The solar system gas giant planets are oblate due to their rapid rotation. A measurement of the planet’s projected oblateness would constrain the planet’s rotational period. Planets that are synchronously rotating with their orbital revolution will be rotating too slowly to be significantly oblate; these include planets with orbital semimajor axes ~<0.2 AU (for MP ~ M(Jupiter) and M* ~ M@). Jupiter-like planets in the range of orbital semimajor axis 0.1 to 0.2 AU will tidally evolve to synchronous rotation on a timescale similar to mainsequence stars’ lifetimes. In this case, an oblateness detection will help constrain the planet’s tidal Q value.
The projected oblateness of a transiting extrasolar giant planet is measurable from a very high photometric precision transit light curve. For a Sun-sized star and a Jupiter-sized planet, the normalized flux difference in the transit ingress/egress light curve between a spherical and an oblate planet is a few to 15 *10^(-5) for oblateness similar to Jupiter and Saturn, respectively. The transit ingress and egress are asymmetric for an oblate planet with orbital inclination different from 90 degree and a nonzero projected obliquity. A photometric precision of 10^(-4) has been reached by Hubble Space Telescope (HST) observations of the known transiting extrasolar planet HD 209458b.
Kepler, a NASA discovery-class mission designed to detect transiting Earth-sized planets, requires a photometric precision of 10^(-5) and expects to find 30 to 40 transiting giant planets with orbital semimajor axes <1 AU, about 20 of which will be at >0.2 AU. Furthermore, part-per-million photometric precision (reached after averaging over several orbital periods) is expected from three other space telescopes to be launched within the next three years. Thus, an oblateness measurement of a transiting giant planet is realistic in the near future.