adsabs/AstroCLIMB huggingface dataset:
Paper: Transmission of a Seismic Wave Generated by Impacts on Granular Asteroids
Authors: Paul Sánchez, Daniel J. Scheeres, Alice C. Quillen
Figure caption: (Left) Kinetic energy of the piston per unit area vs. the speed of the peak in kinetic energy of the system. (Right) Momentum of the piston per unit area vs. the speed of the peak in kinetic energy of the system.
Paper: Transmission of a Seismic Wave Generated by Impacts on Granular Asteroids
Authors: Paul Sánchez, Daniel J. Scheeres, Alice C. Quillen
Figure caption: The different lines represent the distance at which particles of a certain size could have acquired enough energy to escape the gravitational field of the target bodies upon the impacts of the S/C for each space mission. The horizontal line represents r  p  = 5 mm, and its intersections with the mission lines point to the distance R at which these particles would have enough energy to reach escape velocity.
Paper: Transmission of a Seismic Wave Generated by Impacts on Granular Asteroids
Authors: Paul Sánchez, Daniel J. Scheeres, Alice C. Quillen
Figure caption: Fraction of energy loss for all values of confining pressure and impact speed not taking into account the initial energy of the impactor.
Paper: Transmission of a Seismic Wave Generated by Impacts on Granular Asteroids
Authors: Paul Sánchez, Daniel J. Scheeres, Alice C. Quillen
Figure caption: Amplitude of the pressure peak generated by different impacts over time as it is transmitted through the granular medium. (a) Confining pressure of 0.1 Pa, (b) normalized amplitude of the same system (confining pressure 0.1 Pa, where ﹩{P}_{{yy}}^{* }﹩ is the peak value of the pressure generated by the pulse), and (c) normalized amplitude for 5 m s−1 impacts at different confining pressures.
Paper: Transmission of a Seismic Wave Generated by Impacts on Granular Asteroids
Authors: Paul Sánchez, Daniel J. Scheeres, Alice C. Quillen
Figure caption: Schematic view of the assumed expansion of the wave inside a 3D body. Here A 0 is the surface area in contact with the granular medium, R is the distance from any point on the impactor to the closest point in the wave front, and l is the side of the body if the shape of A 0 were a square.
Paper: Transmission of a Seismic Wave Generated by Impacts on Granular Asteroids
Authors: Paul Sánchez, Daniel J. Scheeres, Alice C. Quillen
Figure caption: Velocity of transmission of the peak (U  p ) of the energy of the impact through the granular medium vs. the confining pressure applied to the system.
Paper: Jupiter's Banding and Jets May Be Caused by Tides
Authors: Robert H. Tyler
Figure caption: Using the coordinates of Cases A, B, and C in Figure 6, the tidal solutions are recalculated. For each case, the nondimensional reduced pressure ﹩\tilde{p}﹩ is shown in the left panel. The time-averaged dissipation (middle) shows a number of peaks that correspond with the eigenmode number μ. Regarding the dissipation as a pressure/heat source, an illustration of associated geostrophically balanced jets is shown (right) together with the observed profile of the jets.
Paper: The Promise and Limitations of Precision Gravity: Application to the Interior Structure of Uranus and Neptune
Authors: Naor Movshovitz, Jonathan J. Fortney
Figure caption: Density profiles ρ(s) of the three-layer models of Nettelmann et al. (2013), replotted from their data. Here R m is the mean (volume-equivalent) radius of a surface of constant density, which by hydrostatic equilibrium must also be a surface of constant pressure and potential; s 0 is the mean radius of the 1 bar surface.
Paper: Did Earth Eat Its Leftovers? Impact Ejecta as a Component of the Late Veneer
Authors: Philip J. Carter, Sarah T. Stewart
Figure caption: Mass distribution as a function of semimajor axis and time for bodies in a Grand Tack simulation (left; 022GTJf6hgas) and a calm accretion simulation (right; 022f6sgas_4). The sizes of the points are scaled to the mass of each body. Colors indicate the mean origin distance of mass making up the body, with the corresponding initial colors shown in the bar above the top left panel. The time shown in each row is indicated in the top right corner of the left panels. The evolution of the inner disk is very similar for the first two rows, but after the tack (at 2 Myr), the mass and provenance (color) distribution in the Grand Tack scenario has substantially diverged from that in the calm accretion model.
Paper: Did Earth Eat Its Leftovers? Impact Ejecta as a Component of the Late Veneer
Authors: Philip J. Carter, Sarah T. Stewart
Figure caption: Examples of correlations between pairs of planetary bodies formed in a Grand Tack simulation (022GTJf6hgas). The first column shows the provenance of an embryo (body A) as a pie chart, and the second column shows the corresponding histogram as a function of heliocentric distance. The third and fourth columns show the histogram and pie chart provenance for the comparison body (B). The fifth column indicates the correlation of the bodies’ provenances with the mass fraction of the two bodies originating in each radial bin plotted against each other. The gray line is the 1:1, A = B line and is shown for reference. The number in the top left corner of the panels is the calculated Pearson correlation coefficient for the pair of bodies. The colored circles in the top right corner of the histogram panels indicate the relative sizes of the bodies (according to the scale at the top of the figure) and are colored according to the average color of the body’s provenance histogram.
Paper: Did Earth Eat Its Leftovers? Impact Ejecta as a Component of the Late Veneer
Authors: Philip J. Carter, Sarah T. Stewart
Figure caption: Correlation of bodies to the three most massive embryos (highlighted with black outlines and labeled in each row) as a function of semimajor axis and body mass at the end of an example Grand Tack simulation (022GTJf6hgas). The sizes of the points are scaled to the mass of each body. Colors indicate the mean origin distance of the mass making up the body, as in Figure 2.
Paper: Did Earth Eat Its Leftovers? Impact Ejecta as a Component of the Late Veneer
Authors: Philip J. Carter, Sarah T. Stewart
Figure caption: Correlation of bodies to the three most massive embryos (highlighted with black outlines and labeled in each row) as a function of semimajor axis and body mass at the end of an example calm simulation (022f6sgas_4). The sizes of the points are scaled to the mass of each body. Colors indicate the mean origin distance of the mass making up the body, as in Figure 2.
Paper: The Promise and Limitations of Precision Gravity: Application to the Interior Structure of Uranus and Neptune
Authors: Naor Movshovitz, Jonathan J. Fortney
Figure caption: Barotrope view of sampled profiles of Uranus (left) and Neptune (right) matching currently available observables. The thin vertical line marks the sample’s minimum value of central pressure.
Paper: The Promise and Limitations of Precision Gravity: Application to the Interior Structure of Uranus and Neptune
Authors: Naor Movshovitz, Jonathan J. Fortney
Figure caption: Barotrope view of Uranus (left) and Neptune (right). Green shaded areas are samples obtained with the constraints of the scenario of Section 4.2, showing the 1σ (dark green) and 2σ (light green) sample range overlaid on the samples of Figure 13 (blue) for comparison. The thin vertical line marks the improved sample’s minimum value of central pressure.
Paper: The Promise and Limitations of Precision Gravity: Application to the Interior Structure of Uranus and Neptune
Authors: Naor Movshovitz, Jonathan J. Fortney
Figure caption: Envelope view of Uranus (left) and Neptune (right). Green shaded areas are samples obtained with the constraints of the scenario of Section 4.2, showing the 1σ (dark green) and 2σ (light green) sample range overlaid on the samples of Figure 11 (blue) for comparison.
Paper: The Promise and Limitations of Precision Gravity: Application to the Interior Structure of Uranus and Neptune
Authors: Naor Movshovitz, Jonathan J. Fortney
Figure caption: Ensemble view of sampled ρ(s) profiles of Uranus (left) and Neptune (right) matching currently available observables.
Paper: The Promise and Limitations of Precision Gravity: Application to the Interior Structure of Uranus and Neptune
Authors: Naor Movshovitz, Jonathan J. Fortney
Figure caption: The MOI factor histograms from sampled profiles of Uranus (left) and Neptune (right) matching currently available observables.
Paper: The Promise and Limitations of Precision Gravity: Application to the Interior Structure of Uranus and Neptune
Authors: Naor Movshovitz, Jonathan J. Fortney
Figure caption: Density profiles of a typical ensemble seed state.
Paper: Porosity-filling Metamorphic Brines Explain Ceres’s Low Mantle Density
Authors: Mohit Melwani Daswani, Julie C. Castillo-Rogez
Figure caption: Solute concentrations in fluids resulting from the evolution of two representative bulk compositions for Ceres leading to present-day mantle densities consistent with Dawn observations. Left column: solute concentrations for model 90% CI chondrite plus 10% H2O, Φmax = 30%. Right column: solute concentrations for model 75% CM chondrite plus 25% H2O, ﹩{{\rm{\Phi }}}_{\max 1}=30 \% ﹩, ﹩{{\rm{\Phi }}}_{\max 2}=0 \% ﹩. Top row: fluids produced at a pressure of 50 MPa. Bottom row: fluids at a pressure of 100 MPa. Dotted vertical lines mark the temperature at 100 Myr after formation, dashed vertical lines mark 3 Gyr after formation, and solid vertical lines mark 4.5 Gyr after formation. Dashed vertical lines coincide with the right y-axis position at 100 MPa. Pink shaded areas correspond to supercritical water or immiscible solute regions.
Paper: Porosity-filling Metamorphic Brines Explain Ceres’s Low Mantle Density
Authors: Mohit Melwani Daswani, Julie C. Castillo-Rogez
Figure caption: Average density (ϱ) and fluid-filled porosity (Φ) for chondritic Ceres at discrete points in time during thermal evolution. Arrows point to models consistent with allowable present-day mantle densities.
Paper: Porosity-filling Metamorphic Brines Explain Ceres’s Low Mantle Density
Authors: Mohit Melwani Daswani, Julie C. Castillo-Rogez
Figure caption: Schematic after Vance et al. (2018) and Melwani Daswani et al. (2021) of the thermodynamic fluid extraction structure model to simulate the buildup of Ceres’s ocean from free volatiles that are either present in pores or exsolved during devolatilizing reactions. After each heating step, Gibbs energy is minimized, resulting in an equilibrium phase assemblage in each cell (left wedge). A portion of the fluid phase(s) is then extracted according to a specified rule (see Section 2.1), joins the ocean reservoir, and no longer affects the chemistry and thermodynamics of the deep interior. Finally, Ceres’s structure is resolved (right wedge).
Paper: Porosity-filling Metamorphic Brines Explain Ceres’s Low Mantle Density
Authors: Mohit Melwani Daswani, Julie C. Castillo-Rogez
Figure caption: Fluid pH (left column) and pH recalculated to 298 K and 1 bar (i.e., so neutral pH = 7; right column) for the two representative bulk composition models as a function of pressure and temperature. Dotted lines are the geothermal gradient at 100 Myr after formation, dashed lines are the gradient at 3 Gyr after formation, and solid lines are the gradient at 4.5 Gyr after formation. Blank areas are in the supercritical region or where immiscible fluids coexist.
Paper: Porosity-filling Metamorphic Brines Explain Ceres’s Low Mantle Density
Authors: Mohit Melwani Daswani, Julie C. Castillo-Rogez
Figure caption: Thermal evolution of Ceres from surface to center, used in this work. Inset numbers are temperatures in kelvin. Isotherms are for every 25 K increment. The maximum temperature in the interior is ∼887 K at ∼3052 Myr.
Paper: Porosity-filling Metamorphic Brines Explain Ceres’s Low Mantle Density
Authors: Mohit Melwani Daswani, Julie C. Castillo-Rogez
Figure caption: Average density (ϱ) and fluid-filled porosity (Φ) for Ceres composed of cometary material and 75% CI chondrite plus 25% cometary material at discrete points in time during thermal evolution.
Paper: Porosity-filling Metamorphic Brines Explain Ceres’s Low Mantle Density
Authors: Mohit Melwani Daswani, Julie C. Castillo-Rogez
Figure caption: Isobaric phase assemblage map at 100 MPa for representative models yielding present-day mantle densities consistent with Dawn constraints: (a) 100% CI + 0% H2O, 60% ﹩{{\rm{\Phi }}}_{\max 1}﹩, 0% ﹩{{\rm{\Phi }}}_{\max 2};﹩ (b) 90% CI + 10% H2O, 30% Φmax; (c) 75% CM + 25% H2O, 30% ﹩{{\rm{\Phi }}}_{\max 1}﹩, 0% ﹩{{\rm{\Phi }}}_{\max 2}﹩. None of the cometary models yielded present-day mantle densities consistent with Dawn constraints, but the closest (∼2935 kg m−3) is shown in panel (d): 100% 67P/C-G, 0% Φmax. Vertical lines denote temperatures from the thermal models at 100 MPa at 100 Myr (dotted), 3 Gyr (dashed), and 4.5 Gyr (solid) after formation. Phases are grouped for simplicity (e.g., various molecular solvents are grouped under “Fluid,” two immiscible clinopyroxenes are grouped under “Cpx,” and “Spl” contains various spinel compositional end-members, including magnetite and hercynite). Phase abbreviations are: Atg = antigorite, Bt = biotite, Cal = calcite, Chl = chlorite, Cpx = clinopyroxene, Dol = dolomite, Fanth =ferroanthophyllite, Fluid = retained fluids, Gph = graphite, Glt = greenalite, Gth = goethite, Mgs = magnesite, Minn = minnesotaite, Ne = nepheline, Ol = olivine, Parg = pargasite, Pl = plagioclase, Py = pyrite, Qtz = quartz, Spl = spinel, Stp = stilpnomelane, Tlc = talc, Tr = tremolite, Tro = troilite and pyrrhotite. Here “Σ extracted fluid” is the cumulative mass of fluid extracted with increasing temperature, as fluid volume exceeds the imposed Φmax.
Paper: Porosity-filling Metamorphic Brines Explain Ceres’s Low Mantle Density
Authors: Mohit Melwani Daswani, Julie C. Castillo-Rogez
Figure caption: Evolution of mantle density, fluid-filled porosity in the mantle, and mass of fluids extracted from the mantle for the models 90% CI + 10% H2O, 30% Φmax (top row) and 75% CM + 25% H2O, 30% ﹩{{\rm{\Phi }}}_{\max 1}﹩, 0% ﹩{{\rm{\Phi }}}_{\max 2}﹩ (bottom row). Dotted lines show the geotherm at 100 Myr after formation, dashed lines show the geotherm at 3 Gyr after formation, and solid lines show the geotherm at 4.5 Gyr after formation.
Paper: Porosity-filling Metamorphic Brines Explain Ceres’s Low Mantle Density
Authors: Mohit Melwani Daswani, Julie C. Castillo-Rogez
Figure caption: Time of antigorite dehydration onset and volume fraction of the rocky mantle that reaches complete antigorite dehydration for a broad parametric space describing Ceres’s initial conditions: time of formation after CAIs, rocky thermal conductivity between 0.5 and 3 W m−1 K−1, and fraction of potassium leached from the rock. The arrow points to the thermal evolution studied here (Figure 1).
Paper: Experimental Constraints on Deliquescence of Calcium Perchlorate Mixed with a Mars Regolith Analog
Authors: Rachel A. Slank, Edgard G. Rivera-Valentín, Vincent F. Chevrier
Figure caption: (a) Picture of calcium perchlorate control with LiCl buffer (Experiment 6) before the experiment. (b) Picture of calcium perchlorate with LiCl buffer (Experiment 6) after the experiment. The blue and purple stars are references to the same salt crystals. The red circle is the main area of interest, where deliquescence can be seen in panel (b). This is evident from the change in color of the salt, with the salt becoming more transparent. The salt crystals also reduced in size. (c) Picture of calcium perchlorate control with no buffer (Experiment 5) before the experiment. (d) Picture of calcium perchlorate with no buffer (Experiment 5) after the experiment. The green and pink stars are references to the same salt crystals. There was no visible evidence that deliquescence occurred during this experiment. The salt crystals were the same color and size in the after picture as they were in the before picture.
Paper: Experimental Constraints on Deliquescence of Calcium Perchlorate Mixed with a Mars Regolith Analog
Authors: Rachel A. Slank, Edgard G. Rivera-Valentín, Vincent F. Chevrier
Figure caption: Deliquescence phase diagram of calcium perchlorate with the average (squares) and standard deviation (black horizontal and vertical bars) of the temperature and relative humidity of our experiments, color-coded following the color bar on the right side. The blue line is the DRH, and the red line is the ERH. The gray space indicates the conditions that would permit deliquescence to occur. Five of our experiments were in conditions that should have allowed deliquescence to occur. Four of those were Ca(ClO4)2 mixed with JSC Mars-1 experiments (Experiments 8–11), and one was the Ca(ClO4)2 only with the humidity buffer (Experiment 6). One experiment was not in conditions that would permit deliquescence to occur (Experiment 5, the Ca(ClO4)2 only without the humidity buffer), and one was on the DRH line (Experiment 7) but was considered not in conditions indicative of deliquescence.
Paper: Experimental Constraints on Deliquescence of Calcium Perchlorate Mixed with a Mars Regolith Analog
Authors: Rachel A. Slank, Edgard G. Rivera-Valentín, Vincent F. Chevrier
Figure caption: Picture showing the sample within the Ares Mars simulation chamber. The sample is in the middle of the chamber, sitting on top of the scale. The sample petri dish has the thermocouple secured in place directly above the sample’s surface. The LiCl humidity buffer, seen directly next to the sample, also had a thermocouple secured directly above the saturated solution. The thermocouples that measured the upper and lower atmosphere of the chamber are not visible in this image. The three hygrometers are visible in this picture. As the lid closes on the chamber, the hygrometers move into place, with one directly above the sample, one directly above the humidity buffer, and one high in the chamber to measure the upper atmosphere humidity.
Paper: Experimental Constraints on Deliquescence of Calcium Perchlorate Mixed with a Mars Regolith Analog
Authors: Rachel A. Slank, Edgard G. Rivera-Valentín, Vincent F. Chevrier
Figure caption: Picture and schematic of the Ares Mars simulation chamber and the components that were used to conduct the experiments. (a) Picture of the Ares chamber with the lid open. (b) Schematic of the chamber and the location of the ports. Also illustrated is the location of the chiller coils. (c) Schematic of the inside of the chamber. The diagram shows the location of the hygrometers, thermocouples, sample, scale, and humidity buffer.
Paper: Experimental Constraints on Deliquescence of Calcium Perchlorate Mixed with a Mars Regolith Analog
Authors: Rachel A. Slank, Edgard G. Rivera-Valentín, Vincent F. Chevrier
Figure caption: Mass vs. time (left and green) and water vapor pressure gradient (right and blue) for the experiment that was under conditions that would not permit deliquescence (Experiment 7). The experiment had a positive water vapor pressure gradient, meaning that there was more water vapor in the atmosphere than in the sample. This gradient would result in water vapor diffusion into the sample and should result in mass increase over time.
Paper: NASA’s Double Asteroid Redirection Test (DART): Mutual Orbital Period Change Due to Reshaping in the Near-Earth Binary Asteroid System (65803) Didymos
Authors: Ryota Nakano, Masatoshi Hirabayashi, Harrison F. Agrusa, Fabio Ferrari, Alex J. Meyer, Patrick Michel, Sabina D. Raducan, Paul Sánchez, Yun Zhang
Figure caption: Evolution of the relative angular deviation when Didymos reshapes. All 500 shapes in the ﹩{\gamma }_{{\rm{\max }}}^{A}=1.005﹩ case are plotted (gray lines). The most and least perturbed ones are color coded in red and blue, respectively. The reshaping parameters ﹩\left[{\gamma }_{+x}^{A},{\gamma }_{-x}^{A},{\gamma }_{+y}^{A},{\gamma }_{-y}^{A}\right]﹩ for these two shapes are ﹩\left[1.004\,3,1.003\,6,1.004\,6,1.004\,8\right]﹩ and ﹩\left[1.001\,0,1.001\,4,1.000\,5,1.001\,4\right]﹩, respectively, which correspond to the most and least oblate shapes among the 500 shapes.
Paper: NASA’s Double Asteroid Redirection Test (DART): Mutual Orbital Period Change Due to Reshaping in the Near-Earth Binary Asteroid System (65803) Didymos
Authors: Ryota Nakano, Masatoshi Hirabayashi, Harrison F. Agrusa, Fabio Ferrari, Alex J. Meyer, Patrick Michel, Sabina D. Raducan, Paul Sánchez, Yun Zhang
Figure caption: Idealized impact (red arrow) and considered reshaping mode (dashed line). Panels (a) and (b) show the side and top-down view, respectively. Due to the idealized impact, +y 0, ±x 0, and ±z 0 move to new locations +y 1, ±x 1, and ±z 1, respectively, while −y 0 remains the same (−y 0 = −y 1).
Paper: NASA’s Double Asteroid Redirection Test (DART): Mutual Orbital Period Change Due to Reshaping in the Near-Earth Binary Asteroid System (65803) Didymos
Authors: Ryota Nakano, Masatoshi Hirabayashi, Harrison F. Agrusa, Fabio Ferrari, Alex J. Meyer, Patrick Michel, Sabina D. Raducan, Paul Sánchez, Yun Zhang
Figure caption: Reshaping in the z-axis (δ  z ) vs. orbital period change. The blue stars indicate the simulated results. The black solid line indicates a linear fitted line given by the equation shown in the figure. The blue shaded region represents 1σ in the orbital period change.
Paper: NASA’s Double Asteroid Redirection Test (DART): Mutual Orbital Period Change Due to Reshaping in the Near-Earth Binary Asteroid System (65803) Didymos
Authors: Ryota Nakano, Masatoshi Hirabayashi, Harrison F. Agrusa, Fabio Ferrari, Alex J. Meyer, Patrick Michel, Sabina D. Raducan, Paul Sánchez, Yun Zhang
Figure caption: Synthetic shape model of the reshaped Dimorphos. Panels (a) and (b) show the side views from the x- and y-axis, respectively. Panel (c) shows the top-down view. The black wire frame represents the original shape. The reshaping parameters are ﹩\left[{\gamma }_{+x}^{B},{\gamma }_{-x}^{B},{\gamma }_{+y}^{B},{\gamma }_{-y}^{B},{\gamma }_{+z}^{B},{\gamma }_{-z}^{B}\right]=\left[1.05,1.08,0.79,1.00,1.01,1.09\right]﹩. The reshaping in the +y, δ +y  = L 0 − L, is found to be 16.9 m.
Paper: NASA’s Double Asteroid Redirection Test (DART): Mutual Orbital Period Change Due to Reshaping in the Near-Earth Binary Asteroid System (65803) Didymos
Authors: Ryota Nakano, Masatoshi Hirabayashi, Harrison F. Agrusa, Fabio Ferrari, Alex J. Meyer, Patrick Michel, Sabina D. Raducan, Paul Sánchez, Yun Zhang
Figure caption: Synthetic shape model of reshaped Didymos. Panels (a) and (b) show the side view from the x- and y-axis, respectively. Panel (c) shows the top-down view. The black wire frame represents the original shape. The reshaping parameters are ﹩\left[{\gamma }_{+x}^{A},{\gamma }_{-x}^{A},{\gamma }_{+y}^{A},{\gamma }_{-y}^{A},{\gamma }_{+z}^{A},{\gamma }_{-z}^{A}\right]=\left[1.07,1.06,1.04,1.02,0.91,0.91\right]﹩. The reshaping in the z-axis, δ  z , is 69.4 m.
Paper: NASA’s Double Asteroid Redirection Test (DART): Mutual Orbital Period Change Due to Reshaping in the Near-Earth Binary Asteroid System (65803) Didymos
Authors: Ryota Nakano, Masatoshi Hirabayashi, Harrison F. Agrusa, Fabio Ferrari, Alex J. Meyer, Patrick Michel, Sabina D. Raducan, Paul Sánchez, Yun Zhang
Figure caption: Evolution of the relative angular deviation when Dimorphos reshapes. All 500 shapes in the ﹩{\gamma }_{{\rm{\max }}}^{B}=1.05﹩ case are plotted (gray lines). The most perturbed ones in the positive and negative directions are color coded in red and blue, respectively. The reshaping parameters ﹩\left[{\gamma }_{+x}^{B},{\gamma }_{-x}^{B},{\gamma }_{+z}^{B},{\gamma }_{-z}^{B}\right]﹩ for these two shapes are ﹩\left[1.049,1.049,1.000,1.033\right]﹩ and ﹩\left[1.001,1.001,1.049,1.041\right]﹩, respectively.
Paper: NASA’s Double Asteroid Redirection Test (DART): Mutual Orbital Period Change Due to Reshaping in the Near-Earth Binary Asteroid System (65803) Didymos
Authors: Ryota Nakano, Masatoshi Hirabayashi, Harrison F. Agrusa, Fabio Ferrari, Alex J. Meyer, Patrick Michel, Sabina D. Raducan, Paul Sánchez, Yun Zhang
Figure caption: Geometrical definitions, where ±x 0, ±y 0, and ±z 0, indicated by the arrows, are the surface points located at the intersections between the semiaxes (±x, ±y, ±z) and the body's surface.