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1
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Acuna, M.H.1
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0030707833
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W. M. Folkner et al., Science 278, 1749 (1997).
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Folkner, W.M.1
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M. T. Zuber et al., Science 287,1788 (2000).
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Zuber, M.T.1
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6
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0242569729
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note
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2(1/2 year) ≈ (2.2 ± 0.8)cos(2ℓ′ - 20°).
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7
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0141771979
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T. J. Ahrens, Ed. [American Geophysical Union (AGU), Washington, DC]
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J. Wahr, in A Handbook of Physical Constants: Global Earth Physics, T. J. Ahrens, Ed. [American Geophysical Union (AGU), Washington, DC, 1995], vol 1, pp. 40-46.
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Wahr, J.1
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9
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0242569728
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note
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Starting from an orientation model of Mars similar to that of Folkner et al. (2), the rotational parameters we estimate are the epoch obliquity (ε) and longitude of the Mars pole (ψ), the precession rate of the pole (dψ/dt), the obliquity rate (dε/dt), the rotation rate (dφ/dt), and the seasonal variations in rotation angle as a periodic series Equation percented where ℓ′ is the Mars mean anomaly. The rigid-body nutation model is fixed to that of (10).
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12
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0242654177
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note
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The drag model uses six flat plates to represent the spacecraft bus, antenna, and solar arrays with orientation provided by spacecraft telemetry. The atmospheric density is given by the Mars GRAM 3.4 model in C. J. Justus, D. L. Johnson, B. F. James, NASA Tech. Memo. No. 108513 (1996). We also tested solving for a drag coefficient only once per day, and this did not change the results.
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13
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0242402401
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note
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2n = n′. Also, the MGS orbit elements are: a = 3796 km, e = 0.0084, period = 1.96 hours, and I = 92.9°.
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14
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0242569726
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note
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The nutations of Mars pole (δε and δψ) result in the following changes in orbit inclination relative to a space-fixed reference frame (15, 22): Equation percented The principal annual term for rigid-body response is δε = 0.0 and εδψ = -0.259″sinℓ. This reduces the secular rate by about 10%. The fluid core can further reduce rate by up to 1%.
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15
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0000280554
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C. F. Yoder, Icarus 117, 250 (1995).
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Yoder, C.F.1
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16
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0242569705
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note
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A phase lag (= 1/Q) can be introduced in the angle arguments in Eq. 2 in order to account for solid friction. For example 2(Ω -L′) is replaced with 2(Ω-L′) - 1/Q. This effect reduces the observed signature by about 1%.
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17
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0242654176
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note
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δf/dt ≃-n′tan/δ/) that has about the same amplitude as the secular change in inclination after ∼20 days. Thus, both node and inclination drift contribute to the global Love number solution, However, space craft maneuvers aimed at desaturation of the momentum wheels and maintaining orbit geometry may limit the sensitivity to long-term orbit changes.
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18
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0242402398
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note
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2(ε/2)sin(Ω + ψ - 2L′)]
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19
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0242569706
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note
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2(ε/2)cos(Ω + ψ- L′)] = 0 for sineθ ≈ 0.5, corresponding to 2:00 p.m. local Mars time.
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20
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4243805863
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C. F. Yoder et al., Nature 303, 7S7 (1983).
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Nature
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Yoder, C.F.1
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21
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0242485736
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note
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2) is due primarily to this forcing.
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23
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0242402400
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note
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21 range from -0.1 to 0.1.
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24
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0242402399
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note
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-3 arc sec/year.
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25
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0242402363
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note
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In the estimation process, the Doppler data are treated as uncorrelated measurements, i,e., white noise. Solar plasma, troposphere, and ionosphere can cause correlations in the measurements that are impractical to account for in a least-squares estimation process.
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27
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0242402364
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note
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a ≈ 0.008.
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28
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0013032856
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E. Groten et al., Astron. J. 111, 1388 (1996).
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Astron. J.
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Groten, E.1
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31
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0002927309
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AGU, Washington, DC
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C. F. Yoder, in A Handbook of Physical Constants: Global Earth Physics (AGU, Washington, DC, 1995), vol. 1, pp. 1-31.
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A Handbook of Physical Constants: Global Earth Physics
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Yoder, C.F.1
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32
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0242485715
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R. D. Ray et al., Nature 381, 585 (1996).
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Nature
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Ray, R.D.1
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33
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0242654156
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note
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c = 0), and this poses limits on core size represented by the upper and lower bounds on core radius shown in model calculations in Fig. 2.
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34
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0028024933
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J. O. Dickey et al., Science 265, 482 (1994).
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(1994)
Science
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Dickey, J.O.1
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36
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0242402373
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note
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The most recent lunar Love number from Lunar Prospector (35) is k2 = 0.025 ± 0.003. The model estimate (34) is k2 = 0,022 without partial melt at depth.
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37
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0242654155
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note
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3. This suggests that at least the south cap volume is larger than reported.
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38
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0242654154
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note
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3 is 0.97 for MGS (21) (table 51).
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41
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0242402371
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note
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We thank J, G. Williams, C. K. Shum, and V. Dehant for thoughtful reviews and J. T. Schofield for advice and Pathfinder pressure data, The research described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA.
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