  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]
