We report on H-band, ground-based observations of a transit of the hot Neptune GJ 436b. Once combined to achieve sampling equivalent to archived observations taken with Spitzer, our measurements reach comparable precision levels. We analyze both sets of observations in a consistent way, and measure the rate of orbital inclination change to be of 0.02+/-0.04 degrees in the time span between the two observations (253.8 d, corresponding to 0.03+/-0.05 degrees/yr if extrapolated). This rate allows us to put limits on the relative inclination between the two planets by performing simulations of planetary systems, including a second planet, GJ 436c, whose presence has been recently suggested (Ribas et al. 2008). The allowed inclinations for a 5 M_E super-Earth GJ 436c in a 5.2 d orbit are within ~7 degrees of the one of GJ 436b; for larger differences the observed inclination change can be reproduced only during short sections (<50%) of the orbital evolution of the system. The measured times of three transit centers of the system do not show any departure from linear ephemeris, a result that is only reproduced in <1% of the simulated orbits. Put together, these results argue against the proposed planet candidate GJ 436c.
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