  As a planet transits the face of a star, it accelerates along the
line-of-sight. The changing delay in the propagation of photons produces an
apparent deceleration of the planet across the sky throughout the transit. This
persistent transverse deceleration breaks the time-reversal symmetry in the
transit lightcurve of a spherical planet in a circular orbit around a perfectly
symmetric star. For `hot Jupiter' systems, ingress advances at a higher rate
than egress by a fraction of 10^{-4}-10^{-3}. Forthcoming space telescopes such
as Kepler or COROT will reach the sensitivity required to detect this
asymmetry. The scaling of the fractional asymmetry with stellar mass M and
planetary orbital radius R as M/R^2 is different from the scaling of the
orbital period as (M/R^3)^{-1/2}. Therefore, this effect constitutes a new
method for a purely dynamical determination of the mass of the star, which is
currently inferred indirectly with theoretical uncertainties based on spectral
modeling. Radial velocity data for the reflex motion of the star can then be
used to determine the planet's mass. Although orbital eccentricity could
introduce a larger asymmetry than the light propagation delay, the eccentricity
is expected to decay by tidal dissipation to negligible values for a close-in
planet with no perturbing third body. Future detection of the eclipse of a
planet's emission by its star could be used to measure the light propagation
delay across the orbital diameter, 46.7(R/7x10^{11}cm) seconds, and also
determine the stellar mass from the orbital period.
