Astrophysics and Space Science

, Volume 331, Issue 2, pp 485–496 | Cite as

Classical and relativistic node precessional effects in WASP-33b and perspectives for detecting them

  • Lorenzo IorioEmail author
Original Article


WASP-33 is a fast rotating, main sequence star which hosts a hot Jupiter moving along a retrograde and almost polar orbit with semi-major axis a=0.02 au and eccentricity provisionally set to e=0. The quadrupole mass moment \(J_{2}^{\star}\) and the proper angular momentum S of the star are 1900 and 400 times, respectively, larger than those of the Sun. Thus, huge classical and general relativistic non-Keplerian orbital effects should take place in such a system. In particular, the large inclination Ψ of the orbit of WASP-33b to the star’s equator allows to consider the node precession \(\dot{\Omega}\) and the related time variation dt d /dt of the transit duration t d . The WASP-33b node rate due to \(J_{2}^{\star}\) is 9×109 times larger than the same effect for Mercury induced by the Sun’s oblateness, while the general relativistic gravitomagnetic node precession is 3×105 times larger than the Lense-Thirring effect for Mercury due to the Sun’s rotation. We also consider the effect of the centrifugal oblateness of the planet itself and of a putative distant third body X. The magnitudes of the induced time change in the transit duration are of the order of 3×10−6,2×10−7,8×10−9 for \(J_{2}^{\star}\), the planet’s rotational oblateness and general relativity, respectively. A yet undiscovered planet X with the mass of Jupiter orbiting at more than 1 au would induce a transit duration variation of less than 4×10−9. A conservative evaluation of the accuracy in measuring dt d /dt over 10 yr points towards ≈10−8. The analysis presented here will be applicable also to other exoplanets with similar features if and when they will ne discovered.


Gravitation Planetary systems: individual (WASP-33b) Stars: individual (WASP33) Stars: rotation Stars: binaries: eclipsing 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.M.I.U.R.F.R.A.S.BariItaly

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