IGR J11215-5952 is a hard X-ray transient discovered in 2005 April by INTEGRAL and a member of the new class of HMXB, the Supergiant Fast X-ray Transients (SFXTs). While INTEGRAL and RXTE observations have shown that the outbursts occur with a periodicity of ~330 days, Swift data have recently demonstrated that the true outburst period is ~165 days. IGR J11215-5952 is the first discovered SFXT displaying periodic outbursts, which are possibly related to the orbital period. We performed a Guest Investigator observation with Swift that lasted 20ks and several follow-up Target of Opportunity (ToO) observations, for a total of ~32ks, during the expected apastron passage (defined assuming an orbital period of ~330 days), between 2008 June 16 and July 4. The characteristics of this apastron outburst are quite similar to those previously observed during the periastron outburst of 2007 February 9. The mean spectrum of the bright peaks can be fit with an absorbed power law model with a photon index of 1 and an absorbing column of 1E22 cm^-2. This outburst reached luminosities of ~1E36 erg/s (1-10keV), comparable with the ones measured in 2007. The light curve can be modelled with the parameters obtained by Sidoli et al. (2007) for the 2007 February 9 outburst, although some differences can be observed in its shape. The properties of the rise to this new outburst and the comparison with the previous outbursts allow us to suggest that the true orbital period of IGR J11215-5952 is very likely 164.6 days, and that the orbit is eccentric, with the different outbursts produced at the periastron passage, when the neutron star crosses the inclined equatorial wind from the supergiant companion. Based on a ToO observation performed on 2008 March 25-27, we can exclude that the period is 165/2 days. [Abridged]
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