  We show that the surface gravity of a transiting extrasolar planet can be
calculated from only the spectroscopic orbit of its parent star and the
analysis of its transit light curve. This does not require additional
constraints, such as are often inferred from theoretical stellar models or
model atmospheres. The planet's surface gravity can therefore be measured
precisely and from only directly observable quantities. We outline the method
and apply it to the case of the first known transiting extrasolar planet, HD
209458b. We find a surface gravity of g_p = 9.28 +/- 0.15 m/s, which is an
order of magnitude more precise than the best available measurements of its
mass, radius and density. This confirms that the planet has a much lower
surface gravity that that predicted by published theoretical models of gas
giant planets. We apply our method to all fourteen known transiting extrasolar
planets and find a significant correlation between surface gravity and orbital
period, which is related to the known correlation between mass and period. This
correlation may be the underlying effect as surface gravity is a fundamental
parameter in the evaporation of planetary atmospheres.
