Estimating Small-Body Gravity Field from Shape Model and Navigation Data

2008 ◽  
Author(s):  
Ryan Park ◽  
Robert Werner ◽  
Shyamkumar Bhaskaran
Keyword(s):  
Gravity Field ◽  
Small Body ◽  
Shape Model ◽  
Navigation Data

Estimating Small-Body Gravity Field from Shape Model and Navigation Data

2010 ◽  
Vol 33 (1) ◽  
pp. 212-221 ◽  
Author(s):  
Ryan S. Park ◽  
Robert A. Werner ◽  
Shyam Bhaskaran
Keyword(s):  
Gravity Field ◽  
Small Body ◽  
Shape Model ◽  
Navigation Data

scholarly journals Heterogeneous mass distribution of the rubble-pile asteroid (101955) Bennu

2020 ◽  
Vol 6 (41) ◽  
pp. eabc3350 ◽  
Author(s):  
D. J. Scheeres ◽  
A. S. French ◽  
P. Tricarico ◽  
S. R. Chesley ◽  
Y. Takahashi ◽  
...  
Keyword(s):  
Gravity Field ◽  
Mass Distribution ◽  
Small Body ◽  
Parent Body ◽  
Constant Density ◽  
Internal Mass ◽  
Shape Model ◽  
Rapid Rotation ◽  
Insight Into ◽  
Rubble Pile

The gravity field of a small body provides insight into its internal mass distribution. We used two approaches to measure the gravity field of the rubble-pile asteroid (101955) Bennu: (i) tracking and modeling the spacecraft in orbit about the asteroid and (ii) tracking and modeling pebble-sized particles naturally ejected from Bennu’s surface into sustained orbits. These approaches yield statistically consistent results up to degree and order 3, with the particle-based field being statistically significant up to degree and order 9. Comparisons with a constant-density shape model show that Bennu has a heterogeneous mass distribution. These deviations can be modeled with lower densities at Bennu’s equatorial bulge and center. The lower-density equator is consistent with recent migration and redistribution of material. The lower-density center is consistent with a past period of rapid rotation, either from a previous Yarkovsky-O’Keefe-Radzievskii-Paddack cycle or arising during Bennu’s accretion following the disruption of its parent body.

Estimation of the interior density of a small body given its gravity field

2021 ◽  
Author(s):  
Alfonso Caldiero ◽  
Sébastien Le Maistre ◽  
Véronique Dehant
Keyword(s):  
Gravity Field ◽  
Small Body

scholarly journals An elastic model of Phobos’ libration

2020 ◽  
Vol 636 ◽  
pp. A27
Author(s):  
Yongzhang Yang ◽  
Jianguo Yan ◽  
Xi Guo ◽  
Qingbao He ◽  
Jean-Pierre Barriot
Keyword(s):  
Numerical Model ◽  
Gravity Field ◽  
Numerical Integration ◽  
Elastic Properties ◽  
Rotational Motion ◽  
Space Mission ◽  
Elastic Model ◽  
Shape Model ◽  
Future Space ◽  
Least Squares Fit

Context. Study the rotation of a celestial body is an efficient way to infer its interior structure, and then may give information of its origin and evolution. In this study, based on the latest shape model of Phobos from Mars Express (MEX) mission, the polyhedron approximation approach was used to simulate the gravity field of Phobos. Then, the gravity information was combined with the newest geophysical parameters such as GM and k2 to construct the numerical model of Phobos’ rotation. And with an appropriate angles transformation, we got the librational series respect to Martian mean equator of date. Aims. The purpose of this paper is to develop a numerical model of Phobos’ rotational motion that includes the elastic properties of Phobos. The frequencies analysis of the librational angles calculated from the numerical integration results emphasize the relationship between geophysical properties and dynamics of Phobos. This work will also be useful for a future space mission dedicated to Phobos. Methods. Based on the latest shape model of Phobos from MEX mission, we firstly modeled the gravity field of Phobos, then the gravity coefficients were combined with some of the newest geophysical parameters to simulate the rotational motion of Phobos. To investigate how the elastic properties of Phobos affect its librational motion, we adopted various k2 into our numerical integration. Then the analysis was performed by iterating a frequency analysis and linear least-squares fit of Phobos’ physical librations. From this analysis, we identified the influence of k2 on the largest librational amplitude and its phase. Results. We showed the first ten periods of the librational angles and found that they agree well with the previous numerical results which Phobos was treated as a perfectly rigid body. We also found that the maximum amplitudes of the three parameters of libration are also close to the results from a rigid model, which is mainly due to the inclination of Phobos and moments of inertia. The other amplitudes are slightly different, since the physics contained in our model is different to that of a previous study, specifically, the different low-degree gravity coefficients and ephemeris. The libration in longitude τ has the same quadratic term with previous numerical study, which is consistent with the secular acceleration of Phobos falling onto Mars. We investigated the influence of the tidal Love number k2 on Phobos’ rotation and found a detectable amplitude changes (0.0005°) expected in the future space mission on τ, which provided a potential possibility to constrain the k2 of Phobos by observing its rotation. We also studied the influence of Phobos’ orbit accuracy on its libration and suggested a simultaneous integration of orbit and rotation in future work.

scholarly journals Brief Introduction of Promoting the Chinese Program For Exploring the Martian System

2012 ◽  
Vol 10 (H16) ◽  
pp. 165-165
Author(s):  
Jinsong Ping ◽  
Xian Shi ◽  
Nianchuan Jian ◽  
Sujun Zhang ◽  
Mingyuan Wang ◽  
...  
Keyword(s):  
Gravity Field ◽  
Tracking System ◽  
Small Body ◽  
Open Loop ◽  
Deep Space Exploration ◽  
Global Gravity ◽  
Rosetta Mission ◽  
Phobos Grunt ◽  
Loop Technique ◽  
Mission Teams

AbstractFollowing the progress of Chinese deep space exploration step, since 2006 we started a Mars mission, Yinghuo-1, by join in the Phobos-Grunt mission of Russia. A satellite bus platform and onboard payloads as well as an innovative open-loop radio tracking system have been developed by mission team. Also, together with Russian and German colleagues, we developed a kind of in-beam tracking method for measuring the rotation and nutation of Phobos, and developed the 1st Phobos global gravity field for the mission. We are promoting the Chinese new mission for Mars exploration. Although the joint YH-1 & Phobos-Grunt mission failed, the new techniques and knowledge developed by mission teams may benifit the future missions. In fact, the open-loop technique have been applied into lunar and other planetary missions, and the method in developing Phobos global gravity field will be used in the study of Rosetta mission and future Chinese mission for small body.

scholarly journals The second-degree gravity coefficients of Phobos from two Mars Express flybys

2019 ◽  
Vol 490 (2) ◽  
pp. 2007-2012 ◽  
Author(s):  
X Yang ◽  
J G Yan ◽  
T Andert ◽  
M Ye ◽  
M Pätzold ◽  
...  
Keyword(s):  
Gravity Field ◽  
A Priori ◽  
Equatorial Region ◽  
Constant Density ◽  
Shape Model ◽  
Mars Express ◽  
The Past ◽  
Density Assumption ◽  
Mass Estimate ◽  
Second Degree

ABSTRACT Several close spacecraft flybys of Phobos have been performed over the past 40 yr in order to determine the gravity field of this tiny Martian moon. In this work, the second-degree coefficients of the gravity field of Phobos were derived from the radio tracking data of two combined Mars Express flybys (2010 and 2013), by applying a least squares regularized inverse technique, that introduces as an a priori the gravity field retrieved from a shape model based on constant density hypothesis. A gravitational mass estimate of $(7.0765\pm 0.0075)\times 10^5 \, \mathrm{m^3\, s}^{-2}$ and second-degree gravity coefficients C20 = −0.1378 ± 0.0348 and C22 = 0.0166 ± 0.0153(3σ) were derived. The estimated C20 value, in contrast to the value of C20 computed from the shape model under the constant density assumption, supports an inhomogeneous distribution inside Phobos at a confidence interval of 95 per cent (1.96σ). This result indicates a denser mass in the equatorial region or lighter mass in polar areas.

scholarly journals Tensile strength of 67P/Churyumov–Gerasimenko nucleus material from overhangs

2018 ◽  
Vol 611 ◽  
pp. A33 ◽  
Author(s):  
N. Attree ◽  
O. Groussin ◽  
L. Jorda ◽  
D. Nébouy ◽  
N. Thomas ◽  
...  
Keyword(s):  
Tensile Strength ◽  
Dynamic Stress ◽  
Small Body ◽  
Shape Model ◽  
Lower Limits ◽  
Comet 67P ◽  
Rubble Pile ◽  
Cometary Activity

We directly measured twenty overhanging cliffs on the surface of comet 67P/Churyumov–Gerasimenko extracted from the latest shape model and estimated the minimum tensile strengths needed to support them against collapse under the comet’s gravity. We find extremely low strengths of around 1 Pa or less (1 to 5 Pa, when scaled to a metre length). The presence of eroded material at the base of most overhangs, as well as the observed collapse of two features andthe implied previous collapse of another, suggests that they are prone to failure and that the true material strengths are close to these lower limits (although we only consider static stresses and not dynamic stress from, for example, cometary activity). Thus, a tensile strength of a few pascals is a good approximation for the tensile strength of the 67P nucleus material, which is in agreement with previous work. We find no particular trends in overhang properties either with size over the ~10–100 m range studied here or location on the nucleus. There are no obvious differences, in terms of strength, height or evidence of collapse, between the populations of overhangs on the two cometary lobes, suggesting that 67P is relatively homogenous in terms of tensile strength. Low material strengths are supportive of cometary formation as a primordial rubble pile or by collisional fragmentation of a small body (tens of km).

The Impact of Missing and Error-Prone Auxiliary Information on Sparse-Matrix Sub-Population Parameter Estimates

Methodology ◽  
2015 ◽  
Vol 11 (3) ◽  
pp. 89-99 ◽  
Author(s):  
Leslie Rutkowski ◽  
Yan Zhou
Keyword(s):  
Sparse Matrix ◽  
Small Body ◽  
Auxiliary Information ◽  
Poor Quality ◽  
Quality Data ◽  
Estimation Methods ◽  
Parameter Estimates ◽  
Population Parameter ◽  
Conditioning Model ◽  
The Impact

Abstract. Given a consistent interest in comparing achievement across sub-populations in international assessments such as TIMSS, PIRLS, and PISA, it is critical that sub-population achievement is estimated reliably and with sufficient precision. As such, we systematically examine the limitations to current estimation methods used by these programs. Using a simulation study along with empirical results from the 2007 cycle of TIMSS, we show that a combination of missing and misclassified data in the conditioning model induces biases in sub-population achievement estimates, the magnitude and degree to which can be readily explained by data quality. Importantly, estimated biases in sub-population achievement are limited to the conditioning variable with poor-quality data while other sub-population achievement estimates are unaffected. Findings are generally in line with theory on missing and error-prone covariates. The current research adds to a small body of literature that has noted some of the limitations to sub-population estimation.

Risk Factors for Bleeding during Treatment of Acute Venous Thromboembolism

1996 ◽  
Vol 76 (05) ◽  
pp. 682-688 ◽  
Author(s):  
Jos P J Wester ◽  
Harold W de Valk ◽  
Karel H Nieuwenhuis ◽  
Catherine B Brouwer ◽  
Yolanda van der Graaf ◽  
...  
Keyword(s):  
Risk Factors ◽  
Venous Thromboembolism ◽  
Surface Area ◽  
Body Surface Area ◽  
Body Surface ◽  
Small Body ◽  
Bleeding Risk ◽  
Risk Scores ◽  
Risk Of Bleeding ◽  
Acute Venous Thromboembolism

Summary Objective: Identification of risk factors for bleeding and prospective evaluation of two bleeding risk scores in the treatment of acute venous thromboembolism. Design: Secondary analysis of a prospective, randomized, assessor-blind, multicenter clinical trial. Setting: One university and 2 regional teaching hospitals. Patients: 188 patients treated with heparin or danaparoid for acute venous thromboembolism. Measurements: The presenting clinical features, the doses of the drugs, and the anticoagulant responses were analyzed using univariate and multivariate logistic regression analysis in order to evaluate prognostic factors for bleeding. In addition, the recently developed Utrecht bleeding risk score and Landefeld bleeding risk index were evaluated prospectively. Results: Major bleeding occurred in 4 patients (2.1%) and minor bleeding in 101 patients (53.7%). For all (major and minor combined) bleeding, body surface area ≤2 m2 (odds ratio 2.3, 95% Cl 1.2-4.4; p = 0.01), and malignancy (odds ratio 2.4, 95% Cl 1.1-4.9; p = 0.02) were confirmed to be independent risk factors. An increased treatment-related risk of bleeding was observed in patients treated with high doses of heparin, independent of the concomitant activated partial thromboplastin time ratios. Both bleeding risk scores had low diagnostic value for bleeding in this sample of mainly minor bleeders. Conclusions: A small body surface area and malignancy were associated with a higher frequency of bleeding. The bleeding risk scores merely offer the clinician a general estimation of the risk of bleeding. In patients with a small body surface area or in patients with malignancy, it may be of interest to study whether limited dose reduction of the anticoagulant drug may cause less bleeding without affecting efficacy.

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