravity field. The analysis of the Juno Doppler data will provide a very accurate reconstruction of spatial gravity variations, but these measurements will be very accurate only over a limited latitudinal range. In order to deduce the full gravity field of Jupiter, additional information needs to be incorporated into the analysis, especially regarding the Jovian flow structure and its depth, which can influence the measured gravity field. In this study we propose a new iterative method for the estimation of the Jupiter gravity field, using a simulated Juno trajectory, a trajectory estimation model, and an adjoint-based inverse model for the flow dynamics. We test this method both for zonal harmonics only and with a full gravity field including tesseral harmonics. The results show that this method can fit some of the gravitational harmonics better to the "measured" harmonics, mainly because of the added information from the dynamical model, which includes the flow structure. Thus, it is suggested that the method presented here has the potential of improving the accuracy of the expected gravity harmonics estimated from the Juno and Cassini radio science experiments.
The BepiColombo mission to Mercury is an ESA/JAXA cornerstone mission, consisting of two
spacecraft in orbit around Mercury addressing several scientific issues. One spacecraft is the
Mercury Planetary Orbiter, with full instrumentation to perform radio science experiments.
Very precise radio tracking from Earth, on-board accelerometer and optical measurements
will provide large data sets. From these it will be possible to study the global gravity field of
Mercury and its tidal variations, its rotation state and the orbit of its centre of mass. With the
gravity field and rotation state, it is possible to constrain the internal structure of the planet.
With the orbit of Mercury, it is possible to constrain relativistic theories of gravitation. In order
to assess that all the scientific goals are achievable with the required level of accuracy, full
cycle numerical simulations of the radio science experiment have been performed. Simulated
tracking, accelerometer and optical camera data have been generated, and a long list of
variables including the spacecraft initial conditions, the accelerometer calibrations and the
gravity field coefficients have been determined by a least-squares fit. The simulation results
are encouraging: the experiments are feasible at the required level of accuracy provided that
some critical terms in the accelerometer error are moderated. We will show that BepiColombo
will be able to provide at least an order of magnitude improvement in the knowledge of Love
number k2 , libration amplitudes and obliquity, along with a gravity field determination up to
degree 25 with a signal-to-noise ratio of 10.
Given the extreme accuracy of modern space science, a precise relativistic
modeling of observations is required. We use the Time Transfer Functions
formalism to study light propagation in the field of moving axisymmetric
bodies, which extends the field of application of previous works. We first
derive a space-time metric adapted to describe the geometry of an ensemble of
moving bodies. Then, we show that the expression of the Time Transfer Functions
in the field of a uniformly moving body can be easily derived from its
well-known expression in a stationary field by using a change of variables. We
also give a general expression of the Time Transfer Function in the case where
the motion of the body is arbitrary. This result is given in the form of an
integral easily computable numerically. We also provide the derivatives of the
Time Transfer Function in this case, which are mandatory to compute Doppler and
astrometric observables. We particularize our results in the case of moving
axisymmetric bodies. Finally, we apply our results to study the different
relativistic contributions to the range and Doppler tracking for the Juno
mission in the Jovian system.
The modified Newtonian dynamics (MOND) is an attempt to modify the gravitation theory to solve the dark matter problem. This phenomenology is very successful at the galactic level. The main effect produced by MOND in the Solar System is called the external field effect parametrized by the parameter Q2. We have used nine years of Cassini range and Doppler measurements to constrain Q2. Our estimate of this parameter based on Cassini data is given by Q2=(3±3)×10-27 s-2, which shows no deviation from General Relativity and excludes a large part of the relativistic MOND theories. This limit can also be interpreted as a limit on an external tidal potential acting on the Solar System coming from the internal mass of our Galaxy (including dark matter) or from a new hypothetical body.
Navigation of deep-space probes is accomplished through a variety of different radio observables, namely Doppler, ranging and Delta-Differential One-Way Ranging (Delta-DOR). The particular mix of observations used for navigation mainly depends on the available on-board radio system, the mission phase and orbit determination requirements. The accuracy of current ESA and NASA tracking systems is at level of 0.1 mm/s at 60 s integration time for Doppler, 1–5 m for ranging and 6–15 nrad for Delta-DOR measurements in a wide range of operational conditions. The ASTRA study, funded under ESA's General Studies Programme (GSP), addresses the ways to improve the end-to-end accuracy of Doppler, ranging and Delta-DOR systems by roughly a factor of 10. The target accuracies were set to 0.01 mm/s at 60 s integration time for Doppler, 20 cm for ranging and 1 nrad for Delta-DOR. The companies and universities that took part in the study were the University of Rome Sapienza, ALMASpace, BAE Systems and Thales Alenia Space Italy. The analysis of an extensive data set of radio-metric observables and dedicated tests of the ground station allowed consolidating the error budget for each measurement technique. The radio-metric data set comprises X/X, X/Ka and Ka/Ka range and Doppler observables from the Cassini and Rosetta missions. It includes also measurements from the Advanced Media Calibration System (AMCS) developed by JPL for the radio science experiments of the Cassini mission. The error budget for the three radio-metric observables was consolidated by comparing the statistical properties of the data set with the expected error models. The analysis confirmed the contribution from some error sources, but revealed also some discrepancies and ultimately led to improved error models. The error budget reassessment provides adequate information for building guidelines and strategies to effectively improve the navigation accuracies of future deep space missions. We report both on updated error budget for radio-metric observables and the system configurations proposed for the upgrade of ESA's tracking and orbit determination systems.
The "SPICE"1system is the NASA Planetary Science Division's method of
conveniently packaging, archiving, and subsequently accessing
observation geometry needed to understand science data returned from
robotic spacecraft. This paper provides an overview of "SPICE"-what it
is and how it's used- and then offers a glimpse into how it is being
extended to better support the space science community.
The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) Radio Frequency (RF) Telecommunications Subsystem
is used to send commands to the spacecraft, transmit information on the state of the spacecraft and science-related observations,
and assist in navigating the spacecraft to and in orbit about Mercury by providing precise observations of the spacecraft’s
Doppler velocity and range in the line of sight to Earth. The RF signal is transmitted and received at X-band frequencies
(7.2GHz uplink, 8.4GHz downlink) by the NASA Deep Space Network. The tracking data from MESSENGER will contribute significantly
to achieving the mission’s geophysics objectives. The RF subsystem, as the radio science instrument, will help determine Mercury’s
gravitational field and, in conjunction with the Mercury Laser Altimeter instrument, help determine the topography of the
planet. Further analysis of the data will improve the knowledge of the planet’s orbital ephemeris and rotation state. The
rotational state determination includes refined measurements of the obliquity and forced physical libration, which are necessary
to characterize Mercury’s core state.
Radio science experiments of BepiColombo will provide a detailed mapping of Mercury's gravity field and important information about its deep internal structure. The global orbital solutions, obtained from precise radio metric data, entail also very accurate tests of General Relativity and other metric theories of gravity. The classical tests of the solar gravitational deflection and the precession of perihelion could improve the measurement of the post-Newtonian parameters β and γ by 2–3 orders of magnitude, to a value in the range 10−6–10−5. At these levels, violations of General Relativity due to scalar fields, remnant of the inflation age, could occur. In order to achieve the scientific objectives in geophysics and fundamental physics, a suitable radio frequency instrumentation both for onboard and ground equipment is needed. The target two-way accuracy is 20– for range and for range rate (at 1000– integration time). This precision requires the capability of transmitting and receiving at multiple frequencies (to reduce plasma noise) and larger modulation bandwidths for improved ranging performances. We propose an architecture of the onboard and ground radio frequency subsystems which combines minimization of mass and power, technological feasibility, and adequate phase stability and ranging accuracy.
The ESA mission BepiColombo will include a Mercury Planetary Orbiter equipped with a full complement of instruments to perform Radio Science Experiments. Very precise range and range-rate tracking from Earth, on-board accelerometry, altimetry and accurate angular measurements with optical instruments will provide large data sets. From these it will be possible to study (1) the global gravity field of Mercury and its temporal variations due to tides, (2) the medium to short scale (down do ) gravity anomalies, (3) the rotation state of the planet, in particular the obliquity and the libration with respect to the 3/2 spin orbit resonance and (4) the orbit of the center of mass of the planet.
Peering down through the clouds and deep into Jupiter's atmosphere, Juno reveals fundamental processes of the formation and early evolution of our solar system. Using a simple, solar powered, spinning spacecraft in an innovative, highly elliptical polar orbit, Juno avoids Jupiter's highest radiation regions. The mission combines high heritage instruments and spacecraft with an experienced science and engineering team. The designs of the individual instruments are straightforward and have excellent heritage from previous space missions. Juno's scientific payload includes a dual frequency gravity/radio science system, a six wavelength Microwave Radiometer (MWR) for atmospheric sounding and composition, a dual-technique magnetometer, plasma detectors, energetic particle detectors (EPDs), a radio/plasma wave experiment, and an Ultraviolet Imager/Spectrometer. Juno's payload also includes a color camera to provide the public with their first glimpse of Jupiter's poles. Juno will launch in July, 2010 or August, 2011 and arrive at Jupiter 5.2 years later. The nominal mission ends one year after Jupiter arrival with a deorbit into Jupiter's atmosphere.
We have combined the most recent Pioneer Venus Orbiter (PVO) and Magellan (MGN) data with the earlier 1978-1982 PVO data set to obtain a new 60th degree and order spherical harmonic gravity model and a 120th degree and order spherical harmonic topography model. Free-air gravity maps are shown over regions where the most marked improvement has been obtained (Ishtar-Terra, Alpha, Bell and Artemis). Gravity versus topography relationships are presented as correlations per degree and axes orientation.
We report and characterize anomalous orbital-energy changes observed during six Earth flybys by the Galileo, NEAR, Cassini, Rosetta, and MESSENGER spacecraft. These anomalous energy changes are consistent with an empirical prediction formula which is proportional to the total orbital energy per unit mass and which involves the incoming and outgoing geocentric latitudes of the asymptotic spacecraft velocity vectors. We use this formula to predict a potentially detectable flyby velocity increase of less than 1 mm/s for a second Rosetta flyby on November 13, 2007.
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