Orbital elements

Abstract: At least two arguments suggest that the orbits of a large fraction of binary stars and extrasolar planets shrank by 1-2 orders of magnitude after formation: (i) the physical radius of a star shrinks by a large factor from birth to the main sequence, yet many main-sequence stars have companions orbiting only a few stellar radii away, and (ii) in current theories of planet formation, the region within ~0.1 AU of a protostar is too hot and rarefied for a Jupiter-mass planet to form, yet many "hot Jupiters" are observed at such distances. We investigate orbital shrinkage by the combined effects of secular perturbations from a distant companion star (Kozai oscillations) and tidal friction. We integrate the relevant equations of motion to predict the distribution of orbital elements produced by this process. Binary stars with orbital periods of 0.1 to 10 days, with a median of ~2 d, are produced from binaries with much longer periods (10 d to 10^5 d), consistent with observations indicating that most or all short-period binaries have distant companions (tertiaries). We also make two new testable predictions: (1) For periods between 3 and 10 d, the distribution of the mutual inclination between the inner binary and the tertiary orbit should peak strongly near 40 deg and 140 deg. (2) Extrasolar planets whose host stars have a distant binary companion may also undergo this process, in which case the orbit of the resulting hot Jupiter will typically be misaligned with the equator of its host star.

Abstract: Fourteen-year observations of the binary pulsar PSR 1913 + 16 provided data consistent with a straightforward model allowing for the motion of the earth, special and general relativistic effects within the solar system, dispersive propagation in the interstellar medium, relativistic motion of the pulsar in its orbit, and deterministic spin-down behavior of the pulsar itself. The results indicate that at the present level of precision, the PSR 1913 + 16 can be modeled dynamically as a pair of orbiting point masses. Five Keplerian and five post-Keplerian orbital parameters are therefore mostly determined with remarkably high precision. The masses of the pulsar and its companion are determined to be m1 = 1.442 + or - 0.003 and m2 = 1.386 + or - 0.003 times the mass of the sun, respectively, and the orbit is found to be decaying at a rate equal to 1.01 + or - 0.01 times the general relativistic prediction for gravitational damping. The results represent the first experimental tests of gravitation theory not restricted to the weak-field, slow-motion limit in which nonlinearities and radiation effects are negligible. Excellent agreement between observation and theory indicates conclusively that gravitational radiation exists, at the level predicted by general relativity.more » 70 refs.« less

Abstract: The orbits of the known short-period comets under the influence of the Sun and all the planets except Mercury and Pluto are numerically integrated. The calculation was undertaken in order to determine the dynamical lifetimes for these objects as well as explaining the current orbital element distribution. It is found that a comet can move between Jupiter-family and Halley-family comets several times in its dynamical lifetime. The median lifetime of the known short-period comets from the time they are first injected into a short-period comet orbit to ultimate ejection is approximately 50,000 years. The very flat inclination distribution of Jupiter-family comets is observed to become more distended as it ages. The only possible explanation for the observed flat distribution is that the comets become extinct before their inclination distribution can change significantly. It is shown that the anomalous concentration of the argument of perihelion of Jupiter-family comets near 0 and 180 deg is a direct result of their aphelion distance being close to 5.2AU and the comet being recently perturbed onto a Jupiter-family orbit. Also the concentration of their aphelion near Jupiter's orbit is a result of the conservation of the Tisserand invariant during the capture process.