We observed the massive binary stellar system of Eta Carinae in the 0.3-10 keV energy range with the X-ray Telescope onboard the Swift satellite during the period 15 December 2008 - 11 March 2009 , i.e . 1 month before to 2 months after the X-ray drop from maximum to minimum , thought to be associated with the periastron encounter of the primary star by the hot companion . Beginning a few months before eclipse , the interaction between the winds of the two stars intensifies and the X-ray flux reaches maximum . The flux drops dramatically thereafter , subsiding in about 20 days to a level that is at least a factor 10 lower than the ’ high state ’ , i.e . the X-ray emission state of the system during the largest fraction of its 5.52 yr orbit ( \sim 10 ^ { -11 } erg s ^ { -1 } cm ^ { -2 } ) . Unlike in previous cycles , when the low state lasted about 2.5 months , observations with RXTE showed that the X-ray flux started its recovery to normal level about 1.5 months after the minimum . We suggest that this early recovery may be due to the fact that the companion wind reaches terminal velocity before encountering the shock .