576 research outputs found

### New determination of zonal harmonics coeffi- cients of the earth's gravitational potential special report no. 165

Zonal harmonics coefficient determination of earth gravitational potentia

### Seasonal variations of the geopotential inferred from satellite observations

Annual variation of geopotential determined by tracking satellite

### Tidal torques. A critical review of some techniques

We point out that the MacDonald formula for body-tide torques is valid only
in the zeroth order of e/Q, while its time-average is valid in the first order.
So the formula cannot be used for analysis in higher orders of e/Q. This
necessitates corrections in the theory of tidal despinning and libration
damping.
We prove that when the inclination is low and phase lags are linear in
frequency, the Kaula series is equivalent to a corrected version of the
MacDonald method. The correction to MacDonald's approach would be to set the
phase lag of the integral bulge proportional to the instantaneous frequency.
The equivalence of descriptions gets violated by a nonlinear
frequency-dependence of the lag.
We explain that both the MacDonald- and Darwin-torque-based derivations of
the popular formula for the tidal despinning rate are limited to low
inclinations and to the phase lags being linear in frequency. The
Darwin-torque-based derivation, though, is general enough to accommodate both a
finite inclination and the actual rheology.
Although rheologies with Q scaling as the frequency to a positive power make
the torque diverge at a zero frequency, this reveals not the impossible nature
of the rheology, but a flaw in mathematics, i.e., a common misassumption that
damping merely provides lags to the terms of the Fourier series for the tidal
potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the
magnitudes of the terms, too, get changed. Reinstating of this detail tames the
infinities and rehabilitates the "impossible" scaling law (which happens to be
the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial
text overlap with arXiv:0712.105

### Eccentricities of Planets in Binary Systems

The most puzzling property of the extrasolar planets discovered by recent
radial velocity surveys is their high orbital eccentricities, which are very
difficult to explain within our current theoretical paradigm for planet
formation. Current data reveal that at least 25% of these planets, including
some with particularly high eccentricities, are orbiting a component of a
binary star system. The presence of a distant companion can cause significant
secular perturbations in the orbit of a planet. At high relative inclinations,
large-amplitude, periodic eccentricity perturbations can occur. These are known
as "Kozai cycles" and their amplitude is purely dependent on the relative
orbital inclination. Assuming that every planet host star also has a (possibly
unseen, e.g., substellar) distant companion, with reasonable distributions of
orbital parameters and masses, we determine the resulting eccentricity
distribution of planets and compare it to observations? We find that
perturbations from a binary companion always appear to produce an excess of
planets with both very high (e>0.6) and very low (e<0.1) eccentricities. The
paucity of near-circular orbits in the observed sample implies that at least
one additional mechanism must be increasing eccentricities. On the other hand,
the overproduction of very high eccentricities observed in our models could be
combined with plausible circularization mechanisms (e.g., friction from
residual gas) to create more planets with intermediate eccentricities
(e=0.1-0.6).Comment: 8 pages, to appear in "Close Binaries in the 21st Century: New
Opportunities and Challenges", ed. A. Gimenez et al. (Springer

### Hot Jupiters from Secular Planet--Planet Interactions

About 25 per cent of `hot Jupiters' (extrasolar Jovian-mass planets with
close-in orbits) are actually orbiting counter to the spin direction of the
star. Perturbations from a distant binary star companion can produce high
inclinations, but cannot explain orbits that are retrograde with respect to the
total angular momentum of the system. Such orbits in a stellar context can be
produced through secular (that is, long term) perturbations in hierarchical
triple-star systems. Here we report a similar analysis of planetary bodies,
including both octupole-order effects and tidal friction, and find that we can
produce hot Jupiters in orbits that are retrograde with respect to the total
angular momentum. With distant stellar mass perturbers, such an outcome is not
possible. With planetary perturbers, the inner orbit's angular momentum
component parallel to the total angular momentum need not be constant. In fact,
as we show here, it can even change sign, leading to a retrograde orbit. A
brief excursion to very high eccentricity during the chaotic evolution of the
inner orbit allows planet-star tidal interactions to rapidly circularize that
orbit, decoupling the planets and forming a retrograde hot Jupiter.Comment: accepted for publication by Nature, 3 figures (version after proof -
some typos corrected

### Fuzzy Characterization of Near-Earth-Asteroids

Due to close encounters with the inner planets, Near-Earth-Asteroids (NEAs)
can have very chaotic orbits. Because of this chaoticity, a statistical
treatment of the dynamical properties of NEAs becomes difficult or even
impossible. We propose a new way to classify NEAs by using methods from Fuzzy
Logic. We demonstrate how a fuzzy characterization of NEAs can be obtained and
how a subsequent analysis can deliver valid and quantitative results concerning
the long-term dynamics of NEAs.Comment: 11 pages, presented at the 7th Alexander von Humboldt Colloquium on
Celestial Mechanics (2008), accepted for publication in "Celestial Mechanics
and Dynamical Astronomy

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