An extension of Newton's apsidal precession theorem

Newton's apsidal precession theorem in Proposition 45 of Book I of the 'Principia' has great mathematical, physical, astronomical and historical interest. The lunar theory and the precession of the perihelion of the planet Mercury are but two examples of the applications of this theorem. We have examined the precession of orbits under varying force laws as measured by the apsidal angle θ( N , e ), where N is the index for the centripetal force law, for varying eccentricity e . The paper derives a general function for the apsidal angle, dependent only on e and N as the potential is spherically symmetric. Further, we explore approximate ways of the solution of this equation, in the neighbourhood of   N = 2  which happens to be the case of greatest historical interest. Exact solutions are derived where they are possible. The first derivatives  ∂θ/∂ N   and  ∂θ/∂ h   [where h ( N , e ) is the angular momentum] are analytically expressed in the neighbourhood of   N = 2  (case of the inverse square law). The value of  ∂θ/∂ N   is computed numerically as well for  1 ≤ N < 3  . The resulting integrals are interesting improper integrals with singularities at both limits. Some of the integrals, especially for   N = 2  , can be given in closed form in terms of generalized hypergeometric functions which are reducible in terms of algebraic and logarithmic functions. No evidence was found for isolated cases of zero precession as e was increased. The   N = 1  case of the logarithmic potential is also briefly discussed in view of its interest for the dynamics of eccentric orbits and its relevance to realistic galaxy models. The possibility of apsidal precession was also examined for a few cases of high-eccentricity asteroids and extrasolar planets. We find that these systems may provide interesting new laboratories for studies of gravity.     

Some statistical features of solar radio SVC in the rising branch of cycle 22

For the rising branch of Cycle 22, 1987 January—1989 November, we plot the daily total flux S at each of the five wavelengths 2.0, 3.4, 6.0, 10.7 and 21.2 cm against the apparent sunspot area of the dominant sunspot A_y and find that, for several large active areas, the locus is located below the average regression line, and the increase in the radio flux is insignificant compared to the increase in the sunspot area.     

Chandra observations of Comet 9P/Tempel 1 during the Deep Impact campaign

We present results from the Chandra X-ray Observatory's extensive campaign studying Comet 9P/Tempel 1 (T1) in support of NASA's Deep Impact (DI) mission. T1 was observed for ∼295 ks between 30th June and 24th July 2005, and continuously for ∼64 ks on July 4th during the impact event. X-ray emission qualitatively similar to that observed for the collisionally thin Comet 2P/Encke system [Lisse, C.M., Christian, D.J., Dennerl, K., Wolk, S.J., Bodewits, D., Hoekstra, R., Combi, M.R., Mäkinen, T., Dryer, M., Fry, C.D., Weaver, H., 2005b. Astrophys. J. 635 (2005) 1329-1347] was found, with emission morphology centered on the nucleus and emission lines due to C, N, O, and Ne solar wind minor ions. The comet was relatively faint on July 4th, and the total increase in X-ray flux due to the Deep Impact event was small, ∼20% of the immediate pre-impact value, consistent with estimates that the total coma neutral gas release due to the impact was 5×¹⁰⁶ kg (∼10 h of normal emission). No obvious prompt X-ray flash due to the impact was seen. Extension of the emission in the direction of outflow of the ejecta was observed, suggesting the presence of continued outgassing of this material. Variable spectral features due to changing solar wind flux densities and charge states were clearly seen. Two peaks, much stronger than the man-made increase due to Deep Impact, were found in the observed X-rays on June 30th and July 8th, 2005, and are coincident with increases in the solar wind flux arriving at the comet. Modeling of the Chandra data using observed gas production rates and ACE solar wind ion fluxes with a CXE mechanism for the emission is consistent, overall, with the temporal and spectral behavior expected for a slow, hot wind typical of low latitude emission from the solar corona interacting with the comet's neutral coma, with intermittent impulsive events due to solar flares and coronal mass ejections.     

Solar system constraints on multifield theories of modified dynamics

Any viable theory of modified Newtonian dynamics (MOND) as modified gravity is likely to require fields in addition to the usual tensor field of General Relativity. For these theories, the MOND phenomenology emerges as an effective fifth force probably associated with a scalar field. Here, I consider the constraints imposed on such theories by Solar system phenomenology, primarily by the absence of significant deviations from inverse-square attraction in the inner Solar system as well as detectable local preferred frame effects. The current examples of multifield theories can be constructed to satisfy these constraints and such theories lead inevitably to an anomalous non-inverse-square force in the outer Solar system.     

The scattered disk as a source of Halley-type comets

We investigate a new dynamical mechanism for producing Halley-type comets from the scattered disk of comets. Levison and Duncan [Levison, H., Duncan, M., 1997. Icarus 127, 13-32] and Duncan and Levison [Duncan, M., Levison, H., 1997. Science 276, 1670-1672] showed that a significant number of objects leave the scattered disk by evolving to semi-major axes greater than 1000 AU. We find that once these objects reach semi-major axes on the order of ¹⁰⁴ AU, a significant fraction immediately have their perihelia driven inward by the galactic tides. Approximately 0.01% of the objects that reach ¹⁰⁴ AU then evolve onto orbits similar to the observed Halley-like comets due to gravitational interactions with the giant planets. The orbital element distribution resulting from this process is statistically consistent with observations. We discuss the implications of this model for the number of objects in the scattered disk in the text. The model predicts a temporal variation in the influx of HTCs with a period of ∼118 Myr. At the peak, the model predicts that there should be roughly 10 times as many HTCs as currently observed (i.e., there should be weak HTC showers). However, the model may inflate the importance of these showers because it does not include the effects of passing stars and giant molecular clouds.     

冕洞演化与太阳活动周的关系及在日地预报中的应用

冕洞的研究在近二十多年里取得了丰硕的成果。本文回顾了冕洞的发现及观测历史，系统阐述了冕洞的结构特征、形成及演化规律，讨论了冕洞对日地空间产生的影响，冕洞与超级活动区的关系以及冕洞在太阳活动预报中所起的作用，在此基础上利用１９７０—１９９５年的冕洞资料对冕洞的时空分布和磁极性演化规律与太阳活动周的关系，以及冕洞与太阳风速度、地磁扰动等方面进行分析研究，得出以下结论：（１）冕洞在南北半球的分布在形态上基本是对称的，但在冕洞数量上北半球稍占优势；（２）冕洞的盛衰演化呈周期性，表现为赤道冕洞周期与黑子周期是完全一致的，极冕洞周期与黑子周期相位相差１８０°；（３）赤道冕洞的纬度分布随太阳活动周上升而上升，当太阳活动周达到极大值时，它也达到极大，然后再随太阳活动周下降而下降，极冕洞的纬度延伸方向演化与赤道冕洞相反；（４）极冕洞的极场呈１１年周期性，并且极场反转出现在太阳活动峰年期间；（５）太阳风和地磁扰动与冕洞的演化有着密切的关系