Mean motion resonances (MMRs) play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system and in. exoplanetary systems. Most previous theoretical analyses have focused on the low- to moderate-eccentricity regime, but with new discoveries of high-eccentricity resonant minor planets and even exoplanets, there is increasing motivation to examine MMRs in the high-eccentricity regime. Here we report on a study of the high-eccentricity regime of MMRs in the circular planar restricted three-body problem. Numerical analyses of the 2: 1 and the 3: 2 interior resonances are carried out for a wide range of planet-to-star mass ratio mu, and for a wide range of eccentricity of the test particle. The surface-of-section technique is used to study the phase space structure near resonances. We find that new stable libration zones appear at higher eccentricity at libration centers that are. shifted from those at low eccentricities. We provide physically intuitive explanations for these transitions in phase space, and we present novel results on the mass and eccentricity dependence of the resonance widths. Our results show that MMRs have sizable libration zones at high eccentricities, comparable to those at lower eccentricities.

The first transiting planetesimal orbiting a white dwarf was recently detected in K2 data of WD 1145+017 and has been followed up intensively. The multiple, long and variable transits suggest the transiting objects are dust clouds, probably produced by a disintegrating asteroid. In addition, the system contains circumstellar gas, evident by broad absorption lines, mostly in the u' band, and a dust disc, indicated by an infrared excess. Here we present the first detection of a change in colour of WD 1145+017 during transits, using simultaneous multiband fast-photometry ULTRACAM measurements over the u'g'r'i' bands. The observations reveal what appears to be 'bluing' during transits; transits are deeper in the redder bands, with a u' - r' colour difference of up to similar to-0.05 mag. We explore various possible explanations for the bluing, including limb darkening or peculiar dust properties. 'Spectral' photometry obtained by integrating over bandpasses in the spectroscopic data in and out of transit, compared to the photometric data, shows that the observed colour difference is most likely the result of reduced circumstellar absorption in the spectrum during transits. This indicates that the transiting objects and the gas share the same line of sight and that the gas covers the white dwarf only partially, as would be expected if the gas, the transiting debris and the dust emitting the infrared excess are part of the same general disc structure (although possibly at different radii). In addition, we present the results of a week-long monitoring campaign of the system using a global network of telescopes.