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We present general considerations regarding the derivation of the radialdistances of coronal mass ejections (CMEs) from elongation angle measurementssuch as those provided by SECCHI and SMEI, focusing on measurements in theHeliospheric Imager 2 (HI-2) field of view (i.e. past 0.3 AU). This study isbased on a three-dimensional (3-D) magneto-hydrodynamics (MHD) simulation oftwo CMEs observed by SECCHI on January 24-27, 2007. Having a 3-D simulationwith synthetic HI images, we are able to compare the two basic methods used toderive CME positions from elongation angles, the so-called "Point-P" and"Fixed-Phi" approximations.  We confirm, following similar works, that both methods, while valid in themost inner heliosphere, yield increasingly large errors in HI-2 field of viewfor fast and wide CMEs. Using a simple model of a CME as an expandingself-similar sphere, we derive an analytical relationship between elongationangles and radial distances for wide CMEs. This relationship is simply theharmonic mean of the "Point-P" and "Fixed-Phi'' approximations and it is aimedat complementing 3-D fitting of CMEs by cone models or flux rope shapes. Itproves better at getting the kinematics of the simulated CME right when wecompare the results of our line-of-sights to the MHD simulation. Based on thisapproximation, we re-analyze the J-maps (time-elongation maps) in January26-27, 2007 and present the first observational evidence that the merging ofCMEs is associated with a momentum exchange from the faster ejection to theslower one due to the propagation of the shock wave associated with the fasteruption through the slow eruption.

Deriving the radial distances of wide coronal mass ejections from elongation measurements in the heliosphere - Application to CME-CME interaction