High-resolution spectra of molecular hydrogen in the Homunculus nebula allow for the first direct measurement of the systemic velocity of \eta Carinae . Near-infrared long-slit data for H _ { 2 } 1-0 S ( 1 ) \lambda 21218 obtained with the Phoenix spectrometer on the Gemini South telescope give V _ { sys } = - 8.1 \pm 1 km s ^ { -1 } ( heliocentric ) , or V _ { LSR } = - 19.7 \pm 1 km s ^ { -1 } , from the average of the near and far sides of the Homunculus . This measurement considerably improves the precision for the value of - 7 \pm 10 km s ^ { -1 } inferred from neighboring O-type stars in the Carina nebula . New near-infrared spectra also provide a high-resolution line profile of [ Fe ii ] \lambda 16435 emission from gas condensations known as the Weigelt objects without contamination from the central star , revealing a line shape with complex kinematic structure . Previously , uncertainty in the Weigelt knots ’ kinematics was dominated by the adopted systemic velocity of \eta Car .