Interplanetary missions have typically relied on Radio Science (RS) to recover gravity fields by detecting their signatures on the spacecraft trajectory. The weak gravitational fields of small bodies, coupled with the prominent influence of confounding accelerations, hinder the efficacy of this method. Meanwhile, quantum sensors based on Cold Atom Interferometry (CAI) have demonstrated absolute measurements with inherent stability and repeatability, reaching the utmost accuracy in microgravity. This work addresses the potential of CAI-based Gradiometry (CG) as a means to strengthen the RS gravity experiment for small-body missions. Phobos represents an ideal science case as astronomic observations and recent flybys have conferred enough information to define a robust orbiting strategy, whilst promoting studies linking its geodetic observables to its origin. A covariance analysis was adopted to evaluate the contribution of RS and CG in the gravity field solution, for a coupled Phobos-spacecraft state estimation incorporating one week of data. The favourable observational geometry and the small characteristic period of the gravity signal add to the competitiveness of Doppler observables. Provided that empirical accelerations can be modelled below the nm/s2 level, RS is able to infer the 6 × 6 spherical harmonic spectrum to an accuracy of 0.1–1% with respect to the homogeneous interior values. If this correlates to a density anomaly beneath the Stickney crater, RS would suffice to constrain Phobos’ origin. Yet, in event of a rubble pile or icy moon interior (or a combination thereof) CG remains imperative, enabling an accuracy below 0.1% for most of the 10 × 10 spectrum. Nevertheless, technological advancements will be needed to alleviate the current logistical challenges associated with CG operation. This work also reflects on the sensitivity of the candidate orbits with regard to dynamical model uncertainties, which are common in small-body environments. This brings confidence in the applicability of the identified geodetic estimation strategy for missions targeting other moons, particularly those of the giant planets, which are targets for robotic exploration in the coming decades.
<p class="western" align="justify"><strong>Introduction</strong></p> <p class="western" align="justify"><span lang="en-GB">The Tudat software was created at the Astrodynamics & Space Missions Section (AS) at TU Delft, as a generic C++ tool for astrodynamics research and education. </span><span lang="en-GB">Since 2020, a Python interface named Tudatpy, has been developed.</span><span lang="en-GB"> The core of the software is numerical state propagation and estimation </span><span lang="en-GB">functionality</span><span lang="en-GB">. </span><span lang="en-GB">It has been used for research publications over a wide range of topics, </span><span lang="en-GB">and </span><span lang="en-GB">is embedded in</span><span lang="en-GB"> the </span><span lang="en-GB">TU Delft Spaceflight</span><span lang="en-GB"> M.Sc. curriculum.</span> <span lang="en-GB">The software </span><span lang="en-GB">is</span><span lang="en-GB"> released as a conda packag</span><span lang="en-GB">e</span><span lang="en-GB">. Tudat </span><span lang="en-GB">is</span><span lang="en-GB"> hosted on GitHub (</span><span lang="zxx"><span lang="en-GB">https://github.com/tudat-team/</span></span><span lang="en-GB">), under open-source BSD 3-clause license, with its functionality covered by >200 unit te</span><span lang="en-GB">sts.</span></p> <p class="western" align="justify"><strong>Example applications for planetary missions</strong></p> <p class="western" align="justify">We start by showing three illustrative examples of past and ongoing work with Tudatpy:</p> <ul> <li class="western"><em>Small body orbit design and optimization using fully numerical modeling</em></li> </ul> <p class="western" align="justify">The dynamical environment around small bodies is highly non-linear. In addition, the uncertainty of the gravity field complicates the search for stable spacecraft orbits. In this context, Tudat has been used for several projects, such as the design of a quasi-stable orbit (QSO) around Phobos (Fig. 1), the optimization of an orbit (for maximum coverage/minimum distance) around an asteroid, and the design of robustly stable spacecraft orbits under uncertainties in the asteroid gravity field.</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify"><img src="" width="1070" height="302" name="Image1" align="left" /></p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify"><em>Fig. 1 QSO orbits around Phobos designed using Tudatpy and Pygmo [1]</em></p> <p class="western" align="justify">&#160;</p> <ul> <li class="western"><em>Galilean satellite ephemerides determination from JUICE tracking data</em></li> </ul> <p class="western" align="justify">The JUICE mission will provide data on the dynamics of the Galilean moons to unprecedented accuracy. Using a simulated set of radio tracking data, Tudat has been used to simulate uncertainty of the ephemerides of the Galilean satellites during and after the JUICE mission (see Fig. 2). This analysis will be extended to provide a flexible tool to analyze the potential for a global inversion of Earth- and space-based radio and optical data for satellite ephemerides.&#160;</p> <p class="western" align="justify"><img src="" width="836" height="517" name="Image5" align="left" border="0" /></p> <p class="western" lang="en-GB" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify"><em>Fig. </em><em>2</em><em> </em><em>Galilean satellite ephemeris uncertainty obtained from covariance analysis in a coupled estimation, using simulated JUICE radio tracking data [</em><em>2</em><em>]</em></p> <p class="western" align="justify">&#160;</p> <ul> <li class="western"><em>Interplanetary trajectory design using multiple gravity assists (MGA), deep space maneuvers (DSM), and shape-based low-thrust </em></li> </ul> <p class="western" align="justify">Tudat includes a framework for interplanetary trajectory design (see Fig. 3 for example), where the typical MGA-DSM functionality is enhanced with shape-based (spherical shaping and hodographic shaping) legs. Although the interplanetary trajectory is evaluated/optimized using a (semi-)analytical inner loop, the numerical propagatio of Tudat allows for a direct verification of the final trajectory under perturbations and for the use of differential correction to generate a high-fidelity transfer orbit.</p> <p class="western" align="justify"><img src="" width="739" height="564" name="Image5" align="left" border="0" /></p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify">&#160;</p> <p class="western" align="justify"><em>Fig. 3 Earth-Mercury transfer using EEVM sequence, one DSM per leg, in patched conic approximation(taken from one of the examples on the Tudatpy website)</em></p> <p class="western" align="justify"><strong>Functionality</strong></p> <p class="western" align="justify">Tudat functionality falls into the following broad categories:</p> <ul> <li class="western">Numerical propagation of dynamics, with modular setup and options for solar system bodies, accelerations, propagation schemes, <em>etc.</em> In addition to translation state, it can combine different types of dynamics for any number of bodies, including coupled orbital-rotational motion. No fundamental distinction is made between natural and artificial bodies, and the propagation is capable of both single- and multi-arc (or a combination). Tudat has a broad set of outputs (&#8216;dependent variables&#8217;) that it can generate during numerical propagation that are useful for visualization/post-processing.</li> <li class="western">State and parameter estimation: Tudat contains a large amount of functionality for performing (simulated) state and parameter estimation/covariance analysis from observational data. The framework is set up in a modular fashion, allowing for a combined analysis of a diverse set of types of observations and parameters. It has been used in a large number of simulation studies, with work ongoing to extend the functionality to processing DSN tracking data. It has been applied to the orbit determination of LRO, as well as to preliminary Doppler/VLBI data analysis of Mars and Venus Express.</li> <li class="western">Mission design and optimization: Modules containing mission design tools, such as Lambert targeters and multiple gravity-assist transfers, are included in Tudat. Additionally, Tudat provides an interface to the Pagmo2 optimization software.</li> </ul> <p class="western" lang="en-GB" align="justify"><strong>Documentation and development</strong></p> <p class="western" align="justify">In 2020, development of a Python interface, named TudatPy, was initiated. This has now become the default interface for Tudat and associated documentation, including:</p> <ul> <li class="western">An installation and top-level user guide, supported by a growing set of example applications (<span lang="zxx">https://docs.tudat.space/</span>)</li> <li class="western">Documentation for the Application Programmer Interface (API) of TudatPy (<span lang="zxx">https://py.api.tudat.space/</span>)</li> </ul> <p class="western" lang="en-GB" align="justify">Both parts of the documentation now cover the core aspects of the functionality, and are being continuously expanded. At the time of writing, some C++ functions have yet to be exposed to Python, while other functions are missing their API documentation.</p> <p class="western" align="justify">If you are interested in using or developing Tudat(py), you are most welcome to do so! Any questions about its functionality or suggestions for future implementation are always welcome, and can be addressed to the first author of this abstract. Tudat discussions primarily take place over Slack, open to any potential interested parties.</p> <p class="western" align="justify">[1] Plumaris et al. (2022). <em>"<span dir="ltr" role="presentation">Cold Atom Interferometry for enhancing the Radio Science</span></em><br role="presentation" /><em><span dir="ltr" role="presentation">gravity experiment: a Phobos case study" </span></em>Remote Sensing, (submitted)</p> <p class="western" align="justify">[2] Fayolle et al. (2022). <em>"Decoupled and coupled moons&#8217; ephemerides estimation strategies</em><br /><em>Application to the JUICE mission"</em> Planetary and Space Science, (revision submitted)</p> <p class="western" align="justify">&#160;</p>
Synopsis:The interaction of our protective heliosphere and the Very Local Interstellar Medium (VLISM) is the least explored and most rewarding frontier of space physics. New evidence amplifies the central role of the heliosphere in the evolution of the solar system along its 4.6billion-year journey around the galaxy. In addition to the dense clouds of plasma, gas and dust seeding the early proto solar nebula, recent supernovae have left the entire solar system exposed to extreme fluxes of interstellar material and cosmic radiation with far-reaching implications. Our current knowledge lacks the direct measurements necessary to understand how our star upholds its vast heliosphere and its potentially game-changing role in the evolution of our galactic home. Interstellar Probe provides new, required measurements over more than a solar cycle to uncover the physical processes starting near the Sun responsible for creating our dynamic heliosphere. In April 2022, the pragmatic Interstellar Probe Mission Concept Study was completed after four years, detailing a Large Strategic heliophysics mission that would transect the heliosphere from 1 au to the VLISM. Its journey provides rich science for generations across heliophysics and presents an opportunity to push the frontier of space exploration farther than ever done before. Modest crossdivisional investments enable high-value planetary science and astrophysics, deepening our understanding of the emergence of our habitable planetary system. A trajectory through the forward hemisphere of the heliosphere would be accomplished by a launch in the 2036-2042 timeframe using conventional chemical propulsion and a heavy-lift launch vehicle, such as the Space Launch System (SLS). A Jupiter Gravity Assist could propel an 860-kg spacecraft with an 87-kg payload of ten instruments delivering a unified view of the global heliosphere, reaching the VLISM after 16 years. The spacecraft is designed to a 50-year nominal lifetime using modern-day technology based on successful missions like New Horizons. Two next-generation Radioisotope Thermal Generators (RTGs) would ensure 300 We at end of nominal mission at 375 au and could enable exploration even beyond 500 au.
<p>Within the pre-phase A of the Moonlight project proposed and funded by the European Space Agency (ESA), the ATLAS consortium has proposed an architecture to support a Lunar Radio Navigation System (LRNS) capable of providing PNT (Positioning, Navigation, and Timing) services to various lunar users. The Moonlight LRNS will be a powerful tool in support of the lunar exploration endeavors, both human and robotic.</p><p>The ESA LRNS will consist of a small constellation of 3-4 satellites put in Elliptical Lunar Frozen Orbits (ELFO) with the aposelene above the southern hemisphere to better cover this region, given its interest for future lunar missions. This LRNS will be supported by a ground station network of small dish antennas (~30 cm), which can establish Multiple Spacecraft Per Aperture (MSPA) tracking at K-band. Any Earth station will be capable of sending a single uplink signal to multiple spacecraft thanks to Code Division Multiplexing modulation, while in the downlink multiple carriers can share the same K-band bandwidth by implementing Code Division Multiple Access (CDMA) on the onboard transponders. This allows the implementation of the Same Beam Interferometry (SBI) technique [1], which adds to spread spectrum ranging and Doppler measurements. In the scope of disseminating accurate PNT services to end users, the constellation will also be capable of maintaining a synchronization to the Earth station clocks to the ns level.</p><p>The performances of the proposed architecture have been validated through numerical simulations performed with the ESA GODOT software, enhanced with additional user-defined features and capabilities. For each satellite of the LRNS constellation, the attainable orbital accuracy is at level of a few meters for most orbit mean anomalies and it has been computed considering a setup which includes a perturbed dynamical model (mainly coming from uncertainties in the accelerations induced by the solar radiation pressure and orbital maneuvers) and a realistic error model for Doppler, ranging and SBI measurements.</p><p>REFERENCE:</p><ul><li>Gregnanin, M. et al. (2012). Same beam interferometry as a tool for the investigation of the lunar interior. Planetary and Space Science 74, 194-201</li> </ul>
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