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Phobos mass estimations from MEX and Viking1 data: influence of different noise sources and estimation strategies
Maria Kudryashova1,2, P. Rosenblatt1, J-Ch. Marty3
1 2

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Royal Observatory of Belgium Paris Observatory , France CNES/GRGS, Toulouse, France
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Motivation
· Origin of Martian moons? · We can get clues from geodetic parameters: bulk
density; mass distribution; composition; dissipative properties...
Internal mass distribution related to principal moments of inertia (A

Where M is the mass of Phobos, r0 is the mean radius of Phobos and e is the ellipticity of its orbit around Mars.

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Why are we interested in very precise Phobos mass?
Geodetic parameters (C20, C22) of heterogeneous interior departs by a few percents (<10%) from the homogeneous interior (Rivoldini et al., 2011, Rosenblatt et al, 2013);


C00 (GM) is correlated with C

20

and C22;

Thus, GM need to be known with precision ~0.1% (MEX simulations, Rosenblatt et al, 2013);


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Phobos mass determination from different spacecraft/strategies
PДtzold et al., 2014

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Phobos mass determination from similar strategy: Viking 1 and MEX
Close encounters only
· · · · · · · · Estimated parameters: for both s/c: initial state vector, Phobos GM, radiation pressure coefficients. In case of MEX: atmosph drag, Doppler frequency offset, range bias, thruster parameters

· ·

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Actual precision of Phobos mass determination
· Aim: to quantify the impact of different error sources on the Phobos GM estimations from flyby data. · Considered error sources: ­ Phobos a priori ephemerides; ­ Phobos a priori GM value; ­ measurements noise; ­ different strategies; · Methods: ­ real data analysis; ­ simulations.
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Real data: sensitivity of GM estimations to the errors in a priori Phobos ephemerides
sensitive

not sensitive
Lainey, 2007 (IMCCE), Jacobson, 2010 (JPL) Kudryashova et al., St Petersburg 23, September 2014

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Simulations: impact of errors in a priori Phobos ephemeris on the Phobos GM

Simulations: IMCCE (Lainey, 2007) ephemeris + X-band/S-band noise level for MEX/Viking1; Reconstruction: a) IMCCE Phobos ephemeris -1 km (perturbed) and b) IMCCE ephemeris (unperturbed) + same noise level as for simulations in all cases.
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Simulations: sensitivity of the measurements to the a priori GM value
Simulations: zero noise+ IMCCE a priori ephemerides +GMPH = 7.16 * 105 m3/sec2. Reconstruction: zero noise+ IMCCE a priori ephemerides + GM1PH = 7.66 *105 and GM2PH= 8.16 *105 m3/sec2. Only initial state vector is estimated during simulated orbit reconstruction.

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Simulations: sensitivity of the measurements to the a priori GM value

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Sensitivity of the measurements to the observational/modeling noise
simulations and orbit reconstructions: IMCCE Phobos ephemeris. Viking1 data: noise level 0.06 mm/sec and 1 mm/ sec decreasing the value of the noise diminish the GM formal errors and bringing the values of GM closer to one another

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Sensitivity of the measurements to the observational/modeling noise
MEX data with the noise levels 0.01 and 0.02 mm/sec .

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CONCLUSIONS
Accuracy and precision of GM estimations increase with decreasing of the value of the noise for both spacecraft.
VIKING1:

·neither distances of flybys nor a priori ephemerides show clear correlation with the GMPH estimations and their formal errors; ·the post-fit Doppler residuals are not very sensitive to the errors in GMPH: changes of the spacecraft velocities due to GMPH =105 [m3/sec2] (14% a priori GMPH) are at the level of 0.06 mm/sec which corresponds to the most optimistic estimation of the observational noise level in case of Viking 1; Observational noise dominates all other considered sources of errors
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CONCLUSIONS
MEX: there is a clear dependence between Phobos GM estimations and a priori ephemerides used: the bigger the difference in a priori ephemerides (which reaches 0,5 km for the flyby of the year 2008) the bigger the difference in GM estimations. Changes of the spacecraft velocities due to GMph =105 [m3/sec2] (14% of Gmph) could be observed (>= noise level) from very distant flybys (at distance 467 km it produces vel changes 0.02 mm/sec) and GMph =5*104 (7% of GMph) can be observed starting from closer flybys (2010 at the distance about 78 km); The uncertainties in Phobos a priori position dominate other sources of errors.
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Thank you!
· Acknowledgments: · This work is a part of the European Satellite Partnership Computing Ephemerides (ESPaCE), funded by the European FP7-project. · All computations have been performed with the GINS (Geodesie par Integration Numerique Simultanee) software developed by the French space agency (CNES) and further adapted at ROB for planetary geodesy applications.

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