The 1996-1997 Fading of V651 Monocerotis, the Binary Central Star of the Planetary Nebula NGC 2346
V651 Mon is the binary central star of the bipolar planetary nebula NGC 2346. The star showed the second-ever deep fading in 1996–1997, which was presumably caused by obscuration by a dust cloud in the planetary nebula, as was proposed to explain the 1981–1985 event. The entire duration of the 1996–1997 event was ∼400d, remarkably shorter than the 1981–1985 event, suggesting that the obscuring body was smaller or had a larger tangential velocity. The most remarkable feature in this event was the presence of a sharply defined transient clearing (brightening). From the time-scale of the variation, we propose an upper limit of the projected scale of several times ∼ 10 11 cm of the structure responsible for the brightening. This observation provides the first evidence for a sharply defined,
The Unusual Variability of the Large Magellanic Cloud Planetary Nebula RPJ 053059–683542
We present images and light curves of the bipolar planetary nebula RPJ 053059-683542 that was discovered in the Reid-Parker AAO UKST Hα survey of the Large Magellanic Cloud. The emission from this object appears entirely nebular, with the central star apparently obscured by a central band of absorption that bisects the nebula. The light curves, which were derived from images from the SuperMACHO project at CTIO, showed significant, spatially resolved variability over the period 2002 January through 2005 December. Remarkably, the emission from the two bright lobes of the nebula vary either independently or similarly but with a phase lag of at least 1 yr. The optical spectra show a low level of nebular excitation, and only modest N enrichment. Infrared photometry from the 2MASS and SAGE surveys indicates the presence of a significant quantity of dust. The available data imply that the central star has a close binary companion and that the system has undergone some kind of outburst event that caused the nebular emission to first brighten and then fade. Further monitoring, high-resolution imaging, and detailed IR polarimetry and spectroscopy would uncover the nature of this nebula and the unseen ionizing source.
LYAPUNOV-BASED TRANSFER BETWEEN ELLIPTIC KEPLERIAN ORBITS
We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.