The Motion of Mars' Pole. I. Rigid Body Precession and Nutation

The total precession in longitude for a solid-core, rigid Mars model is found to be A^ = — 7!'296 + 0".01\ yr~ \ This precession includes the motion resulting from the extremely longperiod (> 10 000 yr) nutation components that result from changes in Mars' orbit with time. These same very long-period nutation components also contribute a "precession" in latitude of A£ = 0''4255 + 0!'0012 yr" ^ The nutation components in longitude with amplitudes larger than 0"001 consist of eight solar nutation terms and one nutation each contributed by the motions of the nodes of Phobos and Deimos and a single nutation from the direct gravitational torque of Jupiter. The nutation components in obliquity consist of six solar terms and one nutation term each from the motion of the nodes of Phobos and Deimos. The amplitudes and periods of the solar nutation terms are in agreement with the nutation found by Reasenberg & King [J. Geophys. Res., 84, 6231 (1979) ]. The solar precession rate also agrees with Reasenberg and King's value with the two small corrections resulting from the change in the orientation of Mars' orbit with time added to it. A single nutation in longitude driven by Jupiter is the only significant planetary contribution at the milliarcsecond level. L INTRODUCTION Differences between the observed forced nutation component amplitudes of the Earth and predicted nutation amplitudes for a rigid Earth are a result of differences between the theoretical rigid structure of the Earth used in older models and the actual elastic Earth with a liquid core. However, except for the period of the Chandler wobble, the observations of the motion of the Earth's pole were not accurate enough to observe the effects of the elastic, liquid core Earth until the last 30 years. In more recent works, such as those by Wahr (1981a,b), the nutation resulting from an elastic, liquid core Earth are modeled as perturbations of the rigid Earth model nutation. This is the approach adopted for the 1980 lAU Theory of Nutation to determine the amplitude of the various nutational elements (Kaplan 1981). These perturbations result in modifications to the nutation amplitudes for the Earth from about 1% to 0.01% of the theoretical rigid nutation amplitudes or about 0''019 for the largest term in the series. Since the 1950s the improvement in the measurement of the motion of the Earth's pole have made its observation a powerful probe of the structure of the Earth. The recent increase in the quality of the data available for the precession and nutation for the Earth has started a reevaluation of nutation theory for both rigid and elastic Earth models to improve their accuracies (e.g., Kinoshita & Souchay 1990; Zhu et al. 1990). The most recent work, such as done with VLBI, has made the information on the Earth's interior obtained from observations of precession, nutation, and polar motion of the same quality as can be determined from seismometry (Melchior 1986). This method can be used as a probe of the structure of other planets in the solar system provided that it is possible to observe the planet's orientation in space with high enough accuracy. This requirement can definitely be fulfilled for only one other planet in the solar system. Mars. Mars, the fourth planet from the Sun, is the third in size of the terrestrial planets of the solar system. Its orbit brings Mars to within 0.53 AU of the Earth. Its surface is not covered by clouds like Venus and the gaseous giant planets, and, unlike Mercury, it is observable away from the Sun's glare. These properties make Mars the easiest planet in the solar system, aside from the Earth, to observe. Despite its small size [equatorial radius 3393.4 km and mass 6.42X10^^ kg; Astronomical Almanac for the Year 1990 (1989)], Mars shows many Earthlike properties in its physical ephemeris. Mars has a sidereal day of 1.0260 Earth solar days, the inchnation of its equator to the plane of its orbit of 25!20, and a geometric oblateness of 0.0052 in comparison to the Earth's geometric oblateness of 0.0034. It is, however, a mistake to assume that Mars has an internal composition that is the same as the Earth. First, Mars has a mean density that is only 61.9% of the mean density of the other terrestrial planets. The inertia ratio is a measure of a planet's central condensation defined by q=C/J^R' (1) where C is the principal moment of inertia about the polar axis, ^ is the mass of the planet, and R is the equatorial radius of the planet. The estimates of ^ for Mars range from 0.3654 (Reasenberg 1977) to 0.3452 (Bills 1989) in comparison to 0.3335 for the Earth and 0.4 for a homogeneous sphere. The large value for the inertia ratio means that Mars is less centrally condensed than the Earth, but it is also small enough to show that Mars is not completely homogeneous. Mars may have a very small external magnetic field, the strength of which has not yet been accurately measured, but it has been established that Mars' magnetic field is much smaller than the Earth's. Other information on the interior structure of Mars is very sketchy. The only structural information that is certain is Mars' radius and its mean density. In addition the structure of the surface gravity field to twelfth degree and order has been published by Christensen & Balmino (1979), but the higher order structure of the field is only preliminary. The seismic experiments included in the Viking probes were designed only as a preliminary survey to determine what instruments would be necessary on future missions to Mars. Also, the seismic package functioned properly on only one of the two landers (Anderson et al. 1977). 1510 Astron. J. 102 (4), October 1991 1510 © American Astronomical Society • Provided by the NASA Astrophysics Data System Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. 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