Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.gao.spb.ru/english/as/j2014/presentations/kudryashova.pdf Дата изменения: Sun Sep 28 20:11:27 2014 Дата индексирования: Sun Apr 10 05:56:50 2016 Кодировка: Поисковые слова: stellar nursery

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

3

Royal Observatory of Belgium Paris Observatory , France CNES/GRGS, Toulouse, France
Kudryashova et al., St Petersburg 23, September 2014 1


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.

Kudryashova et al., St Petersburg 23, September 2014

2


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);


Kudryashova et al., St Petersburg 23, September 2014

3

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

Kudryashova et al., St Petersburg 23, September 2014

4


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

· ·

Kudryashova et al., St Petersburg 23, September 2014

5


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.
Kudryashova et al., St Petersburg 23, September 2014

6


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

7


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.
Kudryashova et al., St Petersburg 23, September 2014

8


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.

Kudryashova et al., St Petersburg 23, September 2014

9

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

Kudryashova et al., St Petersburg 23, September 2014

10


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

Kudryashova et al., St Petersburg 23, September 2014

11

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

Kudryashova et al., St Petersburg 23, September 2014

12


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
Kudryashova et al., St Petersburg 23, September 2014

13


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.
Kudryashova et al., St Petersburg 23, September 2014

14


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.

Kudryashova et al., St Petersburg 23, September 2014

15