Secular changes in the orbits of the quadruple system VW LMi

VW~LMi is the tightest known quadruple system with 2+2 hierarchy. It consists of a W UMa-type eclipsing binary (P12 = 0.47755 days) and another detached non-eclipsing binary (P34 = 7.93 days) orbiting around a common center of mass is about P1234 = 355 days. We present new observations of the system extending the time baseline to study long-term perturbations in the system and to improve orbital elements. The multi-dataset modeling of the system (4 radial-velocity curves for the components and the timing data) clearly showed an apsidal motion in the non-eclipsing binary at a rate of 4.6 degrees/yr, but no other perturbations. This is consistent with the nearly co-planarity of the outer, 355-day orbit, and the 7.93-day orbit of the non-eclipsing binary. Extensive N-body simulations enabled us to constrain the mutual inclination of the non-eclipsing binary and the outer orbits to j34-1234 < 10 degrees.