Dynamic portrait of the planetary 2/1 mean-motion resonance – I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (σ-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (  Δϖ  -family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system.
The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low–moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions.
Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.     

Light curves and photometric parameters of the comets C/1999 S4 (LINEAR), C/2001 Q4 (NEAT), C/2002 T7 (LINEAR), C/2002 V1 (NEAT), C2004 Q2 (Machholz), and 153P/2002 C1 (Ikeya-Zhang)

Light curves of six comets, C/1999 S4 (LINEAR), C/2001 Q4 (NEAT), C/2002 T7 (LINEAR), C/2002 V1 (NEAT), C/2004 Q2 (Machholz), and 153P/2002 C1 (Ikeya-Zhang), were built and investigated. The photometric parameters H ₀, H ₁₀, and n were calculated for these comets, and they were found to change both before and after perihelion. The shift of light curve peak with respect to perihelion passage moment was determined for each comet. Our white-light curves are compared to the results of polarimetric and electrophotometric observations of the comets C/2002 T7 (LINEAR) and C/2004 Q2 (Machholz).