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Leake, M.A.1
Chapman, C.R.2
Weidenschilling, S.J.3
Davis, D.R.4
Greenberg, R.5
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7
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A. Pais, Subtle is the Lord. The Science and the Life of Albert Einstein (Oxford University Press, Oxford, 1983).
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11
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I.I. Shapiro, in General Relativity and Gravitation, edited by N. Ashby, D.F. Barlett, and W. Wyss (Cambridge University Press, Cambridge, England, 1990), p. 313.
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C.M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, England, 1981).
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L. Iess, G. Giampieri, J.D. Anderson, and B. Bertotti, Class. Quantum Grav. 16, 1487 (1999).
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Class. Quantum Grav.
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Iess, L.1
Giampieri, G.2
Anderson, J.D.3
Bertotti, B.4
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24
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85042318478
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A.M. Nobili, in Recent Advances in Metrology and Fundamental Constants, edited by T.J. Quinn, S. Leschiutta, and P. Tavella (IOS Press, Amsterdam, 2001), p. 609.
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27
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P.L. Bender, N. Ashby, M.A. Vincent, and J.M. Wahr, Adv. Space Sci. 9, 113 (1989).
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Bender, P.L.1
Ashby, N.2
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N. Ashby, P.L. Bender, and J.M. Wahr, “Gravitational physics tests from ranging to a small Mercury relativity satellite,” preprint (1999).
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A. Balogh et al., BepiColombo: An interdisciplinary cornerstone mission to the planet Mercury, ESA-SCI(2000)1;see also http://sci.esa.int/home/bepicolombo/ for basic information about this mission, and http://solarsystem.estec.esa.nl/Mercury/MercuryAssess.htm for the System and Technology Study Report. Giuseppe (Bepi) Colombo (1920–1984) is credited, among many other achievements, for the theory explaining Mercury’s non-synchronous rotation, which was discovered with the first radar data from that planet.
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33
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85042271445
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The mission will also include a “surface element,” which is a semi-soft lander. Unfortunately, due to the harsh Mercury environment and to power problems, the lander is not planned to survive more than a week, thus a transponder would not be useful in determining either the orbit or the rotation of the planet.
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34
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Anderson, J.D.1
Gross, M.2
Nordtvedt, K.3
Turyshev, S.G.4
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Milani, A.1
Rossi, A.2
Vokrouhlický, D.3
Villani, D.4
Bonanno, C.5
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85042321955
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M.H. Soffel, Relativity in Astrometry, Celestial Mechanics and Geodesy (Springer, Berlin, 1989).
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38
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85042334703
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It might be worth mentioning that the JPL ephemerides in fact already contain partially the PPN analysis described below, since the lunar laser ranging and Viking data were used by JPL to constrain some of the PN parameters (e.g. (Formula presented) However, since these results are so far in perfect agreement with general relativity and since the BepiColombo mission will be found to be able to constrain more tightly these parameters, we regard the JPL ephemerides as a pure general relativity template.
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43
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21444433587
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We disregard the PN parameter (Formula presented) that besides the parametrizing dependence on the preferred cosmological frame also expresses a degree of violation of the conservation laws (e.g. 13). Since these later effects are already of rather speculative character and since the parameter (Formula presented) has been already very tightly constraint by the analysis of the binary pulsar dynamics [J.F. Bell, and T. Damour, Class. Quantum Grav. 13, 3121 (1996)], in fact much more tightly than can be obtained from the Mercury data, the omission of this parameter from our analysis is justified.
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Class. Quantum Grav.
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, pp. 3121
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Bell, J.F.1
Damour, T.2
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44
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85042317506
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P.J.E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, 1993).
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55
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85042322895
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L. Iess (personal communication).
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56
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85042259445
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The measurements are taken from some ground stations, but the geocentric position and rotation of the stations are well known, e.g., by VLBI and other techniques, thus in the discussion which follows we will assume that an accurate topocentric correction has been applied and the observations are considered to be from the center of mass of the Earth.
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57
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0008872376
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A. Milani, M. Carpino, A. Rossi, G. Catastini, and S. Usai, Manuscripta Geodaetica 20, 123 (1995).
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Milani, A.1
Carpino, M.2
Rossi, A.3
Catastini, G.4
Usai, S.5
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58
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85042311257
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Time-dependent phenomena, such as tides, have to be parametrized with time-independent coefficients, such as Love numbers.
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59
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85042259830
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Even if there were significant correlations between local and global parameters, a two step procedure could be used, but in this case the sequence of two steps should be considered as one iteration in an iterative process, to be repeated until convergence.
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60
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85042290701
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A symmetric positive definite matrix is badly conditioned if the ratio between the largest and the smallest eigenvalue is large.
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62
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85042271064
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The group of symmetries is assumed to act effectively; that is, no subgroup larger than the identity acts trivially.
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63
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85042254606
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A.E. Roy, Orbital Motion (Hilger Ltd, Bristol, 1982).
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65
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85042267800
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The results are somewhat sensitive to the choice of the reference time (Formula presented) The figures and tables in this paper refer to tests done with (Formula presented) set to the initial time (at the beginning of the orbital phase of the BepiColombo mission). Because of the particular shape of the systematic range drift, the more usual choice of (Formula presented) at the center of the observation time span does not give better results for all parameters, actually somewhat worse in the case with preferred frame parameters.
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66
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85042315760
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A change in distance (Formula presented) can be the effect of the corrections to the positions of both planets; the fact that, in the multiarc fit, it was obtained by displacing only Mercury in the Earth-Mercury direction does not matter, because a motion of the Earth would produce exactly the same effects.
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67
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0346558634
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a small improvement can be expected if the data from the Europa Orbiter mission, scheduled presently for 2008, were available [R.A. Jacobson (private communication)].
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R.A. Jacobson, Bull. Am. Astron. Soc. 33, 1101 (2001);a small improvement can be expected if the data from the Europa Orbiter mission, scheduled presently for 2008, were available [R.A. Jacobson (private communication)].
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(2001)
Bull. Am. Astron. Soc.
, vol.33
, pp. 1101
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Jacobson, R.A.1
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69
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85042257666
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L.D. Landau and E.M. Lifschitz, Méchanique (Éditions MIR, Moscow, 1966).
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70
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85042254584
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T.M. Eubanks et al., Advances in solar system tests of gravity, preprint available at http://casa.usno.navy.mil/navnet/postscript, file prd_15.ps.
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73
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85042314676
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R.W. Hellings, in General Relativity and Gravitation, edited by B. Bertotti, F. de Felice, and A. Pascolini (Reidel, Dordrecht, 1984), p. 365.
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77
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85042320471
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The solar equator does not coincide with either the ecliptic or with the invariant plane of the solar system. The inclination of the orbit of Mercury with respect to the solar equator is less than half of the inclination of the same orbit with respect to the ecliptic: see 47.
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79
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85042263347
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In Ref. 27 there is a discussion of the possible effects of the “asteroid noise” on the determination of some PN parameters, but their “worst case analysis” is too pessimistic, providing only a loose upper bound for this effect.
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80
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85042273221
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The first tests with a complete 5-way link have shown that it is possible to achieve range rate measurements with accuracies of the order of (Formula presented) (for integration time 1000 s) down to 8 solar radii;L. Iess (private communication).
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83
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If the range drift flattens out after about one year, then the second year of data would be very useful. But, if this is the case, then the transponder should be turned on during the cruise phase, so that the drift takes place before the beginning of the orbital phase (if the calibration was a constant it could be easily eliminated in the data processing, as we have done for the SCE).
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84
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85042274363
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The astronomical unit is known today to an accuracy of (Formula presented) which fractionally means (Formula presented) This accuracy is comparable to the (Formula presented) correction from the first line of Eq. (A3) (given the limit (Formula presented) from lunar laser ranging, Ref. 17).
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